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A Course in Applied Bifurcation Theory, Vemuri Balakotaiah ( PDF )
Book Reviews ( PDF ) Molecular Level Measurements in Chemical Engineering, R.J. Smiley, W.N. Douglas ( PDF ) The Changing Role of Academia, Julio M. Ottino ( PDF ) Applied Stochastics for Engineering, Jay D. Schieber ( PDF ) PICLES: A Simulator for Teaching the Real World of Process Control, Douglas J. Cooper ( PDF ) The Quest for Excellence in Teaching, Raffi M. Turian ( PDF ) The Free Energy of Wetting, William G. Pitt ( PDF ) MicroprocessorBased Controllers at Drexel University, D.R. Coughanowr ( PDF ) What Matters in College, Richard M. Felder ( PDF ) The ASEE Chemical Engineering Division Lectureship Award, George Burnet ( PDF ) Interactive Dynamics of Convection and Crystal Growth, William N. Gill ( PDF ) Thermodynamics and Common Sense, Octave Levenspiel ( PDF ) Learning Through Doing: A Course on Writing a Textbook Chapter, Phillip C. Wankat ( PDF ) The Du Pont Teaching Fellowship Program: 1991 Teaching Experiences, Steven A. McCluney, Ronald D. Shaver, Greg Fisher, Michael Luyben, Linda J. Broadbelt ( PDF ) 
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chnkleineig dcto VOU E2!TIAV A .0 GrdaeEuainIse uw ,N . 'Fat" h IMDSOAARLCUE IttrcieDnmc fCnetinnC sa rwh pg 9 *WmN.Gl and A li e n e .. .. ... .. . .p f ainTerJm )iJ~~ EDITORIAL AND BUSINESS ADDRESS: Chemical Engineering Education Department of Chemical Engineering University of Florida Gainesville, FL 32611 FAX 9043920861 EDITOR Ray W. Fahien (904) 3920857 ASSOCIATE EDITOR T. J. Anderson (904) 3922591 CONSULTING EDITOR Mack Tyner MANAGING EDITOR Carole Yocum (904) 3920861 PROBLEM EDITORS James 0. Wilkes and Mark A. Burns University of Michigan PUBLICATIONS BOARD *CHAIRMAN E. Dendy Sloan, Jr. Colorado School of Mines PAST CHAIRMEN Gary Poehlein Georgia Institute of Technology Klaus Timmerhaus University of Colorado MEMBERS George Burnet Iowa State University Anthony T. DiBenedetto University of Connecticut Thomas F. Edgar University of Texas at Austin Richard M. Felder North Carolina State University Bruce A. Finlayson University of Washington H. Scott Fogler University of Michigan J. David Hellums Rice University Angelo J. Perna New Jersey Institute of Technology Stanley I Sandier University of Delaware Richard C. Seagrave Iowa State University M. Sami Selim Colorado School of Mines James E. Stice University of Texas at Austin Phillip C. Wankat Purdue University Donald R. Woods McMaster University Fall 1993 Chemical Engineering Education Volume 27 Number 4 Fall 1993 AWARD LECTURE 198 Interactive Dynamics of Convection and Crystal Growth, William N. Gill FEATURES 154 A Course in Applied Bifurcation Theory, Vemuri Balakotaiah 162 Molecular Level Measurements in Chemical Engineering, R.J. Smiley, W.N. Delgass 170 Applied Stochastics for Engineering, Jay D. Schieber 176 PICLES: A Simulator for Teaching the Real World of Process Control, Douglas J. Cooper 182 The Quest for Excellence in Teaching, Raffi M. Turian 184 The Free Energy of Wetting, William G. Pitt 188 MicroprocessorBased Controllers at Drexel University, D.R. Coughanowr 208 Learning Through Doing: A Course on Writing a Textbook Chapter, Phillip C. Wankat 212 The Du Pont Teaching Fellowship Program: 1991 Teaching Experiences, Steven A. McCluney, Ronald D. Shaver, Greg Fisher, Michael Luyben, Linda J. Broadbelt CLASS AND HOME PROBLEMS 206 Thermodynamics and Common Sense, Octave Levenspiel RANDOM THOUGHTS 194 What Matters in College, Richard M. Felder REVIEW/OPINION 168 The Changing Role of Academia, Julio M. Ottino DIVISION NEWS 196 The ASEE Chemical Engineering Division Lectureship Award, George Burnet 161, 167 Book Reviews CHEMICAL ENGINEERING EDUCATION (ISSN 00092479) is published quarterly by the Chemical Engineering Division, American Society for Engineering Education, and is edited at the University of Florida. Correspondence regarding editorial matter, circulation, and changes of address should be sent to CEE, Chemical Engineering Department University of Florida, Gainesville, FL 32611. Copyright 1993 by the ChemicalEngineering Division, American SocietyforEngineering Education. The statements and opinions expressed in this periodical are those of the writers and not necessarily those of the ChE Division, ASEE, which body assumes no responsibility for them. Defective copies replaced if notified within 120 days of publication. Write for information on subscription costs and for back copy costs and availability. POSTMASTER: Send address changes to CEE, Chemical Engineering Department.. University of Florida, Gainesville, FL 32611. A Course in... APPLIED BIFURCATION THEORY VEMURI BALAKOTAIAH University ofHouston Houston, TX 772044792 ifurcation theory deals with the solution of nonlinear equations and is useful to chemi cal engineers studying nonlinear phenom ena. Most of the traditional courses on applied math ematics offered by chemical engineering departments cover only linear analysis. While linear analysis is necessary, since it is the foundation of all nonlinear techniques, it does not prepare students to deal with the nonlinear problems that will be encountered later in research. This is especially true for students work ing on stability problems in fluid flow, heat and mass transfer, catalysis, reaction engineering, con trol, and separations. For many years we have sent our University of Houston students to the mathematics department for courses on differential equations and dynamical systems, bifurcation theory, nonlinear dynamics, sin gularity theory, and group theory. We found, how ever, that many of these courses were too special ized, were abstract, and had a narrow focus (from an engineer's point of view). Typically, a student had to take three or four of these courses to grasp a few useful nonlinear techniques. To address these problems, in 1989 the author designed a new course on applied bifurcation theory as a sequel to the twosemester applied mathemat ics course taught by Professor Neal R. Amundson. The course was wellreceived by the students and was repeated in the Spring of 1991, and with some minor changes and updating is scheduled to be taught in the Spring of 1994 and regularly thereafter. Vemurl Balakotaiah is professor of chemical engineering at the University of Houston. He received his BTech degree from the Indian Insti tute of Technology (Madras) in 1978 and his PhD from the University of Houston in 1982, both in chemical engineering. He worked as a Research Engineer at Shell Development Com pany and is a consultant to Exxon, Shell, and the Westem Company of North America. His main research interests are in the area of chemi cal reaction engineering. Copyright ChE Division ofASEE 1993 COURSE DESCRIPTION Introduction to Applied Bifurcation Theory The main goal of the course is to expose chemical engineering graduate students to some important non linear techniques and concepts. Table 1 gives an out line of the material that is covered in a fourteenweek semester. Although the course is for 3 credits, 28 twohour lectures are necessary to cover the topics listed in Table 1. The course is organized into six topics and two in troductory lectures. The introductory lectures give a brief history of bifurcation theory, examples from vari ous disciplines, and the usefulness and limitations of bifurcation theory. Several chemical engineering ex amples covering fluid flow, heat and mass transfer, catalysis and reaction engineering, separations, con trol and multiphase transport are selected as model problems and are used throughout the course to illustrate various concepts. All the examples are deterministic models and vary from the following simple (but nontrivial) two ordinary differential equation models = a+(lx)exp 1+07 (la) Le +B(1x)exp{ a(00c) (lb) describing the dynamic behavior of a CSTR in which a first order exothermic reaction occurs to the follow ing, somewhat complicated, model involving a set of six partial differential equations in three spatial coor dinates and time V.v=0; Vn=v pyez (2a) +v.Vy= V2y+pDaexp 1 c (2b) T Peh )r0~ cc+Y Gc1 2 T1 ' + +v*Vc= VcDaexp 1+y (O boundary conditions: at the wall at the inlet (z=0) at the exit (z=l) ven=0, Vy.en=0, Vcen= (2d) y=O; c=1; vz=l (2e) z=o; l=0; I=I1I (2f) Chemical Engineering Education Chemical Engineering Education describing flow maldistributions and hot spots in a downflow cylindrical packed bed reactor. After a brief discussion of model formulation and the origins of various nonlinearities, we discuss the advantages of using the function space formalism. It is shown that most of the models can be writ ten in the abbreviated form C = F(u,p) (3) where p is a vector of parameters, C is a capacitance matrix, and the vector of state variables u may be expressed in terms of the elements of a function space having certain properties, e.g., satisfying differentiability conditions and the appropriate boundary con ditions. The function spaces of interest are usually Banach or Hilbert spaces. The ca pacitance matrix C, the parameters vector p, and the nonlinear operator F on the func tion space Y are identified for some selected examples. Some of these include cases in which C is not invertible (differential algebraic systems). For example, for Eqs. (1), (1 0 (x(t)] C= LeO, u= (t(t), = 2, pt =(Le,y,B,Da,a,Oc) (4a) and +(lx)exp{0 F(u,p)= Da 1+0/y (4b) a +B(lx)ex 0 }a( 0) while for Eqs. (2) o o 0 0 0 (v(z,r,O,t)'1 o o n(z,r,e,t) C= u= pt=(Ra,Peh,Pem,y,P,Dao,H,ci,a) (5a) o 0 1 0 c(z,r,o,t) o0 0 0 ,y(z,r,9,t), V.v Vnv y ez Peh F(u,p)= vVy+ 1V2y+Daexp c vV eh Vlc +y) v.Vc+ 1 V2cDaex T )c Pem .1+y , TABLE 1 Course Outline for Applied Bifurcation Theory Introduction 1. Definition and examples from different disciplines 2. Behavior of nonlinear systems; uses and limitations of bifurcation theory Nonlinear Functional Analysis 1. Operators on Banach spaces; Frnchet derivatives 2. Contraction mapping theorem; iterative methods for nonlinear operator equations; uniqueness criteria 3. Implicit function theorem; necessary and sufficient condi tions for bifurcation; determination of stationary stability boundary (Bifurcation Set) SteadyState Bifurcation Theory 1. LiapunovSchmidt reduction; elementary catastrophe theory 2. Singularity theory with a distinguished variable; classifica tion of bifurcation diagrams; construction of phase diagrams 3. Effects of discrete symmetry (Z2, D,) 4. Shooting technique with sensitivity functions; determination of singular points of twopoint boundary value problems; singular points of elliptic PDEs 5. Effects of symmetry on boundary value problems (Z2, 0(2)) Branching equations with symmetries Dynamical Systems 1. Invariant manifolds; HartmanGrobman theorem; stable and center manifold theorems, applications 2. Amplitude equations; codimension 1, 2, 3 singularities 3. Poincar6Birkhoff normal form; local codimention 1, 2 bifurcations 4. Floquet theory; degenerate Hopfbifurcations 5. Bifurcation theory for maps; normal forms of codimension one bifurcations ;attractors and basins of attraction 6. Poincar6 maps; averaging method; Melnikov theory 7. Characterization of attractors ; attractor dimensions, K entropy, Lexponents; analysis of experimental data 8. Poincar6Bendixson theory; degree and index theory; group theory and normal forms; Hamiltonian chaos; fractals Nonlinear Partial Differential Equations 1. Linear stability analysis of coupled PDEs 2. Centermanifold reduction of coupled PDEs; amplitude equations 3. Mode interactions; bifurcation with symmetry 4. Bifurcation in large systems (continuous spectrum); Landau and GinzbergLandau equations; phase and amplitude turbulence 5. Energy stability and Liapunov functions 6. Bifurcation theory for delaydifferential, integral, and integrodifferential equations Nonlinear Wave Phenomena 1. Review of basic concepts; physical examples 2. Analysis of traveling waves and pulses Computational Methods in Bifurcation Theory 1. Arc length continuation technique; continuation of steady state and periodic branhces 2. Review of software on nonlinear dynamics and chaos Fall 1993 155 and Y is the space of 6tuples of continuous func tions in the variables (z,r,0) satisfying the appropri ate differentiability conditions and homogeneous boundary conditions. Next, an overview of bifurcation theory, and its potential uses and limitations, are reviewed by a discussion of the following frequently asked ques tions about nonlinear models: 1) Given a nonlinear model of a physical system, what are the different types of behaviors that are possible (for different choices of the parameters vector p)? 2) What are the regions in the parameter space in which the behav ior of a model may be described by a lower dimen sional simplified model containing fewer parameters and/or a lower dimensional state space? What is the simplified form of the model? 3) How does one con struct phase diagrams in the parameter space which classify the p space into regions, in each of which a different type of behavior exists? 4) How do the pre dicted features of a model change when it is sub jected to small perturbations (or equivalently, is the model structurally stable)? Theoretical, experimental, and computational re sults are presented for some model systems to illus trate each of the above four important concepts in some detail. For example, the idea of constructing a phase diagram of a mathematical model or a physi cal system is illustrated by using experimental re sults for TaylorCouette flow'" and theoretical results for the steadystate behavior of a CSTR.[2 It is also noted that phase diagrams for many of the model problems (including the two above) are not available. The limitations of bifurcation theory are also dis cussed by emphasizing that its most important re sults are only local in nature and have to be supple mented by global techniques or numerical simula tions (often guided by the local theory) for a compre hensive analysis of the mathematical model or physi cal system under consideration. Main Topics of Applied Bifurcation Theory We now give a brief description of the six main topics covered in the course. Before doing this, it should be pointed out that each of these topics (and most of the single lectures outlined here) is broad, has considerable literature, and finds enough appli cations in chemical engineering to justify a full se mester course! As stated earlier, however, the pur pose of this general course is to present the most important concepts and techniques in a unified man ner. Due to space limitations, we must omit many details here. A longer version of this article contain ing details, equations, and commentary is available from the author. Nonlinear Functional Analysis The course starts with nonlinear functional analysis which introduces the notation and forms the basis for all later topics. First, the concept of completeness and convergence in normed linear (Banach) spaces is reviewed in a nonabstract manner. This is fol lowed by the definition of a Frichet derivative (or local linearization) of a nonlinear operator, chain rule, partial and higherorder Fr6chet derivatives, and Taylor's theorem in function spaces. The model problems are used for illustra tion with formulas such as DuF(uo.p).v= [F(uo +sv,p)l (6a) D2uF(uo,p)*(v,w)= [F(uo +sv+s2w,p)] 2 (6b) for determining the Fr6chet derivatives of the nonlinear op erators (such as those in Eqs. 4b and 5b). Next, the concept of a nonlinear operator being a contraction is introduced and the contraction mapping theorem is stated. This theorem is used to present a proof of the implicit function theorem. The usefulness of these two main theorems of nonlinear func tional analysis is shown by discussing various applications. For example, the contraction mapping theorem is used to derive convergence criteria for the iterative method Un+l= N(un) (7a) as well as uniqueness criteria for the nonlinear equation u=N(u) (7b) where N is a nonlinear operator on some Banach space Y. Specific examples dealing with algebraic equations (lumped models of reactors with single and multiple reactions, discretized models of convection), twopoint boundary value problems (diffusionreaction and diffusionconvectionreac tion models in one spatial dimension), and elliptic partial differential equations (diffusionreaction models in 2/3 di mensions) are discussed. The implicit function theorem is supplemented by stating sufficient conditions for bifurcation and the form of the bifurcating solution in terms of the eigenfunctions of the linearized operator. Application of the implicit function theorem is illustrated by deriving the sta tionary stability boundaries for various physical systems such as the CSTR with single and multiple reactions, classi cal RayleighB6nard and Lapwood convection problems, and the Brusselator model for stationary patterns. Some lecture material on nonlinear functional analysis is taken from references 3 through 5 and 'translated' by the author into the engineer's language. SteadyState Bifurcation Theory The second topic of the course, steadystate bifurcation theory, is introduced by discussing the idea of reducing the dimensionality of a prob lem, also known as the elimination of passive modes (engi neering), or the slaving principle (physics), or the Liapunov Chemical Engineering Education Schmidt reduction (mathematics). This is followed by a discussion of the branching equations and their Taylor ex pansions for finite dimensional problems and then is ex tended to infinite dimensional problems (Fredholm opera tors of index zero). For example, for the case of a single state variable bifurcation problem (characterized by dim ker DuF(uo,p) = 1), the branching equation is shown to be g(x,p)= (v1,F(xy +W(xy ,p),p)) (8a) where x is a scalar state variable (projection of the solution onto ker L*), and yl,vl are the eigenfunctions corresponding to the zero eigenvalue of L = DuF(uo,p) and L* (adjoint operator), respectively. The function W(xyl,p) containing the slave variables (modes) is defined by the implicit equation (IE)F(xy +W(xy1,p),p)= 0 (8b) where E is the projection operator onto the range of L. Next, the main ideas of elementary catastrophe theory, such as determinacy, transversality, and unfolding are discussed, and Thom's classification and unfolding theorem is stated. The geometry of the elementary catastrophes (fold, cusp, swallowtail, butterfly, wigwam, and star) with the normal form k2 G(Xp = xk yEi+1Xi i=O (k= 2,3,4,5,6,7) and their bifurcation sets in the espace is discussed along with applications to lumped models of reactors and equa tions of state in classical thermodynamics. The next lecture introduces singularity theory with a dis tinguished variable. First, the distinction between elemen tary catastrophe theory and singularity theory with a distin guished parameter is explained. For example, it is noted that the behavior of most physical systems is observed by mea suring their response as a function of a distinguished physi cal parameter or variable (such as residence time, inlet tem perature, etc.). In order to determine the different types of responses (bifurcation diagrams), it is necessary to rewrite the branching equation as g(x,X,p*)=0 (10) where X is the distinguished physical parameter and p* is the vector of other parameters that are independent of X. Next, the concepts of contact equivalence, unfolding, and normal form are discussed, along with a list of defining and non degeneracy conditions for singularities up to codimension three. The different types of bifurcation diagrams that exist next to singularities of codimension one (hysteresis, isola, and double limit), codimension two (pitchfork), and codimension three (winged cusp) are reviewed. This is fol lowed by a discussion of the method of constructing phase diagrams that divide the parameter space into regions with different types of bifurcation diagrams. The appearance and disappearance of solutions at the boundaries of the state Fall 1993 variables and/or parameters is also discussed. The useful ness of the theory is illustrated by application to lumped models of chemical reactors. The third lecture on steadystate bifurcation theory intro duces the effects of symmetry. The occurrence of discrete symmetry is illustrated by giving physical examples with reflectional or Z2 symmetry (two coupled identical cells and discretized models of convection) and permutational or D3 symmetry (three coupled identical cells). Next, some impor tant concepts of finite group theory such as subgroup, group isomorphism, orthogonal representation, and irreducible representation are discussed. The importance of these con cepts is illustrated by discussing the invariance properties of kernel and range of L under the action of the group and the structure of the branching equations in the presence of these symmetries. This is followed by a statement of Thom's clas sification theorem for singularities with Z2 symmetry and the geometry of the elementary catastrophes with this sym metry. The dihedral symmetry (D3) is discussed, using the example of three coupled cells (simplest example where symmetry forces repeated eigenvalues). The next lecture deals with the bifurcation analysis of two point boundary value problems. First, it is shown that the LiapunovSchmidt reduction for many nonlinear twopoint boundary value problems (such as diffusionreaction, con vectionreaction, and diffusionconvectionreaction models in one spatial dimension) can easily be accomplished by using the shooting technique and sensitivity functions. The usefulness of this method is illustrated by deriving stability criteria (cusp locus) for the catalyst particle and the tubular autothermal reactor models. As the shooting technique is not applicable in higher dimensions, a procedure is presented for the determination of singular points of elliptic boundary value problems of the form Lu+N(u,p)=0 inn (u=0 on aL or Vu,n=0onan) (11) where L has discrete spectrum with M zero eigenvalues, and N(u,p) is quadratic or higher order in u. This problem is also used to illustrate the equivalence of the two main approaches to bifurcation theory, namely the LiapunovSchmidt reduc tion and the perturbation (multiscale) approach of looss and Joseph[6] using the Fredholm Alternative. The physical ex amples we discuss include problems of diffusionreaction and diffusionconvectionreaction in higher dimensions con sisting of a single or a pair of nonlinear elliptic partial differential equations with either Dirichlet, Neumann, or Robin boundary conditions. The last lecture on steadystate bifurcation theory deals with the presence of symmetries in boundary value prob lems. First, examples of problems with reflectional (Z2) and rotational symmetry (0(2)) are given (reactiondiffusion equa tions in a disk, ring, or line with Dirichlet or Neumann boundary conditions, problems of flow in pipes as well as artificially imposed periodic boundary conditions on physi 157 cal systems). The presence of hidden symmetries (in the boundary conditions) is also illustrated. Next, the derivation of branching equations in the presence of Z2 symmetry with single and double zero eigenvalue and 0(2) symmetry with single (repeated) and double (repeated) zero eigenvalue is discussed. The occurrence of these bifurcations and the local bifurcation picture is illustrated by application to the buck ling of a rectangular plate and the Brusselator model of pattern formation on a line and on a circular disk. The lecture material on steady state bifurcation theory is taken from references 6 through 19, the author's thesis,[2] research publications, and notes. Dynamical Systems The third major topic, for which more than a quarter of the course is devoted, is bifurcation theory for ordinary differential equations. It begins with a review of the concept of asymptotic stability, the properties of hyperbolic fixed points, and the invariance of the general ized eigenspaces of the linear system with constant coeffi cients (du/dt = Lu). This is followed by the linearization theorem of Hartman and Grobman for the local behavior of the nonlinear system C =Lu+N(u,p); N(0,p)=DuN(0,p)=0 ue YcRn (12) and the stable manifold theorem for a fixed point. Next, the slaving principle is explained in terms of the time scales (eigenvalues) associated with the eigenmodes and the Center Manifold theorem is stated. The usefulness of the Center Manifold theorem as a rigorous perturbation technique (that includes the classical regular perturbation/multiplescale tech niques) is illustrated by considering a twophase model of a packedbed and deriving conditions under which it could be reduced to a single phase (pseudohomogeneous) model and the resulting model to infinite order! The second lecture focuses on the application of Center Manifold theorem to reduce the dimension of the bifurcation problem defined by Eq. (12). First, a general procedure for determining the amplitude equations when L has r eigenval ues on the imaginary axis is presented (the nonlinear func tional analysis and the notation are helpful in doing this in a compact manner). Specific results for the case of single zero eigenvalue, two and three zero eigenvalues, a pair of imagi nary eigenvalues, and zero plus a pair of imaginary eigenval ues is presented. (Students are encouraged to verify and extend some of these formulas using symbolic manipula tion.) For example, when a trivial solution exists for all values of the parameters vector p and there is a single zero eigenvalue at po, it is shown that the amplitude equation to cubic order is given by dt =ai lAiki +Ba +Cal (13) i=l 1 where Xi =Pi Pio (i=1,...,M) are the components of the parameters vector and pio are the parameter values at which 158 there is a simple zero eigenvalue. The coefficients Ai, B, and C can be expressed in terms of some inner products involving the eigenvectors and adjoint eigenvectors of the linearized problem and higher order Fr6chet derivatives of the function F(u,p). The third topic of discussion is normal form theory, or equivalently, the transformation of the amplitude equations into their simplest form. First, it is shown that the calculation of the normal form of a set of amplitude equations involves near identity transformations and the solution of certain lin ear equations in polynomial vector spaces. Next, the normal forms (along with their universal unfoldings) are presented for some codimension one bifurcations (saddlenode and Hopf) and codimension two bifurcations (TakensBogdanov, zero, and a pair of imaginary eigenvalues and two pairs of imaginary eigenvalues) followed by a discussion of the local bifurcation behavior next to these singularities and the con struction of phase diagrams in the unfolding parameter space. The application of the center manifold and normal form theories is illustrated using lumped models of chemical reac tors (CSTR with single and multiple reactions) and discretized models of convection (Lorenz model and the five equation models of thermohaline and binary convection). The fourth topic of discussion is Floquet theory and de generate Hopf bifurcations. First, the general theory of linear systems with periodic coefficients, the method of calculation of the monodromy matrix, and the Floquet multipliers are reviewed. Next, the main theorem that gives the stability of the periodic solution in terms of the Floquet multipliers is stated. The two main degeneracies that may occur when Hopfs hypotheses break down are stated (coalescence of two Hopf points and the vanishing of the cubic co efficient in the normal form). The method of determining periodic solutions by analyzing the zeros of a nonlinear operator defined on the space of 27tperiodic functions is discussed. The FitzhughNagumo equations for nerve impulse, the Glycolytic model for oscillations, the Gray Scott isothermal autocatalysis model, and the CSTR model are used for illustrating the construction of phase diagrams in the parameter space. The next lecture is devoted to discrete dynamical systems. As in the case of continuous systems, the properties of hyperbolic fixed points and invariance of the generalized eigenspaces of the linear discrete system with constant coef ficients (Uk+1 = AUk) are reviewed. This is followed by the stable and center manifold theorems for the local behavior of the nonlinear system Uk+1= F(uk,p)=Auk +N(uk,p); N(0,p)= DN(0,p)= 0 (14) The calculation of the amplitude equations and the normal forms for codimension one bifurcations (saddlenode, transcritical, pitchfork, period doubling, and NaimarkSacker) are illustrated. The different types of attractors (fixed points, periodic attractors, invariant circles, and strange attractors) Chemical Engineering Education of discrete dynamical systems, the types of bifurcations that occur, the basins of attraction, and the fractal nature of the basin boundaries are illustrated using classical examples such as the logistic map, the delayed logistic map, the H6non map, and the complex Newton iteration method for deter mining the fourth roots of unity. The sixth lecture on dynamical systems is devoted to Poincar6 maps, averaging methods, and Melnikov theory. First, the reduction of a continuous dynamical system to a discrete one through the Poincar6 map and the method of construction of this map for three specific cases (near a periodic orbit, near a homoclinic orbit, and for a forced periodic system) as well as in the general case (using the method of H6non) is illustrated. Next, the averaging theorem is used to obtain the Poincar6 map for periodically forced dynamical systems using the forced Duffing equation as an example. At this stage, the dynamics of twodimensional maps near homoclinic points is explained intuitively and the Melnikov method is presented for detecting the transverse homoclinic points. Chemical engineering examples discussed include periodically forced reactors and the dynamics of a gas bubble in a viscous liquid with periodic pressure varia tions. The next lecture deals with the routes to chaos, definition and characterization of attractors, and the treatment of ex perimental data. First, the differences between the flows of conservative and dissipative dynamical systems is reviewed. Next, a strange attractor is defined and the three wellknown routes to chaos are illustrated using the example of two coupled cells with the Brusselator kinetic scheme. Different methods for the analysis of experimentally (or numerically) generated time series are discussed. The calculation of attractor dimensions (using the method of Grassberger and Procaccia), Kolmogorov entropy, Liapunov exponents, and power spectra (using FFT) is illustrated with examples. The last lecture on dynamical systems is a survey of vari ous topics such as the global theory (Poincar6Bendixson) of dynamical systems in the plane, degree and index theory, use of group theory to calculate normal forms, Hamiltonian chaos, and fractals. The lecture material on dynamical sys tems is taken from references 20 through 31 and research articles in Physica D. Examples and applications are taken from the author's notes. Nonlinear Partial Differential Equations The fourth major topic of the course is bifurcation theory for nonlinear partial differential equations. This topic is introduced with the method of linearization of Eq. (3) around some base state (uo), the solution of the system of linear partial differential equations dv LvD C = Lv= DuF(uo)v (15) and the properties of the eigenvalue problem (Ly=piCy) and the adjoint eigenvalue problem (L*v= C*v). Next, the Fall 1993 two main theorems stating the necessary and sufficient conditions for simple and Hopf bifurcations are presented. Applications of the theorems are illustrated by physical ex amples such as TaylorCouette flow, RayleighBenard con vection (principles of exchange of stabilities), Lapwood con vection, and pattern formation on a catalytic disk (station ary/oscillating patterns). The second lecture deals with the application of center manifold theory to partial differential operators in finite domains (discrete spectrum). Center manifold reduction of a system of PDEs and the derivation of the amplitude equa tions for M eigenvalues on the imaginary axis are illustrated. (The unified notation is again helpful as the same formulas are applicable for finite as well as for infinite dimensional problems, the only difference being in the summations.) The reduction of the NavierStokes equations for pipe and plane Poiseuille flows to an infinite set of coupled quadratic ODEs and the computation of the coefficients of the linear and quadratic terms in the amplitude equations are illustrated. Once again, the usefulness of the center manifold theorem as a generalized perturbation technique is shown by discussing a classical chemical engineering problem (TaylorAris dis persion) from a new perspective. (This example was taken from the joint work of the author with Professor Chia Chang, University of Notre Dame.) The third topic of discussion is mode interactions in the presence of symmetries. The derivation of amplitude equa tions in the presence of two zero eigenvalues with Z2 sym metry and two zero eigenvalues (repeated) and a pair of imaginary eigenvalues (repeated) with 0(2) symmetry is illustrated along with the local bifurcation diagrams. The physical examples discussed include the problems of flow maldistributions in packed beds, reaction driven convection in a rectangular box, and stationary and moving temperature patterns on a circular catalytic disk. The fourth lecture is devoted to the case of continuous spectrum (bifurcation in large systems). Here, the multiple scale perturbation technique combined with the Fredholm Alternative is used to derive the Landau (or the nonlinear heat) equation T=V2U+aUbU3 (a,breal, U=realamplitude) (16) for the case of continuous spectrum crossing the imaginary axis at zero and the GinzburgLandau (or the Newell WhiteheadSegal) equation =U+(1+ia)V2U(+ip)U2U; a,3 real,U= complex (17) at amplitude) ' for the case of complex continuous spectrum crossing the imaginary axis. The spatiotemporal patterns predicted by these equations and the concepts of phase and amplitude turbulence are briefly discussed. The fifth lecture on PDEs is devoted to global techniques 159 such as Liapunov functions and energy stability theory. The classical Bdnard problem is used to determine the stabil ity boundary of the conduction state to finite perturbations (which coincides with the linear stability boundary). The example of throughflow in a porous medium is also used to illustrate the possibility of subcritical bifurcations pre dicted by energy stability theory. Finally, the construction of Liapunov functions is illustrated for some finite and in finite dimensional problems. The last lecture is concerned with delaydifferential, integral, and integrodifferential equations (a topic that has applications in many areas of chemical engineering but is often ignored). The three examples include a system with time delay (GlassMackey model), a Fredholm integral equation of first kind with a symmetric kernel describing a diffusionreaction problem, and an integrodifferential equation describing the dynamics of a catalyst particle (with uniform internal temperature but nonuniform concen tration gradients). These models show simple and Hopf bifurcations, period doubling, and chaotic behavior. For some of these cases, the local theory to compute the normal form is outlined. The lecture material and examples on this topic are taken from References 10, 15, and 32 through 36, Physica D, and the author's research articles. Nonlinear Waves The fifth topic is nonlinear waves. Since the students are familiar with linear and hyperbolic (shock) waves covered in the applied mathematics course, some important concepts (such as phase velocity, group velocity, dispersion, and front steepening) are reviewed. Next, two chemical engineering examples (waves on a falling film and temperature waves on a catalytic wire or ribbon) are presented and some model wave equations, such as the long wave equation and the generalized Fisher's equation t = v +f(u,p) (18) at ax2 are derived. The rest of the discussion is concerned with the wave properties of Eq. (18) and the nonlinear partial differ ential equation + uU +V au +a u 4u = (19) at ax ax2 ax3 x4 which includes as special cases some of the most widely studied equations, such as the Burger's equation (g. = 0, ; = 0), the Kortewegde Vries equation (v = 0, X = 0), and the KuramotoSivashinsky equation (L = 0). Substituting the traveling wave assumption u(x,t)= h(z), z= x ct (20) reduces Eq. (18) to a set of two ODEs (which can be ana lyzed by phase plane techniques) and Eq. (19) to a set of three ODEs which exhibit periodic, quasiperiodic, and cha otic solutions. The physical interpretation of these solutions as well as the variation of the wave speed with the param eters of the system are discussed. The lecture material for this topic is taken from references 37 and 38, along with the author's notes. Computational Methods The last two lectures are de voted to computational methods in bifurcation theory. First, the arc length continuation technique as described by Kubicek and Marek[39] is presented. This is followed by a review of the software (such as DERPAR, AUTO2, etc.) for the con tinuation of steadystate and periodic branches. The recent software package KAOS of Kim and Guckenheimer is also reviewed and used by some students. It is also noted that there are very few algorithms available for computing bifur cation branches in the presence of symmetries. The lecture material for this topic is taken from references 39 and 40. STUDENT PERFORMANCE A set of fifty homework problems are given to the students after the introductory lectures and the stu dents are asked to attempt five of them and submit a written report on one problem. More than half of these problems are openended and challenge the students (four of the problems later became topics of the students' PhD dissertations and led to several refereed publications). A combined total of twentyfour students took the course for credit (and many others audited). In gen eral, the students fell into two groups: those who were doing either experimental or theoretical re search on nonlinear systems, and those who took the course to complete their graduate course require ments. The second group of students attempted straightforward homework problems such as com puting the attractor dimensions or extending the LiapunovSchmidt/Center Manifold calculations using symbolic manipulation. The first group of students attempted openended problems, but their solutions were incomplete (some were completed a few years later). CONCLUSIONS Linear analysis played a key role in the develop ment of applied sciences during the nineteenth and firsthalf of the twentieth century. It is believed that nonlinear analysis combined with the power of the computer will play a similar role in the next century. The local nonlinear techniques of bifurcation theory extend the traditional linear analysis and are essen tial in the development of algorithms for computa tion. They also guide the search for solutions of nonlinear systems in multidimensional parameter spaces. The computer experiments play a comple mentary role and extend and validate the local theory Chemical Engineering Education as well as lead to new and unexpected results (such as the discovery of the soliton). It is the author's opinion that some analysis and computational expe rience with nonlinear systems should be part of a standard training program for all graduate chemical engineers. ACKNOWLEDGMENTS The author is indebted to Professors Martin Golubitsky and Giles Auchmuty of the mathematics department at the University of Houston, with whom he has had many discussions on singularity, bifurca tion, and group theories. This article was written while the author was on sabbatical leave at the University of Minnesota. REFERENCES 1. Andereck, C.D., S.S. Liu, and H.L. Swinney, J. Fluid Mech., 164, 155 (1986) 2. Balakotaiah, V., PhD Thesis, University of Houston, Hous ton, TX (1982) 3. Zeidler, E., Nonlinear Functional Analysis and Its Applica tions, Vols. IV, Springer (1986) 4. Chow, S.N., and J.K. Hale, Methods of Bifurcation Theory, Springer (1982) 5. Dieudonnd, J., Foundations of Modern Analysis, Academic Press, New York, NY (1960) 6. Iooss, G., and D.D. Joseph, Elementary Stability and Bifur cation Theory, Springer (1990) 7. Vainberg, M.M., and V.A. Trenogin, Theory of Branching of Solutions of Nonlinear Equations, Noordhoff (1974) 8. Haken, H., Advanced Synergetics, Springer (1986) 9. Golubitsky, M., and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. I, Springer (1985) 10. Golubitsky, M., I. Stewart, and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. II, Springer (1988) 11. Gibson, C.G., "Singular Points of Smooth Mappings," Res. Notes in Math., 25, Pitman, London (1979) 12. Gilmore, R., Catastrophe Theory for Scientists and Engi neers, John Wiley (1981) 13. Thom, R., Structural Stability and Morphogenesis, Ben jamin, Reading, MA (1975) 14. Zeeman, E.C., Catastrophe Theory: Selected Papers, Addison Wesley, Reading, MA (1977) 15. Segal, L.A., Modeling Dynamic Phenomena in Molecular and Cellular Biology, Cambridge University Press, 2nd cor rected printing (1987) 16. Nicolis, G., and I. Prigogine, SelfOrganization in Nonequilibrium Systems, Wiley (1977) 17. Rabinowitz, P.H., ed., Applications of Bifurcation Theory, Academic Press (1977) 18. Murray, J.D., Mathematical Biology, Springer (1988) 19. Vanderbauwhede, A., "Local Bifurcation and Symmetry," Lec. Note in Math. #75, Pitman (1982) 20. Guckenheimer, J., and P.J. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 2nd corrected printing, Springer (1986) 21. Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer (1990) 22. Carr, J., Applications of Centre Manifold Theory, Springer (1981) 23. Marsden, J.E., and M. McCracken, The Hopf Bifurcation and Its Applications, Springer (1976) 24. Arnold, V.I., Geometrical Methods in the Theory of Ordinary Fall 1993 Differential Equations, Springer (1983) 25. Hassard, B.D., N.D. Kazarinoff, and Y.H. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press (1981) 26. Schuster, H.G., Deterministic Chaos, PhysikVerlag (1984) 27. Sparrow, C., The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Springer (1982) 28. Coddington, E.A., and N. Levinson, Theory of Ordinary Differential Equations, Robert E. Kreiger Publishing Com pany (1987) 29. Devaney, R.L., Chaotic Dynamical Systems, Benjamin, Read ing, MA (1987) 30. Marek, M., and I. Schreiber, Chaotic Behavior of Determin istic Dissipative Systems, Cambridge University Press (1988) 31. Moon, F.C., Chaotic Vibrations, John Wiley & Sons (1987) 32. Chandrasekhar, S., Hydrodynamic and Hydromagnetic Sta bility, Oxford University Press (1961) 33. Drazin, P.G., and W.H. Reid, Hydrodynamic Stability, Cam bridge University Press (1987) 34. Kuramoto, Y., Chemical Oscillations, Waves, and Turbu lence, Springer (1984) 35. Collet, P., and J.P. Eckmann, Instabilities and Fronts in Extended Systems, Princeton University Press (1990) 36. Joseph, D., Stability of Fluid Motions, Vols. I and II, Springer (1976) 37. Segal, L.A., Mathematics Applied to Continuum Mechanics, Dover, New York (1987) 38. Toda, M., Nonlinear Waves and Solitons, Kluwer Academic Publishers, Boston, MA (1989) 39. Kubicek, M., and M. Marek, Computational Methods in Bifurcation Theory and Dissipative Structures, Springer (1983) 40. Roose, B.D., B.D. Dier, and A. Spence (eds.), Continuation and Bifurcations: Numerical Techniques and Applications, Kluwer Academic Publishers, Boston, MA (1989) 0 O book review ELEMENTS OF CHEMICAL REACTION ENGINEERING: 2nd Edition by H. Scott Fogler Prentice Hall, Englewood Cliffs, NJ (1992) Reviewed by P. R. Westmoreland University ofMassachusetts The second edition of this text already comes about as close to universal usage as a chemical engineer ing text can, including wide international use in addition to 108 schools (in a recent count) in the U.S. It is not as well suited for graduate study, but (as far as I am concerned) it is the best undergraduate reaction engineering text available, based on its con tent, structure, and wide variety of good problems. This edition, like the first edition did, covers the necessary subject territory of reaction engineering within its fourteen chapters: Continued on page 166. MOLECULAR LEVEL MEASUREMENTS IN CHEMICAL ENGINEERING R. J. SMILEY, W. N. DELGASS Purdue University West Lafayette, IN 47907 or quality control of a complex polymeriza tion, or tracing the cause of poor paint adhe sion, or understanding substandard perfor mance of a catalyst batch, and for a host of other challenges, practicing chemical engineers may well find the greatest benefit by using a molecular level approach to the problem. While it is likely that the engineer will have to call on an expert to bring the full power of a given technique to bear on a given problem, it is important that he or she be sufficiently aware of the molecularlevel tools available to begin asking the right questions. At Purdue, an elective course, called "Molecular Level Measurements in Chemical Engineering," for juniors, seniors, and graduate students, was designed to fill this need by sensitizing students to a variety of microscopic and spectroscopic characterization tools. Most students who graduate with a BS degree in chemical engineering have had only limited expo sure to the characterization tools that will be avail able to them as professionals in industry or aca demia. Undergraduate engineering laboratory courses tend to focus on traditional chemical engi neering equipment, and when chemistry laboratory courses use modern spectroscopic methods, they rarely make a connection to an engineering context. In our course, a brief discussion of the basic theory, instrument design, and sample requirements estab lishes the basic physics of the particular technique and the type of information it can give. Applications drawn from the literature illustrate the utility of the method in addressing engineering problems. COURSE PHILOSOPHY The course grew out of a conviction that chemical engineers can best extend their technical longevity through an understanding of the molecular basis of the properties and behavior of engineering R.J. Smiley is a graduate chemical engineering student at Purdue University. He received his BS degree from Cornell University in 1989. His research interests focus on studying interfacial interactions of composite materials on the mo lecular level by Xray photoelectron spectros copy, electron microscopy, and scanning force microscopy. SW. N. Delgass is Professor of Chemical Engi neering at Purdue University. He received his BS in chemical engineering from the University of Michigan, and his MS and PhD degrees from Stanford University. His research interests are in the kinetic and surface chemical characterization S of solid catalysts and other advanced materials. materials and processes. To use this understand ing, one must be able to make measurements on the molecular level. The primary objective of the course is to introduce students to various tools that will extend their abil ity to solve problems. It is important to note that we stress that the course only introduces the various techniques and is not meant to make the students experts in a particular field. We have chosen breadth over depth to give students a wide scope of applica tions, but we try to include sufficient detail of some techniques to foster an appreciation of the care it takes to get the most information available. The first of two secondary objectives of the course is the effective reading of technical papers. Our reli ance on primary source material gives us an oppor tunity to emphasize critical evaluation of journal articles. Problem sets designed around current ar ticles ask students to challenge and justify state ments they read, to derive equations and discuss assumptions in the paper, and to consider what new or corroborating evidence might be obtained from alternative experimental approaches. For some stu dents, these exercises provide the first recognition of the fallibility of the printed word and are, thus, Copyright ChE Division ofASEE 1993 Chemical Engineering Education important steps in learning the winnowing process that is central to selfeducation. Finally, we have incorporated laboratory exercises into the course that will at least introduce students to the hardware associated with advanced instru mentation. Each class day spent on an instrument limits the breadth of topics the course can cover, but the students confirm that talking about an experi ment does not have the same impact as doing it. This past spring we included three lab periods to cover Xray photoelectron spectroscopy, electron mi croscopy, and infrared and nuclear magnetic reso nance spectroscopies. COURSE DESCRIPTION Table 1 gives the course outline. It begins with a brief overview of the techniques that will be covered in the class. Starting with the Propst diagram (see Figure 1) and the energy spectrum, we discuss the different ways of perturbing a sample with fields, photons, ions, neutrals, and electrons, and point out the types of information one might hope to learn.511 Emphasis on applications shows where the course is heading and is intended to justify the need for the twoweek review of background material that fol lows. Discussion of deBroglie's equation, the uncer tainty principle, and Schrodinger's equation, together with derivations for a particle in a box and simple harmonic motion, and review of atomic and molecu lar orbital theory as well as some simple symmetry concepts provide the foundation on which all the molecular level techniques rest. We begin quantitative surface analysis with a de tailed discussion of Xray photoelectron spectroscopy TABLE 1 Outline of Major Topics 1. Introduction and Background (2 weeks) Propst Diagram Classical and quantum mechanics Symmetry 2. Quantitative Surface Analysis (4 weeks) Xray photoelectron spectroscopy (XPS) Ion scattering spectrometry (ISS) Secondary ion mass spectrometry (SIMS) 3. Bulk and Surface Structural Analysis (4 weeks) Diffraction (XRD, LEED) Electron microscopy (TEM, SEM, AEM) Scanning probe microscopies (STM, SFM) 4. Chemical Characterization (4 weeks) Infrared spectroscopy (IR) Raman spectroscopy Nuclear magnetic resonance spectroscopy (NMR) Mass spectrometry (MS) 5. Case Studies (1 week) Fall 1993 NEUTRALS IONS PHOTONS SAMPLE ELECTRONS HEAT FIELDS Figure 1. The Propst Diagram. Arrows pointed inward represent various probes used to perturb the sample. Dif ferent responses to perturbation, indicated by the outgoing arrows, provide information about the sample. (XPS), including important features such as surface sensitivity, elemental and chemical state analysis, and quantitative capabilities. Detailed lectures fo cus on spectral interpretation by analysis of peak position, area, shape, and splitting. In order to illustrate the potential of XPS, we spend several lectures discussing spectra from papers in the literature. One example of XPS analysis of the interactions between metal and metal oxide films shows students that surface properties are often much different from bulk properties, and that these differences directly affect the quality of the finished product."2' These discussions are often the first time students are asked to extract information from spec tra. Not surprisingly, they are initially reluctant to volunteer opinions, but we find that giving them the papers in advance and providing them with a few key questions to consider stimulates discussion. After a relatively detailed presentation of XPS, we study Auger electron spectroscopy (AES), ion scat tering spectroscopy (ISS), and secondary ion mass spectrometry (SIMS). Because much of the instru mentation and principles of XPS also apply to this next group of techniques, we move quickly through this part of the course to focus on applications of these tools. The next section is on examination of bulk and surface structure by diffraction and microscopy. We begin this part of the course with a discussion of crystal structure and Xray diffraction (XRD), elec tron diffraction, and low energy electron diffraction (LEED). Lectures are designed to compare and con trast the instrumentation as well as the information provided by each technique. Scanning and transmission electron microscopies are introduced next. One class period is a laboratory demonstration of the potential of SEM and TEM for studying biological and structural materials. Be fore the laboratory session, we devote a lecture to 163 contrasting the two types of microscopes and ex plaining the differences in resolving power, instru ment design, and sample requirements. Analytical tools such as energy dispersive Xray analysis (EDX) and electron energy loss spectroscopy (EELS) are also introduced. The last topic is scanning probe techniques, in cluding scanning tunneling and scanning force microscopies. The students read a paper by Hoff man which reviews many of the scanning probe microscopies and applies them to characterization of carbon fiber materials.31 In one problem set, students are asked to compare the types of infor mation obtained by STM/SFM on carbon fibers with the information learned from SEM and TEM, and to explain the advantages and disadvantages of each technique. The last group of techniques we discuss includes mass spectrometry and infrared, Raman, and nuclear magnetic resonance spectroscopies, and focuses on chemical characterization. At this point in the course, students have become familiar with the pat tern of the presentation and can apply many of the concepts they learned earlier to this last set of tools. Thus, introducing each technique requires less time and we are able to shift the lecture con tent to more complex problems requiring multi technique approaches. FTIR and solidstate NMR exercises examine different polymer systems and demonstrate the powerful analytical capabilities of these two instruments. With one week of classes left in the semester at this point, we introduce a case study that involves troubleshooting a process restart. The problem state ment, (developed for us from plant experience by Dr. George Swan, Exxon Research and Development, Baton Rouge, Louisiana) includes a description of the reforming process and the catalyst changeover procedure, along with a flow sheet. Gas chromato graphic analysis of the product stream and discus sion of some of the attempts to find the cause of the low octane rating are also presented and are read by the students before the class discussion. In class, the students seek the solution by suggesting causes and analyzing consequences. When they suggest that new data be gathered, the wisdom of such a move is analyzed for its utility, cost, and time required. The instructor's role is to keep the students on track with a minimum of direction and to supply additional data if it is asked for and available. The twist in this problem is that the chromatography data are incom plete. Mass spectrometry is needed to discover a heatexchanger leak that allows some of the feed to bypass the reactor. Even though this problem is relatively simple from an instrumentation point of view, the thought processes stimulated by the dis cussion are valuable for the students. We hope to develop additional case studies using real plant situ ations as the course evolves. COURSE REQUIREMENTS The course work includes three exams, a term paper, and ten problem sets. Exams focus on apply ing the principles learned. For example, one question on the first exam asks students to formu late a series of experiments to differentiate between three proposed reaction mechanisms, given a labora tory equipped with an XPS, ISS, SIMS, and a full range of isotopes. Other types of questions ask stu dents to interpret spectra or to draw and label a schematic of an instrument. The objective of the term paper is to get students to go into more depth for a particular technique. We give students the option to discuss a specific molecular measurement application of a technique introduced in class, or to discuss a new technique. They must submit paragraphs (which include three references from the literature) presenting their topics a month before the paper duedate so we can make suggestions and be assured they have started the assignment. Students normally choose topics that are too broad in scope and they need help focusing their ideas. A sampling of termpaper top ics is given in Table 2. Finally, we use problem sets to follow students' progress and to demonstrate application of techniques to engineering problems. We find that students re spond most favorably to recent articles because they recognize the importance of these techniques in solv ing existing problems. In one problem set we ask students to read a recent paper, "HighTemperature in Situ Magic Angle Spinning NMR Studies of Chemi cal Reactions on Catalysts."141 Although we do not expect the students to grasp all the details of solid state NMR, we find they can understand how the TABLE 2 Sample Term Paper Projects Positron emission tomography Scanning thermal microscopy Using TEM to determine inhomogeneity of highly crosslinked polymers Solid state NMR investigation of polymer morphology by multiple pulse spin diffusion experiments Chain branching studies of polymers using 3C NMR Xray diffraction for measuring residual stress in materials Chemical Engineering Education technique is applied and what is learned, and they can also answer questions about sample preparation and suggest additional measurements which sup port the authors' overall conclusions. We find it helpful, after handing back graded prob lem sets, to review questions which the students find difficult. These discussions, in addition to ex plaining the specific problem, generate additional questions. Oftentimes a student can be guided to answer his or her own question, and in many cases, help also comes from fellow classmates. Although these lectures break from the traditional lecture format, they are valuable for both the stu dents and the instructor because they foster a more relaxed environment for learning, encourage ques tions, and give a measure of the students' under standing of the material. RESOURCE MATERIALS Because of the number of tools we cover and the broad nature of the material, we do not use one specific textbook. Instead, we use a compilation of review articles, book chapters, and papers in the literature. A chapter, "Catalytic Surfaces and Cata lyst Characterization Methods," in Chemical Indus tries Series'51 serves to introduce many of the topics we cover. Since it focuses on catalytic systems, we use lectures and problem sets to challenge students to apply the techniques to other fields, including composites, polymers, and semiconductors. Papers in the literature are an excellent resource because they can be chosen to demonstrate a particular prin ciple and to tailor the course to the interests of the students. The list of papers used (see Table 3) shows a balance of classics and the newest applications. TABLE 3 Additional References Used Books 1. Czanderna, A.V., and D.M. Hercules, Ion Scattering Spectroscopies, Plenum Press, New York (1991) 2. Delgass, W.N., G.L. Haller, R. Kellerman, and J.H. Lunsford, Spec troscopy in Heterogeneous Catalysis, Academic Press, New York, (1979) 3. Briggs, D., and M.P. Seah, Practical Surface Analysis, 2nd ed., John Wiley and Sons, Inc., New York (1990) 4. Derome, A.E., Moder NMR Techniques for Chemistry Research, Pergamon Press, New York (1987) 5. Harris, R.K., Nuclear Magnetic Resonance Spectroscopy, John Wiley and Sons, Inc., New York (1986) 6. Harrick, N.J., Internal Reflection Spectroscopy, John Wiley and Sons, Inc., New York (1979) 7. Wischnitzer, S., Introduction to Electron Microscopy, Pergamon Press, New York (1981) 8. Kittel, C., Introduction to Solid State Physics, John Wiley and Sons, Inc., New York (1976) 9. Atkins, P.W., Physical Chemistry, 3rd ed., W.H. Freeman and Com pany, New York (1982) 10. Giintherodt, H.J, and R. Wiesendanger, Scanning Tunneling Micros copy I, SpringerVerlag, New York (1992) Monographs 1. Lyman, C.E., "Analytical Electron Microscopy of Heterogeneous Catalyst Particles," in Catalyst Materials: Relationship Between Struc ture and Reactivity, ACS Symposium Series 248 (1984) 2. Stokes, H.T., "NMR Techniques for Studying Platinum Catalysts," in Catalyst Materials: Relationship Between Structure and Reactivity, ACS Symposium Series 248 (1984) 3. Treacy, M.M.J., "Atomic Number Imaging of Supported Catalyst Particles by Scanning Transmission Electron Microscope," in Cata lyst Materials: Relationship Between Structure and Reactivity, ACS Symposium Series 248 (1984) Review Articles 1. Niehus, H., and R. Spitzl, "IonSolid Interaction at Low Energies: Principles and Applications of Quantitative ISS," Surf Interface Anal., 17, 287 (1991) 2. Soethout, L.L., H. Van Kempen, and G.F.A. Van de Walle, "Scanning Tunneling Microscopy: A Mature SurfaceScience Technique," Adv. Electron. Electron Phys., 79, 155 (1990) Journal Articles 1. Bartha, J.W., P.O. Hahn, F. LeGoues, and P.S. Ho, "Photoemission Spectroscopy Study of AluminumPolyimide Interface," J. Vac. Sci. Technol., A3, 1390 (1985) 2. Tjandra, S., and F. Zaera, "Static Secondary Ion Mass Spectrometry as a Tool for Studying Surface Reactions: The Decomposition of Ethyl ene over Ni(100) Surfaces," Langmuir, 7, 1432 (1991) 3. Kim, K.S., T.J. O'Leary, and N. Winograd, "XRay Photoelectron Spectra of Lead Oxides," Anal. Chem., 45, 2214 (1973) 4. Taglauer, E., and W. Heiland, "Low Energy Ion Scattering and Auger Electron Spectroscopy Studies of Clean Nickel Surfaces and Adsorbed Layers," Surf Sci., 47, 234 (1975) 5. Chakraborti, S., A.K. Datye, and N.J. Long, "OxidationReduction Treatment of Rhodium Supported on Nonporous Silica Spheres," J. Catal., 108, 444 (1987) 6. Jang, J.S.C., and C.H. Tsau, "Disordering of the Ni3S, Intermetallic Compound by Mechanical Milling," J. Mater. Sci., 28, 982 (1993) 7. Jean, J.H., and T.K. Gupta, "Devitrification Inhibitor in Binary Boro silicate Glass Composite," J. Mater. Res., 8, 356 (1993) 8. Jean, J.H., and T.K. Gupta, "Crystallization Kinetics of Binary Boro silicate Glass Composite, J. Mater. Res., 7, 3103 (1992) 9. ValletRegi, M., V. Ragel, J.L. Martinez, M. Labeau, and J.M. Gonzalez Calbet, "Texture Evolution of SnO2 Synthesized by Pyrolysis of an Aerosol," J. Mater. Res., 8, 138 (1993) 10. Primet, M., M.V. Mathieu, and W.M.H. Sachtler, "Infrared Spectra of Carbon Monoxide Adsorbed on SilicaSupported PdAg Alloys," J. Catal., 44, 324 (1976) 11. Hughes, T.R., and H.M. White, "A Study of the Surface of Decationized Y Zeolite by Quantitative Infrared Spectroscopy," J. Phys. Chem., 71, 2192 (1967) 12. Chen, X., and J.A. Gardella, Jr., "Fourier Transform Infrared and Electron Spectroscopy for Chemical Analysis Studies of Block Co polymers of Styrene and Dimethylsiloxane," Macromolecules, 25,6621 (1992) 13. Weeding, T.L., W.S. Veeman, L.W. Jenneskens, H. Angad Gaur, H.E.C. Schuurs, and W.G.B. Huysmans, ""3C and 29S, NMR Investiga tions of GlassFilled Polymer Composites," Macromolecules, 22, 706 (1989) 14. Li, Q., J. Megusar, L.J. Masur, and J.A. Cornie, "A High Resolution Transmission Electron Microscopy Study of SiCCoated Graphite Fi berAluminum Composite," Mater. Sci. and Eng., A117, 199 (1989) Fall 1993 161 Finally, we recommend the students dust off their physical chemistry books when we review the back ground material at the beginning of the semester. ON TEACHING TEACHERS We would be remiss in closing this presentation without commenting on the special circumstances that brought Randy Smiley into this educational partnership. Essentially all chemical engineering lec tures are given by faculty at Purdue, but we were encouraged to try this experiment through a Du Pont Fellowship granted to Randy. The success of the experiment is probably best illustrated by his own words: I feel fortunate to have had the opportunity to teach a course during my graduate studies at Purdue. I was amazed at how markedly my lecture preparation and teaching style changed as the semester progressed. I became more efficient in preparing for lectures and much more relaxed in front of the students, which gave me confidence and made the students more responsive in class. The classes in which we discussed journal articles were clearly the most unpredictable and the most fun to teach. I also enjoyed developing the laboratory exercises used in the course. The period we spent at the Electron Microscopy Center gave students a view of the com plexities of the equipment and sample preparation which would have been impossible to achieve in a classroom. Professor Delgass came to class during the first few weeks of the semester and gave me immediate feedback on my teach ing style. In addition, we typically met once a week to discuss the class progress. Initially, this time was spent discussing course content, but later in the semester we talked about the other responsibilities facing a professor, including starting up a research group and writing proposals. In addition to my discussions with Professor Delgass, I found the book Teach ing Engineering"61 helpful. It has hints about teaching skills, and discussions about tests, homework, and grading that are insightful. Overall, teaching in this supportive environment was a rewarding experience which I strongly recommend to any student who has any desire to pursue a career in aca demia. SUMMARY AND CONCLUSIONS Understanding what tools are available and the type of information each technique gives is critical for engineers to be successful problem solvers. This course gives students the foundation of many char acterization tools that will be available to them and should help bring a molecular point of view to their problemsolving skills. Exam questions and problem sets are designed to expose students to the practical potential of these tools and to hone their ability to critically evaluate the technical literature. Labora tory exercises familiarize students with instrumen tation and sample requirements and demonstrate the principles taught during the lectures. Finally, case studies show students how techniques are ap plied directly to problems facing practicing engineers. ACKNOWLEDGMENTS We would like to thank the Du Pont Foundation for awarding Randy Smiley a 199293 Teaching Fel lowship. Many thanks also to Dr. D. Sherman and Professor C.E. Bracker at the Electron Microscopy Center in the School of Agriculture at Purdue, and to Dr. Brett Cowans and Robert Adams for their help with the microscopy NMR and FTIR laboratory demonstrations. REFERENCES 1. Park, R.L., in Experimental Methods in Catalytic Research 111, edited by R.B. Anderson and P.T. Dawson, Academic Press, New York (1976) 2. Winograd, N., W.E. Baitinger, and J.W. Amy, Science, 184, 565 (1974) 3. Hoffman, W.P., Carbon, 30, 315 (1992) 4. Oliver, F.G., E.J. Munson, and James F. Haw, J. Phys. Chem., 96, 8106 (1992) 5. Delgass, W.N. and E.E. Wolf, in Chemical Reaction and Reaction Engineering, edited by J.J. Carberry and A. Varma, Marcel Dekker, Inc., New York (1987) 6. Wankat, P.C., and F.S. Oreovicz, Teaching Engineering, McGrawHill, Inc., New York (1993) 0 REVIEW: Elements of CRE Continued from page 161. * Basic definitions (and the necessary undefinition that rate must not be defined as dC/dt, despite what students have usually learned in physical chemistry courses) Powerlaw and LangmuirHinshelwoodHouganWatson kinet ics Design of ideal reactors, both isothermal and nonisothermal Using data to obtain rate expressions Product selectivity Mass transport in reaction engineering, including porous sol ids, slurry reactors, and mixing in nonideal flows Parallel to the technical exposition are difficulty ranked problem sets and "Thoughts on Problem Solv ing" that are severalpage endsegments of twelve chapters which discuss such formal approaches to problems as KepnerTregoe situation analysis. The most striking additions woven into this edi tion are 1) treatments of chemical vapor deposition, biotechnology, and polymerization, and 2) emphasis on using packages for solving differential equations. The first addition serves the obvious purpose of introducing these areas into the core curriculum, but even more subtly it also teaches how these "emerging technologies" are treatable by the classi cal techniques of reaction engineering. For example, I find the best way to introduce development of cata lytic rate expression for heterogeneous catalysis is to Chemical Engineering Education begin with MichaelisMenten enzyme kinetics, which is done well here. Unlike inorganic catalysis, the "site" is a tangible, specific, and unambiguous loca tion for many enzymes, thanks to experiments and molecular modeling (e.g., Science, 253, 872, 1991). Fogler also treats multiphase reactors more effec tively by treating both classical slurry reactors and aerobic bioreactors where air is bubbled through aqueous slurriess" of cell mass. Student use of O.D.E.solvers in this course is pro moted through the book's examples and problems. POLYMATH (CACHE Corporation) is used in most cases, but other packages are also used or cited (Chem. Eng. Ed., 24, 54, 1991). Simple codes for some computer solutions are still provided, but the equation solvers allow a quicker transition for the students to explore solutions and effects of param eters. Fogler's approach forces emphasis on concepts over techniques, in the spirit that to use an equation solver effectively, you only need to know how it worksnot how to make one. In this text, reaction engineering is the focus, while analytical or numeri cal methods are important tools to be used. A strong point of the examples and problems is that real reactants and reactions are generally used. The types of chemistries involved are not structured beyond homogeneous versus heterogeneous, but it isn't (and shouldn't be) the purpose of this book to organize the suite of chemical engineering chemis try. Many students enter chemical engineering be cause they like chemistry, and the reaction engi neering course is often the one place in the chemical engineering sequence where they seem to realize the connection with their chemistry courses. (Paradoxi cally, the curriculum is full of nonreaction chemis try, too, from chemical thermodynamics to materials to molecular bases of transport properties. We need to do a better job of pointing out the balance of physics and chemistry that go into the chemical en gineering profession.) Some worthwhile material has been omitted to meet space restrictions, but not always seamlessly. For example, analysis of tricklebed reactors was eliminated, apparently to allow inclusion of bioreac tors as multiphase reactors (certainly a defensible choice) but, unfortunately, tricklebed problems are left unchanged from the first edition, as if the rel evant text material was still in place. Other sources may be easily consulted, though, because references for tricklebed analysis and design are retained in the "Supplementary Reading" section. Other topics which are mentioned only briefly include fluidized bed and transport reactors. Of course, not every topic can or should be included in an undergraduate course on reaction engineering. Fogler describes an excellent, semes terlong sequence using about 60% of the book. Its coverage and timeliness make it today's de facto standard text for undergraduate kinetics and reac tion engineering. 0 e M book review HAZOP and HAZAN: Identifying and Assessing Process Industry Hazards, 3rd Edition by Trevor Kletz Published by the Institution of Chemical Engineers, United Kingdom; distributed in the US and Canada by Hemi sphere Publishing Corporation, Bristol, PA; 150 pages, $49.50 (1992) Reviewed by Daniel A. Crowl Michigan Technological University This book is a significant improvement over the last release, a softbound edition published in 1986. This issue includes a hard cover (in standard book size), redrawn and updated figures, new refer ences, and new content. It is divided into seven chapters, with several chapter appendices and sup plemental material. Chapter 1 provides a brief introduction to hazard identification and assessment, including a discus sion of why it is important, how far one must be prepared to go to eliminate hazards, and when in the design of a chemical plant these methods should be applied. Chapter 2 presents the concept of hazard and op erability studies (HAZOP), a hazard identification procedure which has become increasingly important to the chemical industry. A detailed example using the feed section to an olefin dimerization plant is provided. The chapter also includes discussion on why HAZOPs are important, who carries out the HAZOP, and the limitations to HAZOPs. An inter esting appendix to the chapter describes nine acci dents which could have been prevented by a proper HAZOP and one accident which most likely could not have been prevented. Chapter 3 introduces hazard analysis, which Pro fessor Kletz (and perhaps the British) is determined to call HAZAN, for hazard analysis. As Kletz points out, the United States prefers the term "quantita Continued on page 193. Fall 1993 Review / opinion THE CHANGING ROLE OF ACADEMIA JULIO M. OTTINO Northwestern University Evanston, IL 602083120 Academia is in turmoil. Higher education in the United States has never been static, but it is now undergoing rapid transformations, seemingly with no overall plan, seeking a purpose, pulled in many directions by forces that did not even exist a decade ago. Academia is now accountable to media pressure, to alumni, and to government. There are concerns about teaching, tuition costs and allo cation of funding, weights given to graduate and undergraduate education and research, scientific misconduct, and in general about the perceived mis match between academia's wants and society's needs. Critical reports have appeared in major news papers and on television: a Chicago Tribune article on teaching at the University of Illinois at Urbana; a 20/20 report on teaching at Berkeley. A decade ago it would have been unthinkable to conceive of a book like ProfScam.[ l The pressures are irreversible and will not go away. U.S. industry has been forced to deal with both globalization and environmental concerns, and envi ronmental issues will not be reset as they were in the 1950s. Similarly, what is now expected of aca demia is quite different from what was expected in the 1960s and 1970s. Only the institutions that are able to adapt will survive. There is a wide gap between myth and the reality of academic life. For this, academics have no one to blame but themselves, since any attempt to commu nicate ideas to the general public is usually looked upon with suspicion. The result is public ignorance as to how leading science evolves, the prevailing wisdom being that science somehow moves in recti linear fashion to immutable truths. Contrary to popular belief, there is now renewed attention being paid to undergraduate education in many institutions. My own institution, McCormick, Copyright ChE Division ofASEE 1993 Julio M. Ottino is Walter P. Murphy Professor and Chairman, ChE Department, Northwestem University. He received his PhD degree from the University of Minnesota and his undergraduate degree from the University of La Plata, Argen tina. His research interests are in mixing and chaos, pattern formationaggregation, breakup, Sand dispersionand mixing of immiscible and complex fluids. He is the author of The Kinemat ics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, 1989). is a good example: there are financial incentives for good teaching, such as rotating endowed chairs; 80% of the full professors teach at least one undergradu ate course a year; and it is impossible to buy time from teaching. The public at large, however, has little idea of how professors spend their time. Inside and outside forces are taking their toll, par ticularly on young academics who are expected to be all things to all peoplegreat researchers, effective fundraisers, inspirational teachers. Recent statistics are not encouraging: 53% of academics under forty year of age report that "my job is a source of consid erable personal strain."[2] Many institutions are trying to redefine their mis sions. An everincreasing stream of speeches and reports (many originating from captains of industry) are telling academics what to do, how to teach, how to manage their institutions, how to view research, and how to reexamine the rationale for the support of research. Some of this advice is well intended, but naiveand copying models of industrial success and applying things like TQM will help only up to a certain point. In the same way that industry cannot conduct research as if it were a university, univer sity research cannot be managed in an industrial mode. There is just so much that can be left to serendipity'31 but tight organization will undoubt edly kill creativity. Changes do not come without pain. Nevertheless, it is indisputable that in order for academia to re main productive, changes must be made and a new vision of scholarship must be advanced. To echo the Chemical Engineering Education words of Thomas Kuhn, a paradigm shift is in the air. As to what the new paradigm will bethat is hard to predict. What rationale will colleges and universities use to redefine their mission? Will things evolve to a unique model of success? Will expecta tions regarding faculty performance be uniform across institutions? Scholarship Reconsidered"2' offers one of the best reasoned views of how this paradigm might look and what considerations should be im portant when judging alternatives. In the following paragraphs I will quote freely from this work, add ing a few interjections of my own and restricting the remarks to research universities. Universities have been too narrow in defining the boundaries of acceptable behavior, especially when contrasted to the historical record of aca demia's changing mission. The main thesis of this report is that it is essential to broaden our defini tion of scholarship. The current, dominant, picture is that to be a scholar is to be a researcher. This was not always so and, in fact, this view is of rather recent vintage. Explicitly, or implicitly, the mission of academia has changed throughout the years, evolving and trans forming itself from teaching to service to research. The colonial college, patterned after British tradi tions, took a view of collegiate life that was almost monastic. Teaching was a calling. The goal of Harvard College in 1636 was to "advance Learning and per petuate to Posterity." The student was the center of attention, and tutoring was the preferred mode of teaching. This stage lasted for almost two hundred years, until service was added to the role. This transformation did not happen overnight. In stitutions gradually took an increased interest in serving business and economic posterity. Rensselaer Polytechnic Institute was founded in 1824 with the premise that "the United States needs railroad builders, bridgebuilders, builders of all kinds." The practical side of higher learning appeared loud and clear in the Land Grant College Act of 1862 and the Hatch Act of 1887. By 1903, the presidents of Stanford and Harvard would declare that the entire univer sity movement "is toward reality and practicality," and that "at the bottom, most of the American insti tutions of higher education are filled with the mod ern democratic spirit of serviceableness." The first president of Cornell saw graduates "pouring into the legislatures, staffing newspapers, and penetrating the municipal and county boards of America." Aca demia saw itself as a major force in shaping society. There was a conviction that higher education had a moral mission to fulfill. Where was research throughout this period? Cer tainly not within university walls. In fact, it took quite some time before research found a hospitable home within academia. The first advanced degree obtained by an American goes back to early 19th century Germany, and it took another fifty years for the first PhD degree to be awarded in the United States (Yale, 1861followed by Pennsylvania, Harvard, Columbia, and Princeton). Things moved quickly after that, however. The University of Chi cago, founded in 1891, made the PhD degree the pinnacle of its academic program. In fact, within four years of its founding, its president declared that "promotions in rank and salary would depend chiefly upon research productivity." Then, two World Wars and the Depression set the stage for a dramatic allinclusive change, particu larly in the way that research was to be supported by government. The most quoted document involving interaction between government and academia, Science: The Endless Frontiera report written for President Roosevelt at the end of World War II by Vannevar Busch of MIT, and eventually delivered to President Truman provided a blueprint that guided research right up to the present day. Its implicit idea was one of"societal return": that the societal return obtained by government investment would be greater than that produced by the same private investment."4' Agencies such as the National Science Foundation were created, and money started to pour into the halls of academia. By some measures this has served us well. Since 1945 United States scientists have received 56% of the Nobel Prizes in Physics, 60% in Medicine, and 42% in Chemistry. The societal return concept does not work well in a worldintegrated economy; in fact the very idea of only one country having the monopoly in education is questionable and universities would do well to think in broader terms. Nevertheless a firmly in grained consequence of operating under this para digm for the last half century is that academic suc cess (indeed, scholarship) has been associated with research, and research, in turn, exclusively with dis covery. This might have been a narrow viewpoint, but its appeal was unparalleled. All universities tried to fit into the mode and faculty were judged prima rily as researchers; after all, there was money to be garnered from successful academic enterprises. Scholarship goes beyond research, however. By and large, only one type of scholarship is routinely acknowledgedthe Scholarship of Discovery. Based Continued on page 175. Fall 1993 APPLIED STOCHASTICS FOR ENGINEERING JAY D. SCHIEBER University of Houston Houston, TX 772044792 here is an old joke that says that a statisti cian is someone who drowns while trying to cross a river with an average depth of three feet. But that sounds to me like the definition of a bad statistician. On the other hand, I have run across many otherwise good engineers who recognize the perils of considering only an average quantity, but have avoided probabilistic models altogether. I be lieve that engineers might serve themselves better in the long run by becoming good statisticians and good stochastic modelers. There is a perceptible increase in the interest of stochastics in the chemical engineering community, evidenced by two observations: the fall 1993 AIChE meeting is slated to contain a session on "Probabilis tic Models," and no less than three articles from the 1989 issues of this journal included some discussion of stochastic models in a new course description. Clearly, stochastics is playing an increasing role in chemical engineering. Last spring our department initiated a course in introductory stochastics designed to introduce graduate students to this rapidly expanding field. Fourteen students enrolled in the course, two stu dents audited it, and two faculty also attended regu larly. The sophistication of the semester projects that were turned in suggests that the students learned a lot, and the course appeared to generate a great deal of enthusiasm. In this article we will consider the following ques tions in order: * What is Stochastics? * Why is it of interest to chemical engineers? * What tools can be taught in a single semester course? WHAT IS STOCHASTICS? One day in 1910, Albert Einstein had just finished working on a stochastic problem involving Brownian motion when his young son Hans Albert asked him Copyright ChE Division ofASEE 1993 170 Jay D. Schieber is Assistant Professor of ChE at the University of Houston, where he has been since 1991. He received his BS from the University of Illinois, Urbana, and his PhD from the University of Wisconsin in 1982 and 1989, respectively. He spent a year at the University of Freiburg (Germany) and another at McGill University (Canada) as a postdoctoral fellow. He has an active research program in kinetic theory, transport phenomena, fluid mechanics, and polymer rheology. for a Rechenaufgabe." He thought up the following probability problem: "How long will it take til the ground is wet if it rains at the rate of 10mm/hr?" The problem is probabilistic, because rain does not fall uniformly, but rather in drops which cover (roughly) circular regions on the ground when they hit. After some portion of the ground is wet, the next drop may land completely on a dry area, completely on a wet area, or partly on each. There is no way to know where a given drop will land, so it must be treated statistically. Therefore, how long it takes a given portion of land to be completely wetted is not a deterministic question but a statistical one. We can find only the probability that it will take any given time to wet the ground. Or, consider a second problem. Suppose that I take my red 1966 Volkswagen Beetle to a particular point in the salt flats in Arizona, fill it with one quart of gas, pushstart it (as usual), point it north, put it in first gear, set a brick on the gas pedal, and let it go without a driver. Where will the Beetle be when it runs out of gas? If there were no wind we might be able to predict all of the forces on the Beetle and, in principle, calculate where the car will end up. But, in reality there is wind, the strength and di rection of which we cannot predict. If we run the experiment many times, the Beetle will end up in a different place each time. We quickly understand that the car is subject to both random and determin istic forces, and the final position of the Beetle de pends upon both. "Solving" the above two problems means that we seek the probable distribution of possible outcomes. Chemical Engineering Education The corresponding equations are called "stochastic" equations.* We can then roughly define stochastic equations as equations that describe a quantity (the position of the Beetle) whose evolution (in time) is determined by both deterministic (the motor, the grade, etc.) and random (wind) influences. WHY SHOULD CHEMICAL ENGINEERS LEARN STOCHASTICS? The engineer can quickly think up other, more relevant examples of when outside random influ ences can have a result on a final answer than the two given above: outside random influence on labo ratory experiment measurements or plant processes; randomly fluctuating temperatures or pressures; ran dom changes in feed stream compositions. But there are many other examples which are less than obvi ous. For example, concentration is the average num ber of molecules per volume in a region of space, and each molecule is acted upon randomly by other mol ecules. The actual number of molecules in a region of space is stochastic. The pore structure in a catalyst, or in an oil reservoir, is random. The transport of substances through these structures depends upon the random pore network. Cells in vitro undergo Brownian motion as they are bombarded by sur rounding fluid molecules. Populations of cells may be described by stochastic birthdeath equations. Polymer chains may take random conformations and be bombarded by Brownian forces. We can make a general observation here. When working with a large, complex system (and chemical engineers are certainly interested in large, complex systems) in which it is effectively impossible to in clude all degrees of freedom in the system, the num ber of variables being considered must be curtailed. Nonetheless, in any real system, the other degrees of freedom not accounted for explicitly still have an influence, and if this influence is not considered deterministically, it must be considered statistically. At that point, the mathematical equations corre sponding to the physical process are stochastic. We can safely say that chemical engineers need to learn stochastics in order to tackle many of the new problems entering the field. Why? Because chemical engineering is moving toward smaller and smaller length scales as processes become more efficient and less consumptive of material resources. Bugs per forming bioremediation are being jostled by water molecules; electrons in plasmas are colliding and reacting with large neutral species; molecules in low pressure reactors are bouncing off of walls, diffusing * We are using a broader definition of the term "stochastics" than that used by some mathematicians. Fall 1993 on surfaces, and jumping between activation sites. At these length scales, the influence of individual molecules becomes important. But there are still too many molecules to handle explicitly for any timescale of interest, and Brownian forces will be important. On the other hand, many degrees of freedom acting on wildly different length scales appear to be ideally suited for stochastic models. Understanding stochastics allows us to write down wellposed mathematical equations corresponding to intuitive probabilistic pictures. Equally important, that understanding helps us to design simple com puter codes to solve the resulting complex partial differential equations numerically. COURSE STRUCTURE The course structure is outlined in Table 1. No textbooks are required for the course, but two are highly recommended. The first, by C.W. Gardner, is called Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences.[2] It is an excel lent handbook for mathematical solutions, is well organized conceptually, and has a good mix of theo rem and description. But its background in prob ability is too thin for most engineers, the connection to physical problems is often minimal, and it con tains no problems. TABLE 1 Outline of Material in the Applied Stochastics Course (Although not explicitly shown, examples are scattered throughout the course.) 1. Background ideas and definitions Averages, variance, moments Probability density function, cumulative probability Conditional probabilities, Bayes' Rule, joint probabilities Contraction or marginal probabilities Characteristic functions, moment generating functions Sample distribution functions: Gaussian, Poisson 2. Probability transformations General formula Generating random numbers Deterministic processes with random initial conditions Central limit theorem 3. Markovian concept Definition ChapmanKolmogorov equation 4. Equations characterizing Markovian stochastic processes Differential ChapmanKolmogorov equation Liouville equations Master equations FokkerPlanck equations Stochastic differential equations 5. Examples of Markovian processes Problems with analytic solutions Brownian dynamics simulations Dynamic Monte Carlo simulations On the other hand, the second recommended text, by N.G. van Kampen, Stochastic Processes in Phys ics and Chemistry, 3 is organized more like a physics book and contains many problems. In general, we followed more closely the overall organization of Gardiner, but used van Kampen for all develop ments involving master equations. Unfortunately, neither text contains information of numerical meth ods; a few texts do exist with some discussion of numerical techniques."4'5] Typically, most engineers have no formal back ground in probability or statistics, so a significant amount of time must be spent in the beginning with the basic definitions and concepts shown under the first heading in Table 1. For example, while most engineers know what an average and a variance are, less familiar are probability density and autocorrelation functions, or a conditional proba bility. We begin by playing with typically simple probabilistic (gambling) problems, incorporating these ideas so that the student gets a good feel for what information the quantities contain. This section of the course takes about three weeks. Some of the important definitions introduced here are shown in Table 2. This is a also good time to introduce an essential concept used to great extent throughout the course: the dual descriptive character of stochastic processes. We can characterize a Markovian stochastic process either through the deterministicc) time evolution of the probability density function or through the sta tistical properties of an equation describing the evo lution of a single trajectory. These two viewpoints are roughly analogous to Hamilton's versus Liouville's description of classical mechanics. When we reach the second section, probability transformations, we are ready to begin solving physi cal problems. This section deals with the general problem of transforming some random variable, X, to some new random variable, Y := f(X), when the statistics of X are known and we wish to know the statistics ofY. A physical example is the orientation of network strands in a deformed rubber. Before deformation, the strands have random orientations whose distribution is isotropic, but when the rubber is deformed affinely, each strand moves determinis tically to a new orientation. We are interested in finding the new orientation distribution of strands after the deformation. Probability transformation also plays a role in gen erating random numbers with given distributions from random numbers drawn from a uniform distri bution. The mathematician John von Neumann has been quoted as saying, "Anyone who considers arith metical methods of producing random digits is in a state of sin." We largely avoid these problems, how ever, and assume that we have a suitable pseudo random number generator available. Knuth"61 dis cusses statistical tests of pseudorandom number generators, and Press, et al.,"71 provide some concrete examples. A recent article by Hayes"8' (who cites the above quote) discusses more recent ideas and ob stacles of such generators. The ideas contained therein are discussed briefly in class. This is a good time to introduce the central limit theorem for three reasons: it contains all of the probability concepts introduced before; it plays an important role in many physical systems; and a concrete example, namely random walks on a one dimensional lattice, provides a good segue into the next topic. All of the concepts introduced so far are for general stochastic processes. However, the vast bulk of the mathematical literature, most physical models, and nearly all of the numerical work utilizes Markovian processes. Thus, we introduce the mathematical defi nition and physical interpretation of a Markov pro cess. Intuitively speaking, these are processes where we need to know only the current state of the system in order to know future probabilities; knowing all of the past states of the system gives us no additional TABLE 2 NOTE: The symbol Prob {... reads as "the probability that" and := means "is defined as." The integrals must be taken over all possible values of the integration variables. <...> represents taking an ensemble average. Probability density function P(x;t)dx := Prob{The random variable X takes values between x and x+dx at time t} (1) Joint probability function P(x,t;y,t')dxdy := Prob{The random variable X takes values between x and x+dx at time t and values between y and y+dy at time t'. } (2) Conditional probability function P(x;tly;t')dx := Prob{The random variable X takes values between x and x+dx at time t given that it had value y at time t'. (3) Averages may be found from these by (f(X))t = JxP(x,t)dx (4) Autocorrelation functions are found by (X(t)x(t')) = fJxyP(x,t;y,t')dxdy (5) Chemical Engineering Education insight into future probabilities if we know the current state. Using the definition of Markov and Bayes' rule, we can derive the ChapmanKolmogorov equation, a nonlinear, integral equation for the conditional probabilities of Markovian processes. This form of the equa tion has only limited practical use, so we can derive from that the so called differential ChapmanKolmogorov equation which has greater C hapmanKolmogorov Equation ) S Differential ChapmanKolmogorov Equation Liouville Equation Master Equations ) (FokkerPlanck Equations It "$ S " Equations of Motion Langevinlike Equations) (Stochastic Diff. Equations I T 1 T I T Molecular Dynamics Dynamic Monte Carlo Brownian Dynamics Figure 1. Interrelation between important equations for Markovian processes. TABLE 3 The vector A describes the deterministic forces on the random vector, and B (or b) describes the random forces. The transition probability W(xlz,t) de scribes the probability per unit time that the random vector makes a discon tinuous and instantaneous jump from z to x at time t. The Wiener process, dW,, is a deltacorrelated, Gaussian white noise. ChapmanKolmogorov equation: P(x3;t3lx;ti)= P(x;t t2)P;t (x2;t2zxl;tl)dx2 (6) Differential ChapmanKolmogorov equation aP(z;tly;t')= [Ai(z,t)P(z;tJy;t)] 1+ j a2 [Bij(z,t)P(z;t.y;t )] ly' \ ) = 1 ai 2 11ziazj 1 + f[W(zlx;t)P(x; ty;t') W(xlz;t)P(z;tly;t')]dx (7) Master equation P(z;tly;t) = J[W(zlx;t)P(x;tJy;t') W(xlz;t)P(z;tly;t')]dx (8) *FokkerPlanck equation *P(z;tly;t)= ai[Ai(z,t)P(z;tly;t')]+ a [Bi(bz,t)P(z;tly;t')] (9) *Liouville equation P(z;t3Y;t2)= [Ai(z,t3)P(z;t3y;t2 )] (10) i az Langevin equation dXt = A(X,t)dt + b(X,t) dWt (11) Fall 1993 utility for our purposes: namely, the solution and description of stochas tic processes. Most of the equations for the rest of the course are spe cific cases of the differential ChapmanKolmogorov equation. The differential Chapman Kolmogorov equation can also be split into three rough categories: 1) master equations for discrete or dis continuous jump processes; 2) FokkerPlanck equations for con tinuous (but nondifferentiable) dif fusion processes; and 3) the Liouville equation for deterministic processes which may or may not have random initial conditions. The general forms for these equations are shown in Table 3, and the in terconnection between them are shown in Figure 1. Before deriving the differential ChapmanKolmogorov equation from the ChapmanKolmogorov equation, we go through derivations of simple examples of each type of equation. In addition, we repeat Langevin's derivationg91 of the first stochastic differential equation. An entire week is spent deriv ing the differential Chapman Kolmogorov equation and analyz ing its different subclasses as combinations of deterministic mo tion, diffusive motion, and jump processes. Emphasis is placed on interconversion between the evolution equation of the probabil ity density function and sample tra jectories of the equivalent process. In this way the students get a feel for how to translate physical pic tures into, say, master equations, or how to interpret the physical pro cess represented by, for example, a FokkerPlanck equation. Many simple examples are useful here. Finally, in this section we cover stochastic differential equations, which are intuitively very appeal ingbut mathematically they are usually intimidating for students on their first exposure. The primary 173 impediment for students is that this is often the first time they need nonRiemannian calculus to inte grate equations. But we have borrowed an introduc tion strategy from Gardiner that seems to be suc cessful in getting across the importance of attaching an interpretation to any stochastic differential equa tion with multiplicative noise. By the end of the section most students have little problem working with either It6, Stratonovich, or the more recent kinetic interpretations.t101 This sec tion requires two weeks of coverage to make the students comfortable, but the payoff for the hard work is unquestionably great since Brownian dy namics simulations are straightforward once the in terpretation questions have been tackled. I find discussion of numerical techniques to be a natural extension to the analytical solutions found for these equations. It is also at this point in the course that the students begin to see the power of stochastics. They see that complicated master equa tions have straightforward interpretations and may be solved easily by dynamic Monte Carlo techniques. Likewise, a complicated FokkerPlanck equation in thirty dimensions may be solved by a straightfor ward Brownian dynamics simulation without resort ing to finite element methods. The numerical techniques of stochastic dynamic simulations exploit the equivalence between equa tions of the third and fourth rows shown in Figure 1. Just as molecular dynamics techniques solve possible trajectories of interacting particles rather than the distributions function in Liouville's equa tion, Brownian dynamics simulations track the trajectories of realizations to estimate the probabil ity density function in the FokkerPlanck equation. In the course, examples of Brownian dynamics simulations are given for simple polymer and cell motility models. Likewise, the trajectories of realizations of sto chastic processes described by master equations can be described by Langevinlike equations, which suggest dynamic stochastic algorithms. We show detailed examples of nonlinear reaction mod els that can be solved by such dynamic Monte Carlo techniques. We spend most of the rest of the semester going through examples of how to model chemical reac tions,111 cell migration,[121 population balances, poly mer dynamics,"13' transport equations,14' lattice gas dynamics "1 for thermodynamic predictions, etc., as stochastic equations, solve them analytically or nu merically, and interpret the results. These examples 174 TABLE 4 Term Project Topics Chosen by Students Critical Review of Single Technical Paper Modeling of mechanical degradation of dilute polymer solutions A stochastic model of persistent currents in mesoscopic rings General Review of Research Area Application of dynamic Monte Carlo simulation method in study of surface kinetics Stochastic models for turbulent diffusion Diffusion models for characterizing the firing sequences of neurons Stochastic twophase flow in porous media Stochastic representation of reservoir heterogeneity Markov models for behavior Stochastic modeling of air pollution Original Research Stochastic dynamic simulation of cubic autocatalytic reactions to study bifurcations in chemical reactions Stochastic modeling of coalescence of viscous drops in liquid liquid dispersion Stochastic simulation of combined molecular diffusion and chemical reaction Solution of the Boltzmann equation by using dynamic Monte Carlo simulation Brownian dynamics simulation of a Hookean dumbbell with internal viscosity in steady shearing flow pull together all of the ideas introduced in the course, provide concrete examples of their utilization, and show how powerful and simple the techniques are. TERM PROJECTS Many of the examples in engineering are quite new. Nonetheless, I require that the students do a term project that fits into one of three categories: 1. A critical review ofa single technical manuscript that utilizes stochastic modeling. 2. A general review of stochastic modeling in a chosen field critiquing several manuscripts. 3. Original work using stochastic modeling for a re search project. I recommended the third category primarily for those students who may have had an original idea for a simple project while working on a project in the first category. After discussion, I made specific rec ommendations to a few students for original projects which they followed up on. CONCLUSIONS Table 4 shows a list of the projects chosen by the students in each category. Surprisingly, onethird of the class chose projects which were strictly original, whereas the projects in the first category included some original work and research suggestions. The quality of the original work was quite good, Chemical Engineering Education suggesting that problems of interest to chemical en gineers are fertile ground for the use of stochastics. Also, the students doing critiques of manuscripts for projects often found that much wellrespected work can be greatly improved by someone with a working knowledge of stochastics. In summary, I can write with a high probability of certainty that any chemical engineering faculty us ing stochastic modeling in research will find that introducing colleagues and graduate students to these techniques can be very fruitful. REFERENCES 1. Einstein, H.A., "Probability, Statistical and Stochastic Solu tions," in Stochastic Hydraulics: Proceedings of the First International Symposium on Stochastic Hydraulics, edited by ChaoLin Chiu, University of Pittsburgh, School of Engi neering Publication Series, Pittsburgh, PA, p 10 (1971) 2. Gardiner, C.W., Handbook of Stochastic Methods for Phys ics, Chemistry and the Natural Sciences, 2nd ed., Springer Verlag, Berlin (1985) 3. van Kampen, N.G., Stochastic Processes in Physics and Chemistry, 2nd ed., Amsterdam, North Holland (1992) 4. Honerkamp, J., Stochastiche dynamische Systeme, VCH, Weinheim (1990) 5. Kloeden, P.E., and E. Platen, Numerical Solution of Sto chastic Differential Equations, SpringerVerlag, Berlin (1992) 6. Knuth, D., The Art of Programming: Vol. II. Seminumerical Algorithms, 2nd ed., AddisonWesley, Reading, MA, Ch. 3 (1981) 7. Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes, 2nd ed., Cambridge Univer sity Press, Cambridge, England (1992) 8. Hayes, B., "The Wheel of Fortune," Amer. Sci., 81, 114 (1992) 9. Langevin, P., Academie des Sciences, 146, 530 (1908) 10. Klimontovich, Yu L., Physica A, 163, 515 (1990) 11. Erdi, P., and J. T6th, Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models, Princeton University Press, Princeton, NJ (1989) 12. Stokes, C.L., and D.A. Lauffenburger, "Analysis of the Roles of Microvessel Endothelial Cell Random Motility and Che motaxis in Angiogenesis," J. Theor. Biol., 152, 377 (1991) 13. Ottinger, H.C., Stochastic Processes in Polymeric Fluids, Springer Verlag, Berlin: in press 14. Laso, M., A Stochastic Dynamic Approach to Transport Phe nomena, preprint 15. Volume 47 of Physica D (1991) is devoted to articles on lattice gas dynamics O ROLE OF ACADEMIA Continued from page 169. on this historical record, the Scholarship Reconsid ered report argues, however, that there are at least three other types of scholarship: Scholarship of Teach ing, Scholarship of Integration, and Scholarship of Applicationand that our current thinking might be too narrow to value all of them. Scholarship of Teaching entails not only transmit ting knowledge, but also transforming it and extend ing it as well; Scholarship of Integration is to "give meaning to isolated facts, putting them in perspective...making connections across disciplines, placing issues in a larger context, illuminating data in a revealing way, often educating nonspecialists too." This clearly points toward interdisciplinary work and drawing unexpected connections between dis similar areas (without which some disciplines might wane and die). An acceptance of Scholarship of Ap plication demands that we broaden our horizons as well. The usual mode is that pure is better than applied, and that things are discovered and then applied. This need not be so: new intellectual under standings can arise out of the very act of application. The best use of the human potential already in place calls for recognition of diversity. Faculty diver sity should be celebrated, not restricted, and faculty evaluation should be flexible as well as systematic it will be increasingly more difficult to impose uniform standards on something that by its very mission should be diverse. A professor's job descrip tion is often unchanged over an entire lifetime; in stitutions should explore alternatives on how to sustain productivity. Creativity contractsan arrangement where faculty define their profess ional goals for a threetofive year period, possibly shifting from one principal scholarly focus to an othermight offer an alternative. It is imperative that universities become more structurally robust. Only in this way are they going to be able to deal with the pressures imposed by an everbroadening mission. The dual mission of dis seminating and transforming old knowledge while at the same time pushing the boundaries of what is known can only be fulfilled by a combination of tal ents and an acceptance of peaceful and profitable coexistence of various modes of scholarship. Yet, at the same time, universities cannot be all things to all people. A broader viewpoint including different models of success seems to be called for if the institu tions that have served so well in the past are to withstand the pressures of the future. REFERENCES 1. Sykes, Charles J., ProfScam: Professors and the Demise of Higher Education, Regnery Gateway, Washington, DC (1988) 2. Boyer, Ernest, Scholarship Reconsidered: Priorities of the Pro fessoriate, Princeton: The Carnegie Foundation (1990, reprinted 1993) 3. Eliel, Ernest L., Science and Serendipity: The Importance of Basic Research, American Chemical Society (1993) 4. Armstrong, John A., "Research and Competitiveness: The Prob lems of a New Rationale, MRS Bulletin, 18 49 (1993) 0 Fall 1993 PICLES A Simulator for Teaching the Real World of Process Control DOUGLAS J. COOPER University of Connecticut Storrs, CT 062693222 Process control classes often become more like abstract mathematics courses as the semester proceeds. Many instructors rightly believe that there is a need for students to experience the appli cation of classroom theory to real processes so they may appreciate not only the nuances but also the main points of the lectures. Having spent three years in the real world of pro cess control with Chevron Research Company, I be came frustrated when I began teaching at the uni versity level and discovered that (outside of the lab) few tools were available to me to teach many of the lessons I considered important. Too many important concepts are lost when the bulk of assignments begin, "Start with this transfer function and .." For example, students must learn the serious implications that arise because transfer functions disregard that real processes are nonlinear and have measurement noise and other nonideal behaviors. They must learn to quickly and reliably perform identification studies (realworld production people can be downright ornery if one asks to experi ment with their process). If they succeed in obtain ing data from the process, students must learn to use it to reasonably approximate the local process behavior with a linear modeland that only then do they have the transfer function for use with their classroom design theory. When their analysis is complete, students must Copyright ChE Division ofASEE 1993 learn that their controller design, no matter how sophisticated the approach, is only an initial ap proximationthat it must be finetuned on the real process. In the real world, this finetuning proceeds by trialanderror and must consider both set point tracking and disturbance rejection. The best instruction concerning the real world (short of the school of hard knocks) is obtained through carefully constructed laboratory experiences. Although we have several nice process control ex periments in our laboratory at the University of Connecticut, the reality is that each study can take several hours to perform. As such, it is not reason able to have the students explore more than the most major issues in the lab. To teach these important lessons, the Process Iden tification and Control Laboratory Experiment Simu lator (PICLES) was developed. The contribution PICLES brings to an existing course is that it en ables the students to quickly explore many of the lessons by following the same procedures they would have to follow if working with a real process. WHAT IS PICLES? Let me begin by pointing out that PICLES is not a control system analysis or design package. Quite the opposite, this software provides realistic processes that students can use to practice the analysis and design methods they are taught. Students say that PICLES is easy, and even fun, to use. Most com mands can be executed with simple keystrokes. Col orful graphics help the students follow the action on the screen as the results of their decisions unfold. The processes in PICLES encompass a variety of behaviors. The processes have varying degrees of nonlinearity so students can explore how process behavior can change with the operating regime. This also lets them practice compromising controller tunings to maintain stability over a wide range of nonlinear operation. The processes range from low to high order and Chemical Engineering Education Douglas J. Cooper is Associate Professor of Chemical Engineering and has been teaching process control at the graduate and undergradu ate level for the past eight years. He received his BS from the University of Massachusetts in 1977, his MS from the University of Michigan in 1978, and his PhD from the University of Colo rado in 1985 after three years of industrial expe rience with Chevron Research Company Having spent three years in the real world of process control with Chevron Research Company, I became frustrated when I began teaching at the university level and discovered that (outside of the lab)few tools were available to me to teach many of the lessons I considered important. have different process gains, time constants, and apparent dead times, so students can investigate how these phenomena affect process behavior and controller stability. The processes have noise in the sampled data so students can see that, in prac tice, the difference between a 10% overshoot and a 15% overshoot can sometimes be indistinguishable. In the current release (version 2.1), available con trollers are all PID, and with PICLES it is easy to explore all combinations from Ponly to full PID control. Because each process has colorful, dynamic graphics, after performing a controller design stu dents can implement their solution and obtain im mediate visual feedback on system performance. There is a PID Velocity algorithm and a PID Posi tion algorithm, so students can observe the conse quences of reset windup. They can select "Derivative on Measurement" or "Derivative on Error" so they can see what "derivative kick" is all about. Some controllers require the student to enter the bias or null value, while others have a bumpless feature where the bias is automatically set in a fashion similar to what they would encounter with some commercial controllers. There are also modelbased controllers in PICLES. 74150 MINSECI P I C L E S PROCESS GRAVITY DRAINED TANKS CONTROLLER: MANUAL MODE DATA STORAGE: OFF CONTROLLER OUTPUT CCM^3/SEC) 40. 30. 20. to. ____ . o. MEASURED LEVEL (CM) 100. * 75. ... 50. 25. 0. 20 15 10 5 C DATA HISTORY (CINS) Figure 1. Gravity Drained Tanks shows nonlinear beh Fall 1993 A Smith predictor enables students to observe how dead time affects controller performance and that dead time compensation offers real benefits. A Feed Forward element permits them to see how distur bance rejection works using both static and dynamic compensators. Decouplers enable them to explore methods for minimizing loop interaction on the dis tillation column. COMPUTER SYSTEM REQUIREMENTS PICLES is designed to run on IBMcompatible per sonal computers. The computer must have at least EGA graphics, although VGA graphics provides bet ter resolution. For rapid execution, a computer with a '386 or '486 processor should be used. A math coprocessor is not required, but it adds additional speed to program execution. THE PICLES PROCESSES Gravity Drained Tanks This process, shown in Figure 1, is two noninteracting gravitydrained tanks in series (see assignment lb later in this ar ticle for more about the figure). The manipulated variable is the flow rate of liquid entering the first tank. The measured/controlled variable is the liquid level in the second tank. This process displays a nonlinear behavior because the drain rate from each tank is proportional to nODE the square root of the hydrostatic head VALUE (liquid level in the tank). The distur AGE ON/OFF .UE bance, or process load, is a flow out of AL ONLY) the second tank due to a positive dis OR GRAPHIC placement pump. Hence the distur bance is independent of level except that it loses suction at extremely low liquid levels in the second tank. Heat Exchanger This process, shown in Figure 2, is a countercur rent lube oil cooler (see assignment S3e later in this article for more about Z; this figure). The manipulated vari able is the flow rate of cooling water OUIATE on the shell side. The measured/con S.5 trolled variable is lube oil tempera ture exiting the exchanger on the tube side. An interesting characteristic of avior. this nonlinear process is that distur C CHANGE CONTROLLER M D CHANGE DISTURBANCE F TURN DATA FILE STOI S CHANGE SETPOINT VAL I CHANGE INPUT MANUALA T TOGGLE BETWEEN MENU INLET ... FLOWRATE OPEN LOOP LEVEL I 73.9 I DISTURBANCE FLOWRATE 1 2.5 I L 1 bances, generated by changing the flow rate of warm oil that mixes with the hot oil entering the exchanger, display an inverse or nonminimum phase behavior. The process also has a negative steady state gain. Design a Process Design a Process has a display, shown in Figure 3, that is similar to that found on commercial controllers (see assignment 6a for more about this figure). It permits students to input a transfer function and obtain a visual appre ciation when studying problems found in textbooks. Distillation Column The Distillation Col umn, shown in Figure 4, is a binary distillation column that separates water and methanol (see assignment 8a for more about this figure). The col umn dynamics are simulated using a model pub lished by Wood and Berry.'11 There are two con trolled variables and two manipulated variables. The reflux rate controls the distillate composition and the rate of steam to the reboiler controls the bottoms composition. The feed rate to the column is the dis The student can specify a steady state process gain, an apparent dead time, up to three process time constants, and a valve time constant. It is also possible to specify a "linearity factor" if a nonlinear process is to be designed. Mystery Processes These pro cesses are not really mysterious. Rather, they are simply Design a Pro cess with a fanciful name and with all parameters prespecified and hidden from the student. Thus each Mystery Process displays a behavior that ranges from first to fourth order and has different overall process gains, time constants, apparent dead times, and degrees of nonlinearity. Because there is no a priori indication of ex pected process behavior, the student must rely strictly on process identifi cation studies for controller design. This simulates the disassociation that is often felt when tuning controllers from a remote control room and makes the simulations perfect for project work later in the semester. All of the mys tery processes use the same graphic as shown in Figure 3. Pumped Tank This process is a surge tank. The manipulated variable is brine flow rate out of the bottom of the tank and is adjusted with a throt tling valve at the discharge of a con stant pressure pump. This approxi mates the behavior of a centrifugal pump operating at relatively low throughput. The measured/controlled variable is the liquid brine level. This surge tank presents an interesting con trol challenge because of the integrat ing nature of the process. The distur bance variable, or process load, is the flow rate into the tank. 22iii OMINISECI P I C L E S PROCESS HEAT EXCHANGER CONTROLLER: PONLY CONTROL DATA STORAGEl OFF 0 CONTROLLER OUTPUT CGPM) 30. 1 20. 4 ... 40 30 20 10 DATA HISTORY (MINS) C CHANGE CONTROLLER MODE SD CHANGE DISTURBANCE VALUE F TURN DATA FILE STORAGE ON/OFF S CHANGE SETPOINT VALUE I CHANGE INPUT (MANUAL ONLY) I T TOGGLE BETWEEN MENU OR GRAPHIC Figure 2. Heat Exchanger under POnly control with different controller gains. 164130 NINISEC P I C L E S PROCESS MY PROCESS CONTROLLER: PID VELOCITY (D ON MEAS.) DATA STORAGE OFF CONTROLLER OUTPUT (%) MEASURED VARIABLE C%) 40 30 20 DATA HISTORY (MINS) I C CHANGE CONTROLLER MODE D CHANGE DISTURBANCE VALUE F TURN DATA FILE STORAGE ON/OFF S CHANGE SETPOINT VALUE I CHANGE INPUT (MANUAL ONLY) T TOGGLE BETWEEN MENU OR GRAPHIC I 52.0 ) 50.01 52.0 50.0 PROCESS DISTURBANCE INPUT 100 10  80 80  60 60  40 40 20 20 0 0 52. 49.7 0.0 10 0 CONTROLLER MEASURED SETPOINT OUTPUT VARIABLE Figure 3. Design a Process under PI control with differing amounts of dead time. Chemical Engineering Education MEASURED TEMPERATURE C(F) I turbance variable. This process illustrates interac tion between two controllers. AVAILABLE CONTROLLER MODES The control algorithms in the current version of PICLES are all PID and include Manual Control POnly Control (Manual Bias) Velocity PID Control (Derivative on Measurement) Velocity PID Control (Derivative on Error) 136 MINUTES P I C PROCESS: DISTILLATION TOP CONTROLLER: PID VELOCITY UOT CONTROLLER: MANUAL MODE DATA STORAGE' OFF DISTILLATE COMP (%) 97.0 96.5 96.0 95.5 BOTTOMS COMP (X) 2.0 1.5 ... ..... 1.0 0.5 0.0 50 40 30 20 10 DATA HISTORY (MINS) L E S C CHANGE CONTROLLER M COLUMN D CHANGE DISTURBANCE (D ON MEANS ) F TURN DATA FILE STORE S CHANGE SETPOINT VAL I CHANGE INPUT (MANUA SELECTED CONTROLLER TOP FEED RATE 2 CONC 46.50 REFLUX RATE I i_ 1.956] I  SI STEAM RATE S1. 710 _^"s"0 ^^'^ ?c^ Figure 4. Distillation Column with Distillate under PI con Bottoms in Manual I 20440 MINISECI P I C L E S PROCESS HEAT EXCHANGER CONTROLLER: PID VELOCITY CD ON MEANS ) DATA STORAGE: OFF 40. 40. CONTROLLER OUTPUT (GPM) 30. 20. 10. 0. MEASURED TEMPERATURE CF) 160. 150. 130. 40 30 20 10 C DATA HISTORY (MINS) C CHANGE CONTROLLER D CHANGE DISTURBANCE F TURN DATA FILE STO S CHANGE SETPOINT VA I CHANGE INPUT (MANUl T TOGGLE BETWEEN MEN A ACTIVATE DESIGN ME SIMULATION DE DISTURBANCE 10 MEASUREMENT NOISE 2 CONTROLLER DE CONTROLLER PID VELOCI PROCESS INPUT 9 SETPOINT 160 CONTROL BIAS CONTROL GAIN 0. RESET TIME 50 DERIV TIME 20. HIGH ALARM POINT 190 LOW ALARM POINT 130 SMITH PREDICTOR MODEL GAIN PROCESS TAU DEAD TIME Figure 5. Design Menu of Heat Exchanger under PID col measurement noise. Fall 1993 Position PID Control (Bumpless) Velocity PID with Smith Predictor Velocity PID with Feed Forward Velocity PID with Decoupler (Distillation Column Only) Version 3, which will be available in 1994, will include IOnly control and a discrete controller algorithm. Figure 5 shows the Design Menu used to specify controller parameters. The process being simulated in this figure is the Heat Exchanger process (see assignment 5a for more lODE about this figure). Note that the VALUE simulation noise level can be changed AGE ON/OFF if it is appropriate for an assign L ONLY) ment. Also, in the spirit of the "real world," high and low alarms can be DISTILL set to provide additional challenge in RATE 1.1 . :ONC 95.99 using the program. 7 Although the limitation to PID al ........ 4CC) TPINT gorithms is viewed as a serious limi 2. station by some, I try to exploit this fact within the classroom lectures. For ]example, I establish that the PID con troller is a special case of the Internal Model Control design method. Also, I BOTTOMS show how the Smith Predictor is a RATE1 1.269 CONClimiting case of some predictive con S troller design methods. Thus, PICLES can be used to explore certain aspects itrol and of these newer design standards. USING PICLES IN THE COURSE I start with the Gravity Drained MODE Tanks process. The model can be eas RAGE ON/OF ily derived in class, it behaves intu LUE itively, and the nonlinear behavior is AL ONLY) U OR GRAPHIC modest. The simulation graphics also NU BELOW provide realism to help give the stu SIGN dents an understanding of the dy .0 GPM .5 oF namic behavior of the process. SIGN Since I believe that some practice TY CD=MEAS.) .9 GPM in programming is important, I also GPM have the students code up their own 23 GP/F Gravity Drained Tanks process based 00 SEC on the equations derived in class. I .0 OF .0 OF then have them determine the pro MODEL cess parameters which cause their OF/GPM SEC simulation to approximate the dynam SEC ics of the PICLES simulation. After several assignments in pro itrol with cess dynamics and process identifica tion, I move on to the Heat Exchanger. 179 I It is a slightly more complicated process, but it still behaves intuitively. It has a higher degree of nonlinearity and also has a negative steady state gain, which reinforces my lecture that gains not only have magnitude and units, but also a sign. The nonminimum phase or inverse dynamics of the dis turbance response provides another new twist. After they have explored several investigations of process dynamics, some identification methods, and explored a few controllers and design techniques using Gravity Drained Tanks and Heat Exchanger, I use the Mystery Processes for project work. I assign a different Mystery Process to each group of stu dents and let them tie things together by doing an identification, preliminary controller design, and finally determining a single "best" tuning for both set point tracking and disturbance rejection, all as one assignment. Because the processes are non linear, each student can have his or her own project by specifying different ranges of operation for each problem (i.e., Amy must design for an output range of 2030%, etc.). I use Design a Process intermittently to isolate specific process behaviors. For example, I ask the students to implement a true firstorder process un der POnly control and let them demonstrate that such a process is unconditionally stable for all val ues of controller gain. They then show that a second order process under POnly control can approach the limit of stability, and finally, that higher order pro cesses under POnly control can go unstable. When combined with a class discussion on system stability using rootlocus, the students benefit from relating theory to practice while the subject is being taught. As another example of using Design a Process later in the course, I assign a set of time constants and a process gain and ask the students to design and validate a controller. Then, keeping those pro cess variables and tuning parameters fixed, they add dead time to the process and discuss their observations on the effect dead time has on closed loop performance. Finally, they design and imple ment a Smith predictor to relate our inclass derivations and discussions with actual application to assist them in understanding the benefits of deadtime compensation. When the students start feeling confident, I give them the Pumped Tank process. The integrating nature of the process really surprises them and re quires me to do a lot of explaining ("Why is there no offset with a POnly controller?" "How come with a PI controller, this process goes unstable when the controller gain is too high and too low?"). Finally, the Distillation Column lets the students see what can happen when more than one controller is operating on the same process. The interactions show them that optimizing controllers individually does not necessarily produce an optimum solution when the controllers begin to interact. Also, the stu dents can investigate how modelbased decouplers can work to minimize this interaction. EXAMPLE HOMEWORK ASSIGNMENTS To illustrate how PICLES can be integrated into an existing course in process control, this section lists sample homework assignments. These assign ments follow the order of development used in most textbooks and let students visually appreciate these important concepts. The five figures previ ously discussed also serve as partial answers to selected problems. Assignment on Process Dynamics 1. Using Gravity Drained Tanks in Manual mode: a. Plot and discuss how the measured level responds to step changes in the manipulated inlet flow rate and the distur bance flow rate. Comment on the natural stability of the process. b. Starting from three different steady state operating regimes, plot how the measured level responds to manipulated inlet flow rate perturbations of fixed size. Based on these plots, discuss the nonlinear nature of the process. (Answer: Figure 1 shows the nonlinear nature of the process because the measured level responds differently for three step changes of equal size in the manipulated inlet flow rate.) Assignment on Process Identification 2. Using Design a Process: a. Generate an open loop input/output step response curve for a true first, second, and thirdorder process. How does the time to 63.2% of change compare to the time constants assigned? Discuss your conclusions. Assignment on POnly Control 3. Using the Heat Exchanger in POnly mode: a. For a design operating temperature, determine the value and units of the controller bias. b. Obtain a FOPDT (first order plus dead time) model describ ing process dynamics around this design temperature and use it to compute a POnly controller gain using ITAE, direct synthesis, IMC, etc. c. Starting with this controller gain and bias value, use trial anderror to find the "best" gain, where for this assignment "best" is defined as a 10% overshoot for set point steps of a specified size. Now show the ability of this "best" controller to reject step disturbances. d. Starting from the design operating temperature and using your "best" tuning, make set point step changes of various sizes in both directions. Discuss your observations on offset. Chemical Engineering Education e. Pick a specific set point change and plot the response of the process when using your "best" controller gain, half of that gain, and twice that gain. Discuss your observations on the relationship between controller gain and offset. (Answer: Figure 2 shows set points steps with two different controller gains, and that offset and the oscillatory nature of the re sponse changes as controller gain changes.) Assignment of PI Control 4. Using Gravity Drained Tanks or Heat Exchanger in PI velocity mode: a. Explain why no bias is necessary for this controller. b. Obtain FOPDT model describing process dynamics around a design point of operation and use it to compute a PI controller gain and reset time using ITAE, direct synthesis, IMC, etc. c. With these parameters as a starting point, use trialanderror to find the gain and reset which provide a "best" perfor mance. Here, "best" performance is defined as a 10% over shoot and a 25% decay ratio to a set point step of specified size. Why can we design for two performance criteria with a PI controller, but only for one with a POnly controller? d. Plot a matrix of process responses for the same set point step where this matrix includes all combinations of your "best" tuning, a gain that is double and half of your "best," and a reset time that is double and half your "best." Use your observations to explain the roles of gain and reset time on controller performance. Assignment ofPID Control 5. Using the Heat Exchanger in PID velocity mode: a. Design and implement a PID controller and compare its performance to PI control. For this comparison, test a num ber of set point and disturbance scenarios and show where the derivative action really pays off. Plot the distinctive scenarios and use them to explain why or why not any performance benefit occurred. (Answer: Figure 5 shows that derivative action can produce very poor performance when employed on a noisy measured variable.) Assignment on Dead Time and the Smith Predictor 6. Using Design a Process in PID with Smith Predictor mode: a. For the assigned process gain and set of time constants, design and validate a PI or PID velocity mode controller that gives a 10% overshoot and a 25% decay ratio for a given set point step. Keeping the process variables and tuning param eters constant, add dead time to the process and discuss your observations on the effect dead time has on closedloop performance for this same set point step. (Answer: Figure 3 shows two sets of set point steps. PI controller tuning is fixed throughout. Controller performance is markedly different for the first set point steps where the process possesses no dead time compared to the second set of steps where the process possesses thirty seconds of dead time.) b. Keeping the same process gain, set of time constants, and including the dead time, tune your controller to again pro duce a 10% overshoot and a 25% decay ratio. Compare this plot and tunings to the case where no dead time was present. Discuss your observations. c. Now design and implement a Smith Predictor and again tune the controller to produce a 10% overshoot and a 25% decay ratio. Compare this plot and tunings with the previous two cases and discuss the pros and cons of deadtime compensa tion. Assignment on Disturbance Rejection and Feed Forward 7. Using Gravity Drained Tanks or Heat Exchanger in PID with Feed Forward mode: a. For the design point of operation, develop a FOPDT model of the disturbancetooutput dynamic relationship. Using this model, compare a static and a dynamic feedforward com pensator for step changes in the disturbance variable. b. For the Gravity Drained Tanks, the disturbance immediately impacts the measured variable while there is a lag before input variable manipulations can compensate. Explain how this influences your comparison of the static and dynamic compensators. c. For the Heat Exchanger, there is a reasonable lag before a disturbance impacts the measured variable. Discuss how this influences your comparison of the static and dynamic com pensators. Assignment ofMultivariable Control and Decoupling 8. Consider controller design for the Distillation Column when given specified design operating concentrations for the distillate and bottoms. a. While the bottom controller remains in Manual mode, de sign and implement a PI controller for the top controller. Plot the performance of the controller for distillate concen tration set point steps both up and down. (Answer: Figure 4 shows one possible solution to this question.) b. While the top controller remains in Manual mode, design and implement a PI controller for the bottoms controller. Plot the performance of the controller for bottom concentra tion set point steps both up and down. c. Using the controller tuning parameters from a and b above, implement PI controllers on both loops. Make set point changes for both controllers and discuss loop interaction. d. Now design and implement both static and dynamic control lers. Perform the same set point changes as in part c and discuss the impact of modelbased decoupling. FINAL NOTE For more information about PICLES and available teaching materials, write to the author at the Chemi cal Engineering Department, University of Connecti cut U222, Storrs, CT 062693222. ACKNOWLEDGMENTS I would like to thank the students without whom PICLES would not exist. These include Architects: Allen Houtz, Robert Schlegel, and Adam Lalonde, and Builders: Scott Ferrigno, Ralph Hinde, Jr., Larry Megan, C. Steven Micalizzi, Phil Pearson, and Yan Wan. REFERENCES 1. Wood, R.K, and M.W. Berry, "Terminal Composition Con trol of a Binary Distillation Column," Chem. Eng. Sci., 28, 1707(1973) O Fall 1993 THE QUEST FOR EXCELLENCE IN TEACHING RAFFI M. TURIAN University of Illinois at Chicago Chicago, IL 60680 believe that teaching is the most transcendent of all the responsibilities of a university profes sor, and that the search for excellence in teach ing must stand as a continuing quest for each of us. There is a view, held by some, that teaching and research are antagonistic endeavors; that one can only be done well at the expense of the other. I do not share this view. I believe that, carried out in proper balance, teaching and research should be mutually reinforcing. Nonetheless, although it is expected that being a contributor to creating knowledge is a defining at tribute of teaching at the university level, there are good teachers who do not do research. They are not usually recognized. Yet, the obligation to teaching is so primary and broad that, in instances when re search or other obligations are in conflict with it, it must take precedence. I believe the prerequisites for excellence in teach ing to be: mastery of subject; broad knowledge of the field; meticulous preparation; faith in the potential of, and the promise in, each student; the ability to invest one's subject with purpose; the sensitivity to temper rigor with forbearance and firmness with compassion; the courage to hold to one's convictions; and the humility to admit error. It is difficult to measure excellence in teaching with precision. In deed, it is difficult to define good teaching, although one will recognize it when one sees it. Good teachers are shaped by personal experience; the perception of what constitutes excellence in teaching is uniquely personal. This constitutes my personal statement on excellence in teaching. It is a tribute to those who have taught me. My high school was an English boarding school in Cyprus. We took English, French, classical Greek, Latin, biology, differential equations, physics, chemistry, the history of the British Empire, and cold showers at 5:00 every morning. It was rigorous Copyright ChE Division ofASEE 1993 Raffl M. Turlan is Professor of Chemical En gineering at the University of Illinois at Chi cago. He received his BS from the University of Maryland, and his MS and PhD from the University of Wisconsin. He has held faculty positions at Syracuse and Texas Tech Univer sities and has also worked with Shell and the National Science Foundation. His teaching and research are in transport and fluidparticle pro S cesses. and it was hard. But it was bearable, except for the English food. I remember high school as a time when I discov ered that I loved poetry, literature, history, music, the sunrise, and mathematics. High school was a profoundly enriching experience; learning was a con tinual process of discovery. It was also a time of self discovery. I had great teachers. They all had degrees in their subject areas and a deep interest in the subjects they taught. They did not seem to be both ered by whether or not we were having fun. They were very serious about their tasks. We did not study American history in high school. Later, as a freshman at Maryland, my teachers were intrigued by my curiosity and interest in American history. Little did they suspect that when one has been taught to get excited about Disraeli, Palmerston, Metternich, and the politics of the balance of power in Europe, it is not difficult to get excited about Jefferson, Madison, and the politics of the power of human rights in the New World. American history, modern poetry, and Homer stand out as the most memorable subjects from those Mary land days. It was not that chemical engineering couldn't also be excitingbut that was to come later. As a graduate student at Wisconsin I sat in the classes and in the midst of inspiring teachers: Olaf Hougen, R. Byron Bird, W. R. Marshall, Edwin Lightfoot, and Warren Stewart. Chemical engineers recognize them as men of towering scholarly reputa tions. I, however, stand as witness to the fact that of all their impressive achievements, the most memo rable measure of their standing was the special car Chemical Engineering Education ing with which they held the humblest of students. I was in the presence of great teachers, and I felt it. I knew that I would be fortunate if I succeeded in emulating any of them as my personal example. Through the years I have continued to learn and draw inspiration from many others: colleagues such as Chi Tien at Syracuse and Sohail Murad here, and students like Raj Rajagopalan of Houston, Alkis Payatakes of Patras, and Hemant Pendse of Maine. Perhaps I have taken something from each of my different teachers, and if so, I hope I have passed on the legacy to my own students. Great teachers are our link to greatness from the past, as our students are our link to the future. That is why the quest for excellence in teaching is a solemn obligation. Great teachers are also good students. Good teaching is done inside as well as outside the classroom. One must have mastery of subject to enrich content, and broad knowledge of the field to place it in context and to invest it with purpose. But command of subject cannot replace preparation. Good organization, careful writing, and a pace of presentation appropriate to material and audience suggest respect for subject, seriousness of purpose, and sensitivity to student needs. The classroom presentation is not a performance, with the teacher as actor and the students as audience; they are the entire show. Chemical engineering is a human activity. I try to infuse my classroom presentations with examples of brilliant achievements of real chemical engineers, teachers, and practitioners. I tell them that a great nation needs good chemical engineers just as it needs good poets. Otherwise, neither could its chemical engineers do a good job refining its oil, nor its poets reach for refinement in expressing its values or fram ing its ideals. Perhaps, ideally, a great nation needs good chemical engineers who are poets. Good teachers are humorous when appropriate, and try to make their lectures exciting, without mak ing entertainment or the kindling of deep emotions their highest aims. Above all, good teachers stand before students and teach them something that they know well and believe in deeply. There was a time when I told my students that the purpose of education was not to teach them how to make money, but how to spend it well after they made it. That time is gone. Today we must teach them how to make money as well as how to spend it wisely. But I do not lament the passing of those gentler times. The challenge before us now is how to turn our students into concerned, thinking individu I try to infuse my classroom presentations with examples of brilliant achievements of real chemical engineers, teachers, and practitioners. I tell them that a great nation needs good chemical engineers just as it needs good poets. als with durably marketable skills, without making the catering to a current job market our highest aim. Great teachers do not yield to current fads; that is what university administrators do. Being a good teacher means spending a lot of time with the weakest students, without losing touch with the best. It means being able to recognize and cel ebrate what is best in each student, without being blind to what is deficient. It means taking the time to discuss an exam with them, without conceding that the grade they have received is only a first offer. It means writing recommendation letters, even on short notice. It means helping some get scholar ships, others to find jobs or to get into graduate school, and still others to get help or to seek counsel ing. It means meeting with parents, describing to them what we do, and if they have trust in us, as most of them still do, to demonstrate that their trust is wellplaced; and if they have misgivings, as in creasing numbers do, to reassure them that we are aware of their concerns and that we care. Above all, good teaching requires that we call stu dents to duty and that we insist they assume pri mary responsibility for their own learning. The hall mark of education is honesty, and honesty requires that students be told that learning is hard; often painful. That not all of us are great teachers, or even care to be. That it is possible to have fun here, but if that is all they want, there are better places for themperhaps a tropical resort. That if they set their threshold for excitement high they will miss all that is full of wonder around them. That if they learn to have reverence for small wonders, they will discover exaltation in bigger ones. And that there is no entitlement to a degree in chemical engi neering; only a fair chance at earning itthrough hard work and honesty. I believe that excellence in teaching is not a state of being, but rather a continual search. It is said that with prose one transmits thought, with poetry one reaches for revelation. I hope that some day before I take up poetry full time, I will have touched it in my teaching. But then, great teaching is not in the attainment; it is in the quest. 0 Fall 1993 THE FREE ENERGY OF WETTING WILLIAM G. PITT Brigham Young University Provo, UT 84602 he wetting and spreading of liquids on solids is frequently encountered in the chemical in dustry. Examples include the application of herbicides, adhesives, inks, paints and other coat ings, flotation of minerals, containing and cleaning chemical spills, waterproofing, cloud seeding, lubri cation, corrosion protection, enhanced oil recovery, and more. Despite its importance, however, wetting and spreading in the chemical process industries is often without a home in most undergraduate chemi cal engineering curricula. The subject could be taught in classes on engineer ing materials, plant design, or separations. An infor mal survey of nine undergraduate texts19'] on engi neering materials found that six of them mentioned the concept of surface energy, but only in the context of nucleation[15 and fracture propagation.[5'61 Only one of these texts introduced the concept of contact angle and presented Young's equation in a discus sion of heterogeneous nucleation,m and none dis cussed wetting or spreading of liquids on other liq uids or solids. Unfortunately, the only text on engi neering materials that discussed contact angle, spreading, and wetting is no longer in print."10 This paper will present some simple but powerful thermodynamic concepts that can be taught in a 1 hour lecture on wetting and spreading. We approach the subject through the theme of the minimization of free energya concept with which chemical engi neering students are well acquainted. TO SPREAD OR NOT TO SPREAD The two practical questions about spreading and wetting which an engineer usually addresses are: * Does the liquid spread completely or only partially on the solid surface? If partial spreading occurs, what is the contact angle of the drop on the surface? To address these questions we begin with the defi William G. Pitt is an associate professor in the Chemical Engineering Department at Brigham Young University. He is active in AIChE as the student chapter advisor at Brigham Young Uni versity and as chair of the National Student Pa per Competition. He obtained his BS from Brigham Young University and his PhD from the Univer sity of Wisconsin, Madison. His research activi ties deal with adhesion phenomena on biomedi cal polymers and in polymer composites. nition of the surface energy, y, which is defined as the change in free energy as new surface area is created. If new surface is created under reversible conditions at constant pressure, temperature, and number of molecules, this surface energy is the change in Gibbs free energytl" 7= (S)} (1) where G is Gibbs free energy and A is the surface area. If the surface is created at constant volume, temperature, and number of molecules, this surface energy is the change in Helmholtz free energy (2) Because pressure is generally a more constant pa rameter than volume, Eq. (1) is sometimes (but not always) preferred. In this paper, the term free energy can refer to either of these definitions, depending on whether the wetting and spreading occurs under constant pressure or volume. Thus, the free energy associated with the surfaces of a system is simply the surface area of each phase boundary multiplied by y for that boundary. Subscripts of y refer to the surface free energy of the interface between the liq uid, solid, and yapor phases. Next let us perform a thought experiment sug gested by Figure 1 in which we force a small drop to spread over a large surface. Before a drop of liquid contacts the surface, the surface free energy of the system is the solidvapor surface free energy, Ys,, multiplied by the solid area (assuming the original C Copyright ChE Division of ASEE 1993 Chemical Engineering Education area of the drop is much smaller than the solid area). When the liquid is spread completely on the solid, the system now consists of two interfaces (the solidliquid and the liquidvapor interfaces), and the surface energy of the system is y,i + 7y, multiplied by the solid area. One may now ask the question, "Does the system attain the lowest free energy when the drop is spread completely on the solid?" If so, com plete spreading will occur. We can see that if the yv is larger than the sum of y, + y,,, the reduction in free energy will drive the drop to spread completely over the surface. Thus, spreading occurs if 7sv > Ylv + Ysl or 0 < Ysv (Yiv + Ysl) (3) Complete spreading will also occur if Ysv = Yiv + Ysl because the drop will flatten out until it has a con tact angle of zero (as will be shown in the next section). In the early 1920s, Harkins and Feldman[12' stud ied the spreading of organic liquids on a number of solid and liquid substrates. They defined a "spread ing coefficient," S, as the difference between the work of adhesion, Wa, and the work of cohesion We. The work of adhesion is the work per interfacial area needed to separate two adjacent (solid and liquid) phases: Wa = Ylv + Ysv Ysl The work of cohesion is the work per area needed to separate a single liquid phase: Wc = 2 yv Therefore, the spreading coefficient becomes S = Wa Wc (4) S= Ysv (Yiv +Ysi) (5) Harkins and Feldman observed that liquids spread completely when S > 0, which is consistent with Eqs. (3) and (5). One final note on spreading concerns the rate or kinetics of spreading. The velocity of the moving threephase contact line at the edge of the drop can be as high as 30 cm/s and is dependent upon the Before After (Liq uiL ys Yd) YI I ,. v \ Liq,,d /L_.qu Figure 1. Process of complete spreading of a liquid drop on a solid substrate. Fall 1993 This paper presents some simple but powerful thermodynamic concepts that can be taught in a 1hour lecture on wetting and spreading. We approach the subject through the theme of the minimization of free energy... viscosity and surface energy of the spreading liq uid."' Brochard and deGennes show that the change in the drop radius, R, with time (the velocity) is proportional to R9.'31 Thus the latter stages of spread ing can be a slow process. If the spreading occurs on a liquid instead of a solid, the velocity varies inversely with the substrate viscosity.[141 The viscosity of the surrounding fluid also plays a role, especially if the fluid is a liquid (instead of a gas). The spreading velocity increases as the viscosity of the displaced liquid decreases. More importantly, a stable liquid film separating the drop from the substrate prevents the initial for mation of the threephase contact line, and in most practical cases, the stability of this liquid film con trols spreading. Thus, spreading entails multifari ous phenomena, and its complexity should not be underestimated by the simplicity of the thermody namic statement of Eq. (3). PARTIAL SPREADING We will now examine the case in which the solid surface energy is less than y, + y%, or in which S is negative and the spreading is not complete. In this case the drop forms a sphere or spherical cap on the solid as long as the drop is small enough that gravi tational distortion of the shape is negligible. The contact angle is defined as the angle between the solidliquid interface and the liquidgas interface at the edge of the drop. In 1805, Thomas Young stated (without proof) that the equilibrium among the at tractive forces between particles of fluid and par ticles of solid will cause the fluid to form a certain angle with the solid.116 This angle was defined by Fs =Fs +FIcosO (6) where the F,, F,,, and F, refer to the forces of the solid, the common surface, and the liquid, respec tively. This was the genesis of Young's equation, a mechanical balance of rather illdefined forces. In introductory texts, Young's equation is often taught as a force balance at the edge of the drop. While this model of a force balance is convenient and easy to teach, many students find it unsettling. They see little logic in a force balance in the horizontal direc tion, but not in the vertical direction. They may also 185 have trouble conceiving surface energy as a force per linear distance because most chem istry courses introduce y as an energy per surface area. Of course, both of these apparent incon sistencies can be adequately addressed.17'181 There is a force balance in the vertical di rection: just as students learn in their intro ductory physics course, when you push against an immovable wall, the wall exerts an equal force in the opposite direction, so the solid substrate exerts an equal force in the downward direction at the threephase boundary. Interesting experimental evidence of this vertical force is shown by drops of liquids on elastic hydrogelsthe drops ac tually pull the hydrogel upward at the pe riphery of the drop.1 19 Unlike Young, Willard Gibbs related the contact angle to the more familiar concept of surface energy. He proposed that the threephase boundary line (between an in soluble solid and two fluids) would displace along the solid surface until it reached a point at which any further displacement of the line would create an increase in the free energy associated with the threephase boundary line.'20' This condition of equilib rium reduces to Yiv cos 0 = Ysv Ysi (7) which has the same form as Young's equa tion, but which employs surface energies instead of surface forces. While the student may feel more familiar with the language of surface energy, Gibb's derivation is usually not intuitively obvious. It also has the draw back (as does Young's derivation) that the derivation is done in twodimensional space. Most classical textbooks on colloidal and sur face chemistry derive Young's equation us ing free energy concepts and a differential change in contact area. 1151 A CONCEPTUALLY STRAIGHTFORWARD APPROACH A straightforward approach to teaching the concept of contact angle and incomplete wetting is to combine the familiar rule that "a system moves to its state of lowest free energy" with a simple model of a liquid drop contacting a solid surface. Referring to the discussion of the spreading coefficient, we see that if Ysv < Yiv + Ysi then the free energy of the system is not minimized at a state of complete spreading, and so the drop will not spread completely. The question now becomes, "How far must the drop spread to minimize the free energy of the system?" The answer is given by formulating the equation that describes the change in free energy: we simply subtract the energy "before" from the energy "after" the drop wets the surface. The surface energy before the drop contacts the surface is Total surface energy before = STYsv + 4 n rd Y1v (8) where ST is the total area of the solid surface and rd is the radius of the drop. After the drop has contacted the surface, it spreads to form a spherical cap with a contact angle 0 as shown in Figure 2. The total surface energy after the wetting of the drop is Total surface energy after = (ST AI)Ysv + AcYiv + AIys (9) where AI is the area of the interface between liquid and solid, and A, is the liquidvapor interfacial area of the spherical cap of liquid. AI and A, are given by AI = r(21 Cos2 ) Ac = 2r2(1 cos0) where r, is the radius of curvature of the spherical cap. The change in free energy of the system is found by subtracting Eq. (8) and Eq. (9) AG = 2 y (r2 (1cos )2 r2)+ n r (1cos2 )(sl Ysv) (12) The minimum in free energy is found by equating to zero the derivative of Eq. (12) with respect to cos 0, and then solving for cos 0 dAcQ0 O .[(1 ySV)+(1c2)(yS y 2)} dAG =0= 2[l (. ) dr 22rf(Ysi )Ysv). d(cos0) do :12c (13) where o is a shorthand notation for cos 0. The spherical cap has constant volume Figure 2. Process of partial spreading of a liquid drop to form a spherical cap with radius r, and contact angle 0 on the solid. Chemical Engineering Education v=r3 +3 so we can use implicit differentiation under condi tions of constant volume to derive that dr2 _2r2 (1)2 da 2 30 + 0 Combining Eqs. (13) and (14) and solving for a gives S=cos = (sv s (15) Ylv which is identical to Eq. (7). DISCUSSION This derivation contains several important points that the students should understand about wetting and contact angles. On the practical side, nearly all liquids partially or completely spread on solid sur faces. It is very rare to have a contact angle of 1800 (no wetting). Equation (15) indicates that an angle of 1800 would require ys, = yv + yv. This is rarely the case for aqueous solutions or organic liquids because the interfacial free energy usually has a value that is less than yv. In the case of liquid metals (such as mercury) on organic solids, y, and y., are both so high that y, becomes negligible and a contact angle of 180 is approached. This does not mean that "water proofing" a porous surface is impossible. If the con tact angle is greater than 90, capillary pressure will resist the penetration of a liquid into a porous solid. Another point on the practical side is that this derivation employed an ideal system that assumed the absence of gravity, surface roughness, surface contamination, surface chemical heterogeneity, sur face mobility, liquid viscosity, line tension, or other real effects that often cause contact angles to depart Ideal Tntermediate Figure 3. Real and hypothetical ideal paths of an arbi trarily shaped liquid forming a spherical cap on a solid. Fall 1993 from the contact angle predicted by Eq. (15).[211 These real complications and departures from the ideal case can often aid in understanding the nature of complex surfaces, but they are not the focus of this discussion. (More information on these topics can be found in references 17 and 21.) In some very clean and specialized experiments, all of these complica tions can be eliminated with the exception of gravity and line tension. If one cannot eliminate gravity and line tension effects in real measurements, one should at least understand what perturbations they may impose upon the theoretical contact angle. Gravity always distorts the drop shape from a spherical cap to an oblate spheroidal cap, but this distortion is negli gible for sufficiently small drops. For example, with water on polyethylene, gravity distortion becomes noticeable if the drop volume is greater than about 2pl. This distortion causes the surface area of the cap (A,) and the interface area (AI) to increase over that of the ideal case. Line tension is the onedimensional analog to sur face tension and can be defined as the excess free energy per distance at the threephase boundary line between the liquid, solid, and vapor at the pe rimeter of the cap. Assuming that the free energy contribution from line tension is positive, a drop will not spread as far (compared to the case without line tension) before it reaches the minimum in free en ergy, and thus it will have a larger contact angle than predicted by Eq. (15). Both gravity and line tension contribute to the free energy of the system, and the net result upon equilibrium contact angle is still a subject of controversy.[221 In the ideal case neglecting gravity and line ten sion, the contact angle is independent of the initial spherical drop size. The following argument also shows that contact angle is independent of initial drop shape; i.e., a volume of liquid or arbitrary ini tial shape will form a spherical cap having Young's contact angle. Given that the resultant drop shape and contact angle is only a function of the free en ergy state, we can break the pathway of going from initial to final energy state into two hypothetical paths, neither of which may have actually occurred, but which represent the change in free energy states of the system (see Figure 3). The first path mini mizes the free energy of the liquid shape by forming a sphere not yet in contact with the surface. The second step minimizes the free energy after the liq uid sphere contacts the surface and results in a Young's contact angle according to the derivation presented above. Since both steps are minimizations Continued on Page 193. MICROPROCESSORBASED CONTROLLERS at Drexel University D. R. COUGHANOWR Drexel University Philadelphia, PA 19104 In the United States, all chemical engineering curricula accredited by ABET (Accreditation Board for Engineering and Technology) must have a course in process dynamics and control. Very few students, however, have any exposure to mod ern industrial microprocessorbased control systems. During the past six years, the Department of Chemi cal Engineering at Drexel University has offered an elective course in advanced control which provides such exposure to these modern control systems. In the first phase of the development, we used Taylor MOD30 controllers, but more recently, we have used Foxboro I/A (integrated automation) systems. Many reasons are given for not providing students with handson experience on modern control sys tems: some faculty members who teach control be lieve that students need only a fundamental theo retical course and that a laboratory involving mod ern control equipment is unnecessary; other reasons include the high cost of the equipment and the com plexity of the software. Furthermore, the vendors of control hardware and software have shown very little interest in trying to introduce their equipment into the laboratories of engineering schools. The author of this paper, however, believes that exposing stu dents to modern industrial control equipment can be a valuable experience for them, that it motivates the application of control theory, and that the acquisi Donald R. Coughanowr has been at Drexel University since 1967. Before coming to Drexel, he taught at Purdue University for eleven years. He received his BS degree from RoseHulman, his MS from the University of Pennsylvania, and his PhD from the University of Illinois, all in chemical engineering. His areas of research include process dynamics and control, aerosol technology and environmental engineering, dif fusion with chemical reaction, and mathemati cal modeling. Copyright ChE Division of ASEE 1993 The emphasis in the course was on the use of the control hardware and software, while the use of mathematics was limited to stability calculations and tuning. tion and use of such control equipment is financially feasible. Our department offers a series of three courses in process control. They combine theory, applications, and laboratory experience, and make extensive use of digital computers to simulate and control chemi cal processes. The courses and the number of hours per week during a tenweek term are: 4.5 cr. Process Systems Engineering; 3 hr. lecture, 3 hr. laboratory 3 cr. Process Systems Engineering; 3 hr. lecture (graduate course) 3 cr. Applications of Computers to Control; 2 hr. lecture, 2 hr. labo ratory The first course, Process Systems Engineering, is required of all undergraduate students in chemical engineering and covers openloop systems, closed loop systems, stability, frequency response, and con troller tuning. In the laboratory, the students simu late control processes with simulation software (TUTSIM) and operate a modern industrial micro processorbased control system (Foxboro I/A system). It is also a prerequisite for the third course, Applica tions of Computers to Control. In the second course (a graduate course), advanced topics such as stability, root locus, sampleddata control, multiloop control (cascade, feedforward, internal model control, etc.), and nonlinear control are covered. The third course, Applications of Computers to Control, is an elective course which is primarily de voted to the study of a modern industrial micropro cessorbased control system, and covers configura tion, tuning, and operation of a Foxboro I/A system. Control applications include singleloop and multi loop control systems. Chemical Engineering Education A TYPICAL MICROPROCESSORBASED CONTROL SYSTEM This paper will describe the use of the Foxboro I/A system in the graduate course Applications of Com puters to Control. The equipment for the course was obtained with the help of an NSF grant from the program on Instrumentation and Laboratory Im provement. This grant, a 5050 matching grant, pro vided three Foxboro systems. The 50% funding to match the NSF share came from industry, Drexel University, and a grant in the form of a discount from the Foxboro Company (the NSF program per mits a discount from the equipment supplier to be part of the matching funds). Each of the three control systems costs about $22,000 and consists of the following components: HP Vectra ES/12 Computer with 70 Mb hard disk, color monitor, mouse, and keyboard OK Data 80column printer Local enclosure including power supply and two fieldbus modules (FBM) for communication with real processes: One FBM transmits 010 volt signals; the other 420 ma signals Allen Datagraph strip chart recorder The equipment described above can be used to control a process which is either a simulated process in the computer or which is a real process connected through hard wiring to the fieldbus modules. The Foxboro I/A system, which was first released in 1986, is a powerful distributed parameter control system which is able to control many loops of a complex industrial process. For the purpose of in struction in a university setting, the simplest ver sion of the system, referred to as Personal Worksta tion for Fieldbus Interface (PWFB), was purchased. The version used for a large plant would include several computers, a larger enclosure with more fieldbus modules, and more input/output devices (such as printers, monitors, operator input panels, etc.). The software provided in the simpler PWFB system, however, is exactly the same as that used in the most extensive systems. Figure 1 shows the con nections between the computer and the process for the PWFB system. Foxboro provides different types of FBMs for analog signals and for digital signals. Each FBM can handle several inputs and outputs. Up to sixteen FBMs can be connected to the com puter for the PWFB system. Each control system comes with a fivevolume set of user's manuals. As with most manuals provided with complex equipment, their availability does not guarantee that one can simply hook up the compo nents and begin using the equipment. Even though the software packages are loaded into the computer's hard disk at the factory and a field engineer from Fall 1993 Figure 1. PWFB connections to process the company sets up the equipment, it is recom mended that the purchaser attend one or two courses on using the equipment that are offered by the manu facturer. The Foxboro Company (among many other suppliers of control equipment), offers a wide variety of short courses that last from just a few days to several weeks. The author took two twoweek courses on the Foxboro I/A system. The Foxboro Company also sells a training kit for the PWFB system that consists of a manual, computer disks, and audio visual tapes. This kit is very useful for selfstudy of the Foxboro I/A system. The primary task of a microprocessorbased con troller is implementation of a control algorithm; but the presence of a computer makes it possible to also assign a number of peripheral tasks that are useful in process control. Some of these tasks provided in a modern control system are to Implement classical and advanced control algorithms Provide static and dynamic displays on the monitor Provide process and diagnostic alarms Provide mathematical functions Provide data acquisition and storage (archiving) More detail on the nature of these tasks can be found in Chapter 35 of Coughanowr.111 The soft ware to support all of these tasks is supplied by the manufacturer of the control equipment. In the Foxboro I/A system, these tasks are supported by the following seven software elements: Control subsystem Process display File utility Workstation environment System management Historian (optional) Spreadsheet (optional) Only the first five elements are essential for using the system. The spreadsheet and historian elements were omitted at some savings in cost (they are con sidered luxuries in a university teaching laboratory). In an undergraduate laboratory course, the students need to use only the control subsystem and process display software. The teacher or laboratory techni cian will use the system management, file utility, and workstation environment software to set up the computer control system for laboratory experiments. Specific examples of the use of these three software elements for course development will be given later. FEATURES OF THE FOXBORO I/A SYSTEM All of the software for the Foxboro PWFB system is stored on a 70Mb hard disk. The control strategy for a control loop is configured by connecting several blocks together to form a structure called a com pound. The connections are made by computer commands entered through the keyboard and mouse. There are about forty blocks available. A partial listing of the blocks (along with their names) is as follows: analog input (AIN) analog output (AOUT) conventional control (PID) control with selftuning (PIDE) lead lag (LLAG) dead time (DTIME) switch (SWCH) There are also blocks which process digital (or logic) signals (on/off) such as comparators, selectors, and timers which are needed for automatic plant start up and shutdown and for batch operations. Figure 2 shows that the block diagram for a com pound for conventional singleloop control requires three blocks: AIN, PID, and AOUT. The AIN and AOUT blocks are used for converting and conditioning signals to and from the process for use in the computer. The PID block performs the control function. A compound for a cascade control system requires five blocks: two AIN, one AOUT, and two PID blocks. One of the most important and complex blocks is the PID block, which has 81 parameters. Initially, one may be bewildered by the number of parameters to be set, but most of them can be left at their default values for a number of experiments. Many of these parameters are concerned with measurement alarms and limits on control variables. One parameter that is common to most of the blocks is the sampling period, which can be varied FBM FBM AIN PID AOUT PROCESS Figure 2. Compound for singleloop control from 0.1 sec to 1 hr. For the PWFB system, the lowest sampling period is 0.5 sec. Most of the experi ments for the elective control course use a sampling period of 0.5 sec. CONTENT OF THE ELECTIVE CONTROL COURSE In the prerequisite undergraduate control course, the experiment using the Foxboro system is at the end of the course, after the student has studied tuning of closedloop systems. It consists of using a preconfigured control law (PID) to tune a third order system which is simulated on an analog com puter. This limited experience stimulated enough interest that many students subsequently consid ered taking the elective control course, which covers the use of the Foxboro system in greater detail. Because the elective course is limited to four hours per week for ten weeks, only continuous control blocks are used in the experiments. An outline of the course is shown in Table 1. In addition to the topics listed in the table, lectures are given on sampled data control, implementation of practical control al gorithms, multiloop control strategies (cascade, feedforward, etc.), and process identification and tun ing. Some knowledge of sampleddata control is needed in order to understand the difference be tween continuous control (pneumatic and electronic) and microprocessorbased (digital) control and the destabilizing effect of sampling on the stability of the closedloop system. In the lecture on the implementation of practical control algorithms, we discuss the use of external feedback to show how the integral action is obtained, which avoids reset windup. We also discuss a practi cal method used for obtaining a derivative action in which the measurement signal (not the error signal) is sent through a filter such as a leadlag filter. The Foxboro software uses a Butterworth filter to obtain derivative action. For years, one of the goals of control engineers has been to develop a device for automatically tuning a process online. Many suppliers of control hardware Chemical Engineering Education now provide selftuners; Foxboro's version is called EXACT, which stands for EXpert Automatic Con trol Tuning. The selftuning algorithm, being proprietary information, is described only in general terms in the user's manual accompanying the con trol equipment. The lecture on system ident ification and tuning gives the students some idea of how the tuning algorithm may work, especially the pretune phase which analyzes an openloop response. In this case, the CohenCoon tuning method is conceivably the approach used to obtain prelimi nary tuning parameters. With the availability of modern computer control systems and their great variety of blocks (such as those mentioned above), the control engineer has for the first time the possibility of configuring complex control strategies which are limited only by his/her imagination and knowledge of the process. It is now feasible to implement advanced control strategies, such as Smith predictor control and internal model control, by blocks which simulate firstorder, lead lag, and transport lag transfer functions. The configurators for creating displays are a very important part of the Foxboro software. The dis plays make it possible for the operator to observe the process variables and to control the process. In the elective control course, the students use the group display configurator since it is easy to use; they are not required to use the software (Display Builder and Display Configurator) which is needed to create elaborate dynamic displays showing flow diagrams TABLE 1 Applications of Computers to Control 2 hr. lecture, 2 hr. lab: 3 creditsfor 10 weeks This course, which is primarily devoted to the study of a modern industrial microprocessorbased control system, covers configuration, tuning, and operation of a Foxboro (PWFB) I/A system. Control applications include singleloop and multiloop control systems. 1. Overview of microprocessorbased control system hardware and software 2. Tasks performed by a distributed control system: control algo rithms, displays, alarms, mathematical functions, data storage, reports 3. Operation and control of a singleloop process using a Foxboro I/A control system; observe effect of sampling on stability 4. Configuration of control systems using various blocks 5. File utilities: storage and transfer of control data bases 6. Configuration of displays: detail, group, process 7. Alarms: system alarms, process alarms 8. Use of Foxboro I/A control system for Advanced Control Strategies: cascade, feedforward, internal model, selftuning, etc. 9. System management: monitoring the state of control equipment Fall 1993 of a process and which connect display objects (tank level, number fields, etc.) dynamically to block pa rameters and system variables. These process dis play configurators require too much time and effort and provide little educational benefit. Those experi ments which use such process displays were config ured in advance by the instructor. The experiments performed in the course are listed in Table 2 on the following page (with a brief de scription and the objective of each experiment). The emphasis in the course was on the use of the control hardware and software, while the use of mathematics was limited to stability calculations and tuning. Some students were pleasantly sur prised to find a course in control that was not overburdened by mathematics, as is usually the case in the first course in control. The experiments involved the control of processes simulated in the digital computer and processes simu lated by an analog computer. The analog computer simulated process is considered a "real" process since 010 volt signals are transmitted to and from the analog computer through wires connected to the fieldbus module. A more realistic situation would be to control processes such as liquidlevel, heat ex change, or pH, although such processes would re quire a substantial investment in measuring ele ments, control valves, and process equipment. At the Foxboro training center, one of the laborato ries uses with each microprocessor a process cart which holds a secondorder liquid level system. If funds were available, such a process would provide the student with a more realistic view of the hard ware components of a process control system. As a compromise, one such "real" process should be added to the laboratory. For those interested in using an analog computer for simulation of the process, Comdyna, Inc., of Great Barrington, Illinois, sells an 8amplifier, 10volt computer for about $2,000. SUGGESTIONS FOR PLANNING A COMPUTER CONTROL LABORATORY After acquiring the control equipment and the knowledge to use it, time must be found to develop interesting experiments that provide a balance be tween practice and theory. An excellent way to pre pare laboratory experiments is to direct one or two students in a special projects course to develop and test several experiments. Laboratory outlines and some course notes on using the software must be written; the user's manuals are too detailed for use as course notes, although they can be used as a reference and should be available in the laboratory 191 TABLE 2 Applications of Computer to Control Experimentsfor Foxboro I/A System Experiment 1 * Control of tank level in a "get acquainted" experiment In this experiment, the student uses a compound and displays which are already configured. The objective is to learn how to use the keyboard and a mouse to enter commands and parameters and to see the types of displays which can be provided by the software. The process being controlled is simulated in the digital computer using Foxboro blocks. Experiment 2 * PI control of a thirdorder process simulated on an analog computer In this experiment, a thirdorder system [1/(rs+lY] simulated on the analog computer is controlled by a PID controller. The student tunes the controller by using ZieglerNichols rules. The time constant of the process, r, is set to 4 seconds, with the result that the system responds quickly. Experiment 3 * Configuration of a compound for PID control of a thirdorder process and configuration of a group display The objective of this experiment is to learn how to use the control configurator software to devise a PID controller that controls a third order process simulated on the analog computer. The same process of Experiment 2 is controlled. Experiment 4 * Changes in configuration of compound of Experiment 3 (set point tracking, alarm parameters, etc.) In this experiment the PID controller compound of Experiment 3 is for students to use. No more than two students should be assigned to a computer workstation. The use of the software can be learnbypractice (trialander ror) at the keyboard. If more than two people are assigned to a workstation, only the most assertive member of the group will learn much. In addition to the usual tasks involved in running a laboratory, the instructor should reserve time for maintaining equipment and computer files. After a course is completed, the old files for compounds and displays must be deleted so that they do not get used by students when the course is offered again. It is also necessary to restore preconfigured compounds to their original form as required in some of the experiments, and master copies of files for compounds and displays must be saved. The file utility software is used to maintain files. The workstation environment software is needed to develop new environments and to passwordpro tect existing and new environments. An environ ment is a selection of "buttons" along the top menu bar of the monitor which is used by the operator to gain access to configurators, displays, compounds, and other software items. The Foxboro I/A system comes with some standard environments, such as modified to include process alarms, limits on process variables, and set point tracking. The control system is operated to see that the system actually responds to the changes in configuration. Experiment 5 * Control of a simulated process To see that the process can be simulated by controller blocks in the computer, the student controls a process consisting of a firstorder transfer function and a dead time. Experiment 6 * Cascade control This experiment shows how the control blocks can be configured for cascade control. The process controlled is a thirdorder system simu lated on the analog computer. The student shows the benefit of cascade control by comparing the responses of cascade control and singleloop control of the same process. Experiment 7 * PID control with PIDE block (selftuning) In this experiment, a PID block with selftuning is used to control a third order [1/(Ts+l)3] process simulated in the computer. After obtaining preliminary controller settings with the pretune phase of the tuning algorithm, the process is placed on automatic and the closedloop system is tuned online by introducing a sequence of step changes in set point. After about five changes in set point, the tuning parameters (PB, ,z T,) settle at values which are not too far from the tuning parameters calcu lated by ZieglerNichols rules. Watching the online selftuning algo rithm update the tuning parameters with each disturbance is fascinating. "process operator's environment," "process control engineer's environment," etc. All of the environments can be prevented from being used by requiring a password to open an environment and all the fea tures associated with that particular environment. In a course which has many inexperienced users, it may be advisable to passwordprotect all environ ments except those needed to perform the experi ments. In this way, the corruption of files and sys tem breakdowns will be reduced. The use of commercially available microprocessor based control systems in undergraduate courses at Drexel has been favorably received by the students. The first time the elective course was offered, more students registered for the course than could be ac cepted. Since there are only three Foxboro systems, enrollment was limited to six people per course sec tion. If more time is available, more experiments could be introduced which involve complex multi loop strategies and batch operation. Short courses using microprocessorbased controllers should be of interest to engineers in industry. REFERENCES 1. Coughanowr, D.R., Process Systems Analysis and Control, 2nd ed., McGrawHill (1991) 0 Chemical Engineering Education FREE ENERGY OF WETTING Continued from page 187. in free energy, the total path represents a minimum in free energy, and Young's angle is the result. In summary, when a liquid contacts a solid, either partial or complete wetting occurs. The extent of wetting is determined by a simple thermodynamic rule familiar to all students: the system will move to the state of lowest free energy. Although the rules are simple, the implications of the rules are pro found and can have important consequences in many areas of applied chemistry. ACKNOWLEDGMENTS The author would like to thank the Exxon Educa tion Foundation for a grant supporting education and research associated with this study. REFERENCES 1. Smith, William F., Principles of Materials Science and En gineering, 2nd ed., McGrawHill, Inc., New York, NY (1990) 2. Shackelford, James F., Introduction to Materials Science for Engineers, 3rd ed., Macmillan Publishing, New York, NY (1992) 3. Askeland, Donald R., The Science and Engineering of Mate rials, 2nd ed., PWSKENT Publishing, Boston, MA (1989) 4. VanVlack, Lawrence H., Elements of Materials Science and Engineering, 6th ed., AddisonWesley Publishing, New York, NY (1989) 5. Flinn, Richard A., and Paul K Trojan, Engineering Materi als and Their Applications, 3rd ed., Houghton Mifflin Co., Boston, MA (1990) 6. Callister, William D., Materials Science and Engineering, 2nd ed., John Wiley and Sons, New York, NY (1991) 7. Budinski, Kenneth G., Engineering Materials, 4th ed., Prentice Hall, New Jersey (1992) 8. Newey, Charles, and Graham Weaver, Materials Principles and Practice, The Open University, England (1990) 9. Keyser, Carl A., Materials Science in Engineering, 4th ed., Charles Merrill Publishing Company, Ohio (1986) 10. Jastrzebski, Zbigniew D., The Nature and Properties of En gineering Materials, 3rd ed., John Wiley & Sons, New York, NY (1987) 11. Adamson, A.W., Physical Chemistry of Surfaces, 4th ed., John Wiley & Sons, New York, NY (1982) 12. Harkins, W.D., and A. Feldman, J. Amer. Chem. Soc., 44, 2665(1922) 13. Brochard, F., and P.G. deGennes, J. Physique Lett., 45, L 597 (1984) 14. Ahmad, J., and R.S. Hansen, J. Colloid Interface Sci., 601 (1972) 15. Ross, S., and I.D. Morrison, Colloidal Systems and Inter faces, John Wiley and Sons, New York, NY; p. 87 (1988) 16. Young, T., Miscellaneous Works, G. Peacock, Ed., Murray, London, England; Vol. 1, 432 (1855) 17. Andrade, J.D., L.M. Smith, and D.E. Gregonis, Surface and Interfacial Aspects of Biomedical Polymers, J.D. Andrade, Ed., Plenum Publishing Co., New York, NY; Vol. 1, 260 (1985) 18. Pirie, B.J.S., and D.W. Gregory, J. Chem. Educ., 50, 682 (1973) 19. Andrade, J.D., R.N. King, D.E. Gregonis, and D.L. Coleman, Fall 1993 J. Polym. Sci. Symp., 66, 313 (1979) 20. Gibbs, J.W., The Scientific Papers of J. Willard Gibbs, Do ver, New York, NY; Vol. 1, 326 (1961) 21. Morra, M., E. Occhiello, and F. Garbassi, Adv. Colloid Inter face Sci., 32, 79 (1990) 22. Gaydos, J., and A.W. Neumann, J. Colloid Interface Sci., 120, 76 (1987) a REVIEW: HAZOP and HAZAN Continued from page 167. tive risk assessment" (QRA) or "probabilistic risk assessment" (PRA). This chapter includes very introductory material on calculating human risks and equipment reliability. There is an interesting section on calculating the cost of saving a life, demonstrating a huge range of cost values for various activities. Chapter 4 is a manager's guide to hazard analysis and discusses the problems associated with hazard analysis in a managerial environment. Chapter 5 discusses the most common objections raised against HAZOP and HAZAN, and the author provides a convincing case for applying these techniques. Chapter 6 is a very short chapter which dis cusses sources of data and confidence limits, and Chapter 7 presents an interesting history of HAZOP and HAZAN. I am a considerable fan of the author, Trevor Kletz, and buy all of his books as soon as they are pub lished. He uses a powerful technique of mixing case histories with discussion to provide convincing cases for his material. Furthermore, he has a unique way of looking at things and often arrives at an "obvious" result that no one else even thought of. The content of this book is introductory in nature and would be suitable for anyone with an interest in learning about basic HAZOP and HAZAN methods. It does not discuss techniques for decomposing large process units into suitable subunits for HAZOP analysis, a major problem for industrial practi tioners, nor does it include some of the more recent organizational methods for managing a large HAZOP. There are some simple calculations related to equip ment reliability, but nothing particularly difficult for chemical engineering students. This book, along with Trevor's other books, would be a suitable reference or supplemental material for a chemical engineering design course or a course in chemical process safety. The students would be most responsive to the case histories and examples that are provided. 0 Random Thoughts... WHAT MATTERS IN COLLEGE RICHARD M. FIELDER North Carolina State University Raleigh, NC 276957905 Most faculty lounge discussions of educa tional matters are not exactly models of rigorous logic. The "everyone knows" argu ment offered with no substantiation whatever is per haps the most common gambit ("Student evalua tions don't mean anythingeveryone knows the high est student ratings always go to the easiest graders"), and the straight line through one data point is a close second ("Herman Frobish in Me chanical Engineering published eighteen papers last year and also won an outstanding teaching award, which proves that the best researchers are also the best teachers"). If you occasionally get into discussions about edu cation and would like to buttress your arguments with something a bit more substantial, I recommend that you keep within easy reach a monumental work by Alexander Astin titled What Matters in College.'1' No single data point here! Astin collected longitudi nal data on 24,847 students at 309 different institu tions and determined the influences of a host of institutional characteristics on the students' college experience. The data include 146 input variables that characterize the entering students, including demographic measures, information about parental education and socioeconomic status, precollege aca demic performance measures, and selfpredictions of a number of outcome variables; 192 environmental variables relating to institutional and faculty char acteristics, including measures of the size and type of the institution, faculty demographics and atti tudes, institutional emphasis on research, and the nature and extent of studentfaculty and student peer group interactions; and 82 outcome variables, including measures of academic achievement, reten Richard M. Felder is Hoechst Celanese Pro fessor of Chemical Engineering at North Caro lina State University. He received his BChE from City College of CUNY and his PhD from Princeton. He has presented courses on chemical engineering principles, reactor de sign, process optimization, and effective teach ing to various American and foreign industries and institutions. He is coauthor of the text Elementary Principles of Chemical Processes (Wiley, 1986). tion, career choice, selfconcept, patterns of behav ior, selfreported growth in skills, and perceptions of and satisfaction with the college experience. Several results that I find particularly noteworthy are listed below. All of the cited correlations are positive (unless otherwise noted) and significant at a levelp < .0001. The quality of the college experience is strongly affected by studentfaculty interactions. The fre quency with which students talk with professors outside class, work with them on research projects, assist them in teaching, and visit their homes, corre lates with student gradepoint average, degree at tainment, enrollment in graduate or professional school, every selfreported area of intellectual and personal growth, satisfaction with quality of in struction, and likelihood of choosing a career in college teaching.1: 3833841 A frequently debated issue is whether institutional size affects educational quality. Astin's findings in dicate that smaller may indeed be better. Both smaller enrollments and lower student/faculty ra tios correlate with satisfaction with instructional quality, enrollment in graduate school, interest in college teaching careers, and selfreported increases in overall academic development, cultural aware ness, writing skills, critical thinking, analytic and problemsolving skills, leadership skills, public speak Copyright ChE Division ofASEE 1993 Chemical Engineering Education ing ability, and interpersonal skills.[: 326329] The bet ter showing of smaller institutions is undoubtedly due in part to the greater incidence of personal stu dentfaculty contacts at such institutions, suggest ing the desirability of trying to increase such con tacts at large universities. Astin concludes, however, that as important as the studentfaculty relationship may be, "...the student's peer group is the single most potent source of influ ence on growth and development during the under graduate years."[: 3981 Frequency of studentstudent interactions (including discussing course content with other students, working on group projects, tutoring other students, and participating in intramural sports) correlates with improvement in GPA, gradu ating with honors, analytical and problemsolving skills, leadership ability, public speaking skills, in terpersonal skills, preparation for graduate and pro fessional school, and general knowledge, and corre lates negatively with feeling depressed."' 3851 Many of the study findings specifically point to the benefits of cooperative learningstudents working in teams toward a common goal. Frequency of group work has positive correlations with most areas of satisfaction, all selfratings, and all areas of self reported growth except foreign language skills. Tu toring other studentswhich may be done formally but also occurs in a natural way when teams of students work and study togetherhas positive cor relations with all academic outcomes and with choice of careers in college teaching.1 3871 As Astin notes: Classroom research has consistently shown that cooperative learning approaches produce outcomes that are superior to those obtained through traditional competitive approaches, and it may well be that our findings concern ing the power of the peer group offer a possible explanation: cooperative learning may be more potent... because it motivates students to become more active and more involved partici pants in the learning process. This greater involvement could come in at least two differ ent ways. First, students may be motivated to expend more effort if they know that their work is going to be scrutinized by peers; and second, students may learn course material in greater depth if they are involved in helping teach it to fellow students.1: 4271 A number of results illustrate how emphasis on Fall 1993 research at an institution affects the quality of that institution's instructional program. Astin's conclu sion is that Attending a college whose faculty is heavily researchoriented increases student dissatisfac tion and impacts negatively on most measures of cognitive and affective development. Attend ing a college that is strongly oriented toward student development shows the opposite pattern of effects.1:3631 A disturbing finding is that majoring in engineer ing correlates negatively with students' satisfaction with the quality of their instruction and overall college experience and positively with feeling overwhelmed and depressed. "Clearly, these find ings indicate that the climate characterizing the typical institution with a strong emphasis on engi neering is not ideal for student learning and per sonal development."1: 3603611 In the concluding chapters of the book, Astin proposes possible solutions to the educational qual ity problems raised by his study, suggesting that the first step is having an institutional leader ship that understands the problems and is willing to do something to deal with them. "As long as faculty in the research universities are expected simulta neously to perform research, teaching, advising, uni versity service, and outside professional activities, teaching and advising will continue to receive low priority." He proposes negotiated contracts with faculty members that would provide for a better institutional balance among the different functions of the professoriate.1: 4211 He also suggests that cur ricular planning efforts will pay off better if they focus less on formal structure and content and put more emphasis on pedagogy and other features of the delivery system.1: 427] This brief synopsiswhich is intended only to whet your appetiteshould raise all sorts of questions in your mind about the data and statistical methodol ogy that led to the stated conclusions, how possible variable interactions and competing effects were ac counted for, and what else Astin discovered. I en courage you to get the book and find the answers. REFERENCE 1. Astin. A.W., What Matters in College: Four Critical Years Revisited, JosseyBass, San Francisco, CA (1993) 0 195 THE ASEE CHEMICAL ENGINEERING DIVISION LECTURESHIP AWARD ThirtyOne Years of Recognizing Outstanding Achievement in Fundamental Chemical Engineering Theory or Practice GEORGE BURNET Iowa State University Ames, IA 50011 he first time I heard a divisional lectureship sug gested was during an informal discussion following a meeting of the AIChE Education Projects Commit tee at the Institute's 1962 national meeting in Chicago. In addition to this writer, Charlie Wilke and Max Peters were present. The discussion dealt with what could be done to strengthen the program of the Chemical Engineering Divi sion of ASEE and to make membership in the Division more attractive to chemical engineering educators. A number of suggestions were made, including joint ASEE/ AIChE sessions at AIChE meetings, promoting the journal Chemical Engineering Education, emphasizing research ad ministration and funding in programs at ASEE annual con ferences, and increasing industrial participation. It was Max Peters who first suggested an annual lecture ship with the purpose of recognizing and encouraging outstanding achievement in an important field of fundamen tal chemical engineering theory or practice. A chemical engineering educator would deliver the lecture as part of the annual program of the Division. The idea was adopted quickly, and the Executive Committee of the Division proceeded to name Art Metzner as the first annual lecturer. The winner received a framed certificate in recognition of the lecture. The annual lectureship proved to be popular and was well received. Attendance at the 1964 lecture exceeded 150 people. Publicity about the lectureship and each year's lecture was submitted to Chemical Week, Chemical & Engineering News, Chemical Engineering Progress, and Chemical Engineer ing, where news items and accompanying photographs of the lecturer were often published. At the 1965 Annual Conference, the Executive Committee of the Division, under the chairmanship of John West, rec ommended that the annual lectureship become an award and that an industrial sponsor for the award be sought. This writer was asked to spearhead the effort, and a formal pro posal was developed calling for an honorarium of $1,000, reimbursement of travel expenses, $300 for publication of the full text of the lecture in Chemical Engineering Educa tion, and reimbursement to ASEE headquarters for the cost of administering the award. In addition, the proposal identified the following accom plishments that were to be considered by the annual lecture ship award committee in selecting the recipient. 1. Achievement, through formulation or creative application offundamental theory and principles, or important advances which have been accepted by colleagues and by others in the field of specialization, with promise of making further significant contributions. 2. Improvements oflasting influence to chemical engineer ing education through books, technical articles or laboratory or other teaching equipment, and demonstra tion of success as a teacher as well as the ability to inspire students to high levels of accomplishment. 3. Evidence of the ability to conduct original, sound, and productive research, personally or as a director of a research team, and to evaluate and report the significant results obtained. 4. Interest in furthering technical progress in chemical engineering through participation in professional and educational societies. The proposal further specified the duties and terms of service of an annual lectureship award committee and the information to be required in a nomination. Finally, it was noted that the award recipient would be required to submit a suitable manuscript based on the lecture to the journal Chemi cal Engineering Education. Largely through the efforts of Wendel W. Burton, at that time Director of Employment for the 3M Company, 3M agreed to sponsor the award on a continuing basis. Mr. Burton had been active in ASEE for many years, having served most recently as its national treasurer. In 1965, the Executive Committee of the Division en dorsed the overall plan, and the proposal went simultaneously Copyright ChE Division ofASEE 1993 Chemical Engineering Education to Glenn Murphy, ASEE Vice President for the Projects Operating Unit, Harold E. Heath, Chair of the ASEE Awards Policy Committee, and Leighton Collins, ASEE Executive Secretary. By May, 1966, the Division had autho rization to proceed, and Octave Levenspiel was named the first 3M Lecturer. A booksize brochure containing infor mation about the award, a list of previous lecturers, and biographical information of the recipient was widely distrib uted at the Annual Conference and was used in other ways to publicize the award. The first lectureship award committee was appointed in 1966, and consisted of Robert Beckmann, Robert L. Pigford, and this writer. Over the next few years Joseph A. Bergantz, Andreas Acrivos, Myron Chetrick, and William Corcoran also served on this committee. In 1973, Wendel Burton asked the Division to suggest ways the lectureship award could be enhanced to insure that its stature be maintained, and the following year a lecture tour by the awardee was implemented. Additional funds were provided by 3M to cover travel and subsistence to deliver the lecture at three universities during the academic year following its presentation at the ASEE annual confer ence. An additional honorarium of $500 was paid the awardee when the lecture tour was completed. In 1989 the award was increased to $2,000, with a lecture tour honorarium of $1,000, and every fifth year the lecture has been presented at the ChE Division summer school. 3M continued its sponsorship of the award up to and including the 1991 annual conference. During 1992 and 1993 the Division continued the award without an industrial sponsor. Expenses and a reduced hono rarium were paid to the recipient, using funds from the Division treasury. Thanks to the efforts of John Friedly, Chair of the Division for 199293, and Lewis Derzansky, University Relations Representative from Union Carbide, we will have the Union Carbide Lectureship Award beginning with the 1994 annual conference. The criteria, selection procedure, and responsibilities of the lecturer remain unchanged, the lecture will continue as a major event of the ASEE annual confer ence, and the full text of the lecture will be published in CEE. A lecture tour by the awardee remains as an option open to Union Carbide. The lectureship award was the first and is still one of the most highly regarded of the twentyone divisional awards. It is acknowledged as the premier award of the chemical engi neering education community in the United States. A sig nificant measure of the importance of the lectureship award lies in the prestige of its recipients. This list is a veritable "Who's Who" of chemical engineering education (see the boxed listing of winners). Twenty of the thirtyone recipi ents have been elected to the National Academy of Engi neering, the highest professional recognition our country confers upon an engineer. Much of the credit for the long and distinguished history of the award must go to the 3M Company for its encourage ment, active participation in Division affairs, and financial support. The award has promoted quality and new advances in ChE education that have benefited the entire profession. As we look to the future, we must note with approbation the commitment Union Carbide has made to a longterm association with the Lectureship Award. The rapid and chal lenging changes in science and technology will place in creasing demands on chemical engineering education and practice. The lectureship award will continue to play an important role in meeting these demands. O Editor's Note: The 1992 Award Lecture, given by William N. Gill at the ASEE ChE Division Summer School in June of 1992, appears on the following pages. SChemical Engineering Division Lectureship Awardees 1963 Arthur B. Metzner; NonNewtonian Fluids 1964 Charles R. Wilke; Mass Transfer in Turbulent Flow 1965 Leon Lapidus; Aspects of Moder Control Theory and Application 1966 Octave Levenspiel; Changing Attitudes to Reactor Design 1967 Andreas Acrivos; Matched Asymptotic Expansion 1968 L. E. Scriven; Flow and Transfer at Fluid Interfaces 1969 Cornelius J. Pings; Some Current Studies in Liquid State Physics 1970 Joe M. Smith; Photochemical Processing: PhotoDecomposition of Pollutants in Water 1971 William R. Schowalter; The Art and Science ofRheology 1972 Dale F. Rudd; Synthesis and Analysis in Engineering 1973 Rutherford Aris; Diffusion and Reaction in Porous Catalysts 1974 Elmer L. Gaden, Jr.; Biotechnology: An Old Solution to a New Problem 1975 John M. Prausnitz; Molecular Thermodynamics for Chemical Process Design 1976 Abraham E. Dukler; The Role of Waves in TwoPhase Flow 1977 Robert C. Reid; Superheated Liquids: A Laboratory Curiosity and an Industrial Curse 1978 Theodore Vermeulen; Dynamics of Runaway Systems 1979 Daniel D. Perlmutter; A New Look at an Old Fossil 1980 Klaus D. Timmerhaus; Fundamental Concepts and Application of Cryogenic Heat Transfer 1981 Arthur Westerberg; Design Research: Both Theory and Strategy 1982 Lowell B. Koppel; Input Multiplicities in Process Control 1983 Warren E. Stewart; Simulation and Estimation by Orthogonal Collocation 1984 TW Fraser Russell; Semiconductor Chemical Reaction Engineering 1985 Dan Luss; Analysis and Modeling of Steady State Multiplicities 1986 Robert S. Brodkey; The Potential for Image Processing and Analysis in Turbulence Research 1987 James J. Christensen; Reflections on Teaching Creativity 1988 Stanley I. Sandler; Physical Properties and Process Design 1989 J.L. Duda; A Random Walk Through Porous Media 1990 Brice Carahan; Computers in Engineering Education 1991 Darsh T. Wasan; Interfacial Transport Processes and Rheology 1992 Willian N. Gill; Interactive Dynamics of Convection and Crystal Growth 1993 Morton M. Denn; Polymer Flow Instabilities Fall 1993 197 Award Lecture ... INTERACTIVE DYNAMICS OF CONVECTION AND CRYSTAL GROWTH WILLIAM N. GILL Rensselaer Polytechnic Institute Troy, NY 121803590 Would have liked this article to be the story of how basic theoretical and experimental break throughs have contributed to the spectacular advances in making and using new materials for the various "revolutions" we have witnessed since World War II. But it quickly became clear to me that the scope of such a story is beyond my competence to tell coherently. Therefore, I will attempt to give here a chemical engineer's view of some rather recent work on dendritic growth, which has generated many sur prises over the last fifty yearsonly a part of the story I had hoped to tell. The macroscopic properties of materials and the uses to which they can be put depend on their inter nal structure. In turn, the microstructure of materi als depends on the details of the processes used to make them. Furthermore, the making of a material and its placement in a system for final use may occur simultaneously as, for example, with thin di electric or metallic films made by chemical vapor deposition for integrated circuits. In this case, both the microstructure and the macrostructure (unifor William N. Gill was presented with the Thirtieth Annual Chemical Engineering Division Lectureship Award for this lecture, which he gave at the ASEE ChE Division summer school meeting at Montana State University in August of 1992. The award is bestowed annually on a distinguished engineer ing educator and is designed to recognize and encourage outstanding achievements in important fields of fundamental chemical engineering theory or practice. Professor Gill is Russell Sage Professor in Chemi cal Engineering and the Center for Integrated Electronics at Rensselaer Polytechnic Institute, and has been a faculty member at Syracuse University, Clarkson University, and the State University of New York at Buffalo. He served as chairman of the ChE departments at Clarkson and RPI, Dean of Engineering at Buffalo, Fulbright Senior Research Scholar in England and Australia, and Glenn Murphy Distinguished Professor at Iowa State. Gill's research has focused on several areas, including turbulent convec tion, Taylor diffusion, membrane separations, and various aspects of crystal mity, absence of keyholes, step coverage, etc.) of the materials profoundly influence the performance of the devices which are made from them. Microstructure and composition determine the properties of advanced materials, including alloy cast ings, polymerceramic composites, and films, and convection may profoundly affect all of them. The transport of energy and the redistribution of solute in the solidification of alloys are influenced by con vection in different ways (depending on whether the transformation occurs in the vapor or liquid phase) because the transport properties differ enormously in gases and liquids. The subject of interactive dynamics has very prac tical implications because it includes efforts to un derstand how process conditions, the microstructure, and macroscopic configuration of materials go to gether, as they are manufactured, to maximize their usefulness in various applications. If our goal is to create materials and structures with the properties we wish them to have, then an understanding of how to control the way they may be made to achieve this goal is of prime importance. When crystals grow in a melt of pure liquid, from a solution of several components or from the vapor growth. His contributions are summarized in more than 150 articles balanced between theoretical and experimental content. His motivation is the under standing of chemical and physical phenomena that underlie processes of practical importance from both industrial and environmental viewpoints. His work has been cited about 2000 times in a large number of joumals and books in many fields, including medicine, biophysics and biochemistry, chem istry, geophysics, applied mathematics, condensed matter physics, virtually all areas of engineering, and materials science. He has investigated the effects of concentration polarization, the interac tion among components in the feed, ways to model hollow fiber and spiral wound systems, and the fundamental processes that underlie transport in membranes. His most recent area of interest has been crystallization, includ ing dendritic growth and rapid solidification, and currently with chemical vapor deposition of copper and interlayer dielectric films for integrated circuits. Gill has worked with many graduate students and has been thesis advisor to thirtyone PhD recipients. These former students currently have faculty positions at universities in the United States, Israel, Korea, Taiwan, India, Iran, and Europe. He has been editor of Chemical Engineering Communica tions since 1979 and serves on several boards. Copyright ChE Division ofASEE 1993 198 Chemical Engineering Education The subject of interactive dynamics has very practical implications because it includes efforts to understand how process conditions, the microstructure, and macroscopic configuration of materials go together.... If our goal is to create materials and structures with the properties we wish them to have, then an understanding of how to control the way they may be made to achieve this goal is of prime importance. phase by deposition on a substrate, an interface is created, the shape and movement of which depends on the conditions that prevail on both sides of the interfacial region and within that region itself. In other words, the movement and shape of the inter face creates an active pattern which evolves in time and which is inherently threedimensional in sys tems of practical interest. The quantitative descrip tion of this spontaneous nonlinear dynamic process is one of the objectives of the theory of pattern for mation, and one particular aspect of it includes the interactive dynamics of convection and crystal growth. Convection is coupled with the growth of the crystals involved, and each affects the other because of the movement of the mobile interface. The problems associated with studying interactive dynamics are formidable, but progress is being made which will contribute to the development of some of the extraordinary materials of the future. The Octo ber 1986 issue of Scientific American contains thir teen articles, well worth reading, on various aspects of the development of materials, providing an interesting perspective on the modern aspects of ma terials engineering and science by people who are not chemical engineers. A physicist's viewpoint on dendrites and the theory of pattern formation is given by J.S. Langer in Science (March 1989); this perspective was updated with his more recent ar ticle in Physics Today (October 1992) in which he appealed for a rational approach to materials re search on the national level. An applied mathematician's viewpoint on interac tive dynamics in crystal growth is given in two review articles published recently by Huppert"1 and Davis[2' in the Journal of Fluid Mechanics. Brown,3"' a chemical engineer, has reviewed various interesting aspects of single semiconductor crystal growth from the melt, especially for electronic and optoelectronic devices. The Handbook of Crystal Growth (Edited by Hurle; Elsevier, 1993) contains a number of chap ters which review subjects related to this one. Also, a conference was held in March of 1992 in Chamonix, France, the papers from which have been pub lished as Interactive Dynamics of Convection and Solidification (Kluwer Academic Publishers, edited by Davis, et al.). Fall 1993 L. r Figure 1. Photographs of an anisotropic ice dendrite with AT= 0.60K, R,/R,28, magnification 26x: (A) edge view with tip radius, R,; (B) Basal plane with tip radius, R2. When they are still undergraduates, chemical en gineers begin learning to deal with heat, mass, and momentum transport coupled with chemical reac tions in the bulk phase or on the boundaries of the system. At Rensselaer, for example, individual courses in fluid mechanics, heat transfer, separation processes, and chemical reactor design are required in the third and fourth years of the undergraduate program. The exposure to separation processes, re actor design, and the option to take a fourthyear course in transport phenomena provides a good foun dation for graduatelevel course work and research in materials processing. THE ROLE OF TRANSPORT PROCESSES IN CRYSTAL GROWTH It is important to understand the roles of heat, mass, and momentum transfer in crystal growth processes. One or more of these phenomena may be of crucial importance, depending on the phase change system involved and how the process is carried out. To illustrate this, we will consider dendritic growth which, according to Glicksman and Marsh,[4] is the most prevalent form of solidification. In the simplest case involving dendrites, the free growth of crystals (unencumbered by walls) from pure undercooled melts produces dendritic structures in which the leading tip of the main stem of the dendrite propagates in the preferred crystallographic direction, as shown in Figure 1. These reproducible patterns have small dimensions and large cur vature. They seem to occur in nature due to the competition among the kinetic resistance to the at tachment of molecules at the surface, the effect of the surface energy of the solidliquid interface, and the rate of removal of heat from the surface into the subcooled melt. The underlying reasons for why dendrites form the patterns they do are not com pletely clear and currently are being investigated on a worldwide basis. Figure 1 illustrates how different ice dendrites appear when viewed from the basal plane, where one sees a rich sidebranch struc ture, and from the edge plane, which has no sidebranches at all. Figure 2 shows the typical shape of a water drop in equilibrium with the ice matrix in which it is encased. This drop also demon strates strong anisotropy. Surface tension depresses the melting point of an interface which is convex to the melt, and attach ment kinetics reduce the driving force for heat trans fer, both of which stabilize the solidification front. The rate of heat removal by conduction to the under cooled melt may be influenced significantly by ther mal or forced convection, which will have an effect on the properties of the crystal. A successful theory of this seemingly straightforward problem from which one hopes to predict the size, shape, and growth rate of the crystal, has proved to be elusive. Grain size (and its distribution in a material) is one of the properties that is of importance in crystal growth processes, ranging from the making of steel to the deposition of thin metallic films in integrated circuits. Within each grain of a structural material (such as a titaniumbased alloy) is a microstructure formed by dendritic growth. The microstructure consists of a pattern in which the interstices be tween the main stems and the sidebranches of alloy dendrites are filled with material which is rich in solute. The solution in the interstices solidifies more slowly than that contained in the dendrites. This microstructure determines many of the macroscopic properties of structural materials, and thus the uses for them. Therefore it is of major importance to un derstand how to control the rate of dendritic growth, the size of the dendrites, and the spacing between their sidebranches. It has been known for a long time that processing techniques can have a profound influence on the microstructure of materials. Indeed, the basic ideas regarding some of the methods currently used 200 to produce exotic materials, such as directional so lidification, modified directional solidification to pro duce single crystals, and rapid solidification, had their roots in the 1960s. These processing methods have had a major impact on the development of advanced structural materials because they influ ence the microstructure in predictable ways. Fur thermore, the methods used are all related to con trolling the transport processes involved in the mak ing of these materials. Examples of the dramatic improvements in mate rials due to the procedures used to process them abound. The use of directionally solidified metal struc tures has resulted in an increase of 1500C to 200C in inlet temperatures for turbines, which substan tially increases their efficiency. One can actually obtain amorphous metal alloys by rapid solidifica tion, and these have properties which may substan tially reduce the energy losses which occur in the distribution of power. Thus it is important from both a basic and a practical viewpoint to understand the role of various transport mechanisms in determin ing rates of production, the length scales that corre spond to the rates of production, and how a particu 0.2mm 1 Ii (A) Figure 2. Equilibrium shape of highly anisotropic water drop in ice matrix: (A) basal plane; (B) edge plane. Chemical Engineering Education Convection is the organized movement of large groups of molecules on a macroscale, and (as required by Newton's laws of motions) it results from force fields which may be subtle and difficult to manipulate or control. lar growth path is selected, which determines what the length scales and rates are. Here, I will concen trate on some of the ways natural and forced convec tion affect the crystal growth processit is a subject on which some of my students and I have spent a considerable amount of time. CONVECTION AND CRYSTAL GROWTH Convection is the organized movement of large groups of molecules on a macroscale, and (as re quired by Newton's laws of motions) it results from force fields which may be subtle and difficult to manipulate or control. For example, flow may be caused primarily by buoyancy forces which are ubiquitous on earth due to its gravitational field. If one uses the microgravity levels offered by a space station to reduce gravity by several orders of magnitude, surface tension forces may become more important than gravity in determining the na ture of the flow and, therefore, in materials process ing. Also, convection may be useful in enhancing heat and mass transfer rates and in reducing pro cessing time. Or it may adversely affect product uniformity, as can happen in the chemical vapor deposition (CVD), of thin films in a flow field that is not oriented properly. Essentially, all of the mathematical work aimed at understanding the role of convection in dendritic growth has dealt with needle crystals in which the sidebranches are neglected and one concentrates on the region near the tip of the dendrite. The first exact solution for the growth of a dendrite from the melt was obtained by Ivantsov almost fifty years ago. His classical analysis applied to isothermal needle crystals growing in a stationary melt with zero velocity, U = 0. Some of the work my students and I have done has focused on trying to add a realistic description of convection in the melt to gen eralize Ivantsov's analysis. Thus, Dash and Gill5"' showed that a similarity variable could be used to solve the energy equation given by T + U VT = aV2T (1) for an isothermal needle crystal including convec tion in the melt, if the velocity field U in the convec tive term U VT on the lefthand side of Eq. (1) is given by the Oseen or potential flow models. Fall 1993 Ananth and Gill'6' and Saville and Beaghton[71 for Oseen flow, and Ananth[81, and BenAmar, et al., 9 for potential flow, used variations on the similarity ap proach to study the growth of parabolic dendrites. Ananth and Gill considered the growth of crystals in the form of an elliptical paraboloid and gave exact solutions to the Oseen flow and energy equations in an effort to understand better the growth of ice crystals which are anisotropic. The body shapes, flow fields, and thermal fields which yield self consistent solutions for the steady growth of den drites into a melt which itself is in motion, U # 0, were determined by Ananth and Gill. Among sur faces of revolution only a parabolic crystal grows steadily, and either the Stokes flow, Oseen viscous flow, or potential flow approximations must be made in order to obtain an exact solution for the growth Peclet number VGR PG  where VG is the growth velocity, R is the tip radius, and a is the thermal conductivity of the melt. Stokes and potential flows are valid in the limit Re = UR 0 and Re>  respectively. As discussed by Lagerstrom and Cole"o0 and Lagerstrom,[11 the Oseen approximation to the NavierStokes equations is uniformly valid for a semi infinite threedimensional paraboloid of revolution at very small Reynolds numbers. The growth of shapepreserving (near the tip) den drites in subcooled melts has been observed experi mentally in detail for succinonitrile (SCN) by Huang and Glicksman[121 and for ice by Fujioka,[131 Tirmizi and Gill,1141 and Koo, et al.[5' In these experiments crystals grow from a capillary tube into a melt which is quiescent. Near the crystalmelt interface, how ever, there is a natural convection flow generated by gravity acting on a density distribution created by the temperature gradients, caused by the spreading of the heat of fusion into the melt. The intensity of this natural convection is indicated by the Grashof number, Gr. In order to compare their Oseen flow solutions to experimental data on the dendritic growth of SCN, Ananth and Gill interpreted Re = VGr and showed reasonable agreement with the data of Huang and Glicksman. They found that the Grashof number increases as undercooling, AT, which is the driving force for the flow, decreases. This counterintuitive result occurs because the length scale, R, which ap pears as R3 in Gr = gATR3 v2 increases as AT decreases in the experiments on SCN. Koo, et al., demonstrated that the same behav ior is observed with ice dendrites if one uses the harmonic mean 2 RIR2 mR1+R2 of the tip radii, RI and R, of the edge and basal planes as the length scale. This result is shown in Figure 3, and Gr is seen to change by several orders of magnitude. Ananth and Gill also solved approxi mately the fully nonlinear thermal convection prob lem, where Gr arises naturally, and they demon strated excellent agreement between the mathemati cal results and the data on SCN. Subsequently, Canright and Davis[161 studied the limiting case of the effect of very weak buoyancy driven flows on the shape of dendrites and showed that their analysis was complementary to that of Ananth and Gill. THEORIES OF SELECTION IN DENDRITIC GROWTH The experiments mentioned above all show that the growth velocity, VG, and the tip radius of the dendrite, R, are determined uniquely when the un dercooling, AT, is fixed. In contrast, Ivantsov's pure conduction solution indicates that the Peclet number, PG, is fixed when the dimensionless undercooling given by the Stefan number, St, is specified. Consequently, only the product, VGR, is determined by fixing AT, and the individual values of VG and R cannot be predicted. Thus, the theory is incomplete if one assumes that the dendrites are isothermal and smooth. If one includes natural convection, or forced con vection, VG increases and R decreases, but the same degeneracy exists in the theory. Therefore consider able effort has been expended over many years to find a selection criterion for VG and R, and these efforts in one way or another revolve around the introduction of surface tension in the problem. The selection criterion is an additional relationship be tween VG and R which enables each of them to be chosen uniquely for given values of AT and U,. Until the middle of the 1970s, the maximumveloc ity hypothesis was used for this purpose, and it assumed that the operating point was the maximum in the VG versus R curve. This assumption was used for about thirty years until it was shown to be incor rect by the careful experiments on succinonitrile of Glicksman, et al.,'171 in which both VG and R were measured as a function of AT with U, = 0. I Dimensionless Subcooling, St = AT/(L/Cp) Figure 3. Use of thermal convection analogy, Gr = Re2,, with selection parameter, a* = 0.075 to estimate level of natural convection. Comparison of Grashof numbers observed experimentally with those predicted by Stokes flow theory. Then Langer and MullerKrumbhaar[181 proposed the marginal stability theory based on the introduc tion of surface tension as a perturbation. This led to the relationship = = constant (2) VGR2 where do = mC C/L2, the capillary length a = thermal diffusivity y = surface tension Tm,Cp,L = melting point, heat capacity, heat of fusion The notion that VGR2 is independent of AT also had been proposed by Oldfield"'19 on the basis of com puter experiments in which he balanced the heat transfer by conduction against the stabilizing effect of surface tension. More recently the selection of the growth velocity and length scale in the absence of fluid flow has been addressed in many articles which discuss the micro scopic solvability theories. For detailed reviews of this work I refer the reader to the work by Langer[23' and Kessler, et al.[201 They showed that no solutions can be found in the presence of finite surface tension unless anisotropic effects (variation in surface ten sion around the surface of the crystal), no matter Chemical Engineering Education Figure 4. Forced convection growth cell provides rigid body motion of melt with dendrite fixed in space. how small, are taken into account, and that the fastest growing tip is selected because it gives the only dynamically stable solution. Anisotropy refers to the variation in surface ten sion around the dendrite in the azimuthal direction. When the anisotropy, e, is about 0.5%, the micro scopic solvability theory yields according to Mushol, et al.,[211 a result which is given by *= do .0.01 VGR2 This result is smaller by a factor of two than that obtained from the marginal stability hypothesis of Langer and MullerKrumbhaar which neglects the anisotropic effects. Both theories are in qualitative agreement with the experimental value of o* 0.02 for the data on succinonitrile of Huang and Glicksman, and Lee, et al.,1221 when the subcooling is large and the effect of convection is small. The agreement between microscopic solvability theory (MST) and the experiments for succinonitrile was encouraging, and it led to a feeling that real progress was being made in our understanding of dendritic growth. But Langer,[231 who is an original contributor to MST, raised warning signals several years ago, indicating that the predictions of MST had not been confirmed experimentally. Unfortu nately, the experimental evidence which has been accumulating lately on different materials does not seem to be consistent with MST and suggests that Langer's concerns were well founded. Fall 1993 SOME EXPERIMENTAL TESTS OF SELECTION THEORIES Two types of experiments yield results which are significantly different from those predicted by MST. I will try to describe both of these experiments, but I will concentrate more on the forced convection ex periments carried out by my research group. Be cause we had worked on the theoretical problem of including forced convection in the melt, my students and I naturally were interested in performing ex periments under conditions which corresponded as closely as possible with the assumptions we made to obtain forced convection solutions of Eq. (1). Forced convection experiments seemed attractive because they introduced the velocity of the melt at a large distance from the crystal, which is a new quan tity, U, that can be varied independently of AT. As usual, these experiments proved to be more diffi cult and time consuming than we originally thought they would be. First, we wanted to study a material whose prop erties were well known so that we could reproduce previous results for U~ = 0 before attempting to do something entirely new. Second, the material (succinonitrile) which we settled on had to be ultrapure (99.999% or better) and was extremely expensive at the time. Therefore we had to think small in designing an apparatus. Third, we realized that our forced convection velocities, U, would have to be very well defined and large enough to render natural convection negligible. Fourth, the melt had to be transparent because we wanted to track the crystalmelt interface and measure precisely both the growth rate and the tip radius in real time. Fifth, we would have to photograph and make video tapes of the experiments to enhance our understand ing of the physical processes involved. Sixth, we would have to control the temperature of the growth cell to extremely close limits. The solutions to these and other problems are described in a thesis by Lee'[" which had significant contributions by Ananth (who was working with me as a post doc at the time). In forced convection experiments on crystal growth, one has to deal with three different velocities: VG, Us, and U.. It is important to understand clearly the meaning of each because they all exist simulta neously. In our experiments we observed the shape of the interface of the dendrite which we character ize by the tip radius, R, the motion of the interface denoted by the velocity VG, and the velocity of the melt with respect to a fixed frame of reference, U,. We could not observe or measure the velocity due to natural convection, UN. Therefore we used theory to estimate it and conducted our experiments so that UJUN and UJVG ranged up to about 40 and 300, respectively, as indicated by Gill, et al.[251 The apparatus in which the forced convection ex periments were carried out is described in detail by Lee1241 and is shown in Figure 4. The basic idea is to keep stationary the capillary from which the crystal emerges and to have the cell containing about 100 cm3 of SCN move so that it creates a rigid body motion of the melt relative to the crystal over the range 0 < U_ < 1 cm/sec. The cell is operated in a constanttemperature bath which is controlled to 0.001 K, and after purification the SCN re mains hermetically sealed throughout the experi ments. The patterns formed by the dendritemelt interface are observed through a microscope and recorded on video film. The measurements of VG and R deviated from their mean values by less than 2.5% and 5%, respectively. The goals of this work were to measure various characteristics of the dendrite, including VG, R, dis tance from the tip to the first sidebranch, distance between sidebranches, and other quantities, as func tions of the undercooling, AT, and the forced convec tion velocity, U, which can be varied independently. However, here I shall discuss only the steady state measurements of VG and R and their implications when they are combined to obtain o*, which is de fined in Eq. (2). In this way we can obtain o*=o*(AT,U,) (3) The results obtained by Lee, et al., 22] show that V increases and R decreases monotonically with bot] AT and UI. All four of the quantities (VG, R, AT, an U,) were measured in our experiments. There fore we were able to determine if VG increases more or less quickly than R2 decreases, and this shows how VGR2 behaves either with AT or U,. In this way one can establish experimentally the behavior of the selection parameter, o*, as a function of (AT, U). By determining the dependence of r* on (AT, U,), we can test one of the basic pre dictions of microscopic solvability theory. Bouissou and Pelce[261 used microscopic solvabil ity theory to calculate this dependence, and they reported that o* decreases with increased (UJVG), which is the opposite of what the ex periments of Gill, et al.,[251 and Lee, et al.,1221 show. Figure 5 displays the measured values of Y* as a function of UJVG. In Figure 5 we see that o* increases by more than 50% as UJV, increases, as shown by Gill, et al.1251 Since this behavior is contrary to that pre dicted by the twodimensional analysis of Bouissou and Pelce, it appears that microscopic solvability theory does not predict even qualitatively the cor rect dependence of o* on U_ for SCN. A more dra matic contrast between theory and experiment is shown by Lee, et al.,[221 in their Figure 4 in which the slope of the data is negative and opposite to the prediction of MST. Let us now consider the growth in quiescent melt of dendrites other than SCN and attempt to deter mine ifMST predicts the proper dependence ofo* on the anisotropy, e. Muschol, et al., made careful mea surements of e, and we shall outline briefly only their results and the information needed to under stand them qualitatively. The GibbsThompson equa tion for a cubic crystal can be written Ti = T[1(y +yee) / L] (4) where y surface tension y7e second derivative of y with the angular coordi nate, e 0 measures position around the surface of the dendrite K total curvature L heat of fusion Tm melting point of a flat surface T. local interfacial temperature If the surface tension is represented by y= Yo[l+em cos me] combining Eqs. (4) and (5) obtains the tion G h d (5) approxima Ti=Tm 2 T[1 acosme] (6: RL Figure 5. Selection parameter, a* = (2ad,)/(VGR2) for SCN den drites increases by more than 50% as ratio of forced convection velocity, U,, to growth velocity, V,, increases. Chemical Engineering Education AT 0.035 0.230 cm 0 0.346 0.1 X 0.772 A 1.000 0.030 0 O S.(2a do 0 0.025 V 0.020  0.015 II III 0 50 100 150 200 250 U, V 0.0195 300 where R mean value of the tip radius a anisotropy factor used by Mushol, et al.[21] In Eq. (5), a is related to em by a = (m21)em. As pointed out by Glicksman and Marsh, (who subse quently made similar comparisons to those of Mushol, et al.) Eq. (6) shows that the equilibrium melting point at a point on an anisotropic solidliquid inter face depends on both its curvature and the orienta tion of the interface normal with respect to the prin cipal crystallographic axes. Mushol, et al., computed theoretical values for the selection parameter, ao, based on various MST ana lytical models and numerical codes for materials for which a had been measured. The results were disap pointing, and they concluded (as did Glicksman and Marsh) that the predictions of MST do not agree well with the available experimental evidence for dendrites grown in quiescent melts. Therefore, it seems that both forced convection experiments (UI > 0) with SCN[22'25J and experiments on the rela tionship of o* with E for other materials including alloys, do not support MST. It would appear that something fundamental is missing from the theory. CONCLUDING REMARKS Where does this leave us? Where do we go from here? It is obvious that great progress has been made in developing new materials, and this pro gress has been aided and abetted by a continually expanding body of experimental and theoretical knowledge about crystal growth. Furthermore, the available experiments have been getting more pre cise, which is important when testing new ideas and insights. Indeed, one can expect that as new ex periments accumulate, they will suggest new theo retical concepts, as has been the case in virtually all fields of science. Also, incredibly fast computers and intriguing mathematical methods have been developed which will facilitate the integration of theory and experiments. It is impossible to predict just when a fully satis factory, predictive theory of dendritic growth will be available. I doubt it will take another 350 years, as apparently has been required to prove Fermat's last theorem. When it arrives, new doors no doubt will open up, and it probably will be helpful in control ling the microstructure of even more useful and ex otic materials. In the meantime, there is a need for precise experiments on multicomponent materials of practical importance. Based on past experience, I think such experiments will stimulate new develop Fall 1993 ments of technological importanceand deeper theo retical understanding as well. ACKNOWLEDGMENT Work on this article was supported in part by the New York State Energy Research and Development Authority and by the New York SEMATECH Center of Excellence at Rensselaer. REFERENCES 1. Huppert, H.E., J. Fluid Mech., 212 209 (1990) 2. Davis, S.H., J. Fluid Mech., 212, 241 (1990) 3. Brown, L.A., AIChE J., 34, 881 (1988) 4. Glicksman, M.E., and S.P. Marsh, 'The Dendrite," in Hand book of Crystal Growth, D.T. Hurle, ed., North Holland, New York (1993) 5. Dash, S.K., and W.N. Gill, Int. J. Heat and Mass Trans., 27, 1345 (1984) 6. Ananth, R., and W.N. Gill, Chem. Eng. Commun., 68, 1 (1988); J. Crys. Growth, 91, 587 (1988), 108, 173 (1991); J. Fluid Mech., 208, 575 (1989) 7. Saville, D., and J.P. Beagleton, Phys. Rev., A37, 3423 (1988) 8. Ananth, R., PhD Thesis, State University of New York at Buffalo, NY (1988) 9. BenAmar, M., P.H. Bouissou, and P. Pelce, J. Crys. Growth, 92, 97 (1988) 10. Lagerstrom, P.A., and J.D. Cole, J. Rat. Mech. Anal., 4, 817 (1955) 11. Lagerstrom, P.A., High Speed Aerodynamics and Jet Pro pulsion, Vol IV (ed., F.K. Moore), Princeton University Press, Ch. 2 (1964) 12. Huang, S.C., and M.E. Glicksman, Acta Met., 29, 701, 717 (1981) 13. Fujioka, T., PhD Thesis, CarnegieMellon University (1978) 14. Tirmizi, S.H., and W.N. Gill, J. Cryst. Growth, 96, 277 (1989) 15. Koo, K.K., R. Ananth, W.N. Gill, Phys. Rev., 44A, 3782 (1991); AIChE J., 38, 945 (1992); Phys. Rev. E., "Comments on SurfaceTensionAnisotropy Measurements of Succinonitrile and Pivalic Acid: Comparison with Micro scopic Solvability Theory," in press (1993) 16. Canright, D., and S.H. Davids, J. Cryst. Growth, 114 153 (1991) 17. Glicksman, M.E., R.J. Shaefer, and J.D. Ayers, Metal. Trans., A7, 1747 (1976) 18. Langer, J.S., and H. MullerKrumbhaar, Acta. Metal., 26, 1681, 1689, 1697 (1978) 19. Oldfield, W., Mat Sci. and Eng., 11 211 (1973) 20. Kessler, D.A., J. Koplik, and H. Levine, Adv. Phys., 37, 255 (1988) 21. Muschol, M., O. Liu, and H.Z. Cummins, Phys. Rev., A46, 1038(1992) 22. Lee, Y.W., R. Ananth, and W.N. Gill, "Selection of a Length Scale in Unconstrained Dendritic Growth with Convection in the Melt," J. Cryst. Growth, in press (1993) 23. Langer, J.S., in Chance and Matter, 629, eds J. Souletie, J. Vannimenus, and R. Stora, North Holland, New York (1987); Science, 243, 1150 (1989); Physics Today, 24 October (1992) 24. Lee, Y.W., PhD Thesis, Rensselaer Polytechnic Institute (1991) 25. Gill, W.N., Y.W. Lee, K.K. Koo, and R. Ananth, "Interaction of Thermal and Forced Convection with the Growth of Den dritic Crystal," p. 93 in Interactive Dynamics of Convection and Solidification, NATO ASI Series, Kluwer Academic Publishers, S.H. Davis, et al., eds (1992) 26. Bouissou, P., and P. Pelce, Phys. Rev., A40, 6673 (1989) O 205  class and home problems The object of this column is to enhance our readers' collection of interesting and novel problems in chemical engineering. Problems of the type that can be used to motivate the student by presenting a particular principle in class, or in a new light, or that can be assigned as a novel home problem, are requested, as well as those that are more traditional in nature and which elucidate difficult concepts. Please submit them to Professors James 0. Wilkes and Mark A. Burns, Chemical Engineering Department, Univer sity of Michigan, Ann Arbor, MI 481092136. THERMODYNAMICS AND COMMON SENSE OCTAVE LEVENSPIEL Oregon State University Corvallis, OR 973312702 Though it is one of science's grandest pure logic structures which awes and enraptures its faithful, thermodynamics unfortunately causes much grief for the student who is studying the subject. Why? Let's look at a simple situationthat of a batch system of internal energy U going from state 1 to state 2. Here we see written in all texts AU= QW (1) But if the system is raised or lowered (potential energy change, AEp), speeded or slowed (kinetic energy change, AEk), or swelled or shrunk (expan sion work, Wpv) then the above first law expres sion becomes more generally Octave Levensplel is author of four chemi cal engineering texts. One of them is over thirty years old but is still widely used and has been translated into ten languages. Another, his favorite and funniest, is practi cally unknown today. Octave is now a re tired (emeritus) professor, enjoying him self and struggling to understand thermo dynamics. AU+ AEp + AEk= Q Whaft Wpv (2) Clear? Do you accept this? Yes? GOOD! Let us apply this to a column of isothermal ideal gas, such as air, at equilibrium. What hap pens to the pressure as a chunk of this gas is raised slowly from elevation Z, to elevation Z,? Applying the above general first law expression, noting that AU = 0 at constant temperature, we find 2 + AEp + A4k =9sXhaft JpdV (3) 1 Now, for an isothermal ideal gas we can write nRT P V V2 P1 V1 P2 so for a mass m (or n moles) of gas raised from Z, to Z, we get Copyright ChE Division ofASEE 1993 Chemical Engineering Education 2 mg(Z2 Z) nRT dV gc V 1 and, since the molecular mass mw = n Z2 l 'P2V2 column of isothermal volume ideal gas changes at equilibrium z / / piVi Zo=O  Fall 1993 rearranging gives, finally g(Z2 Z) = RTn P2 (4) mw Pl This is an interesting expression. Look at the lefthand side. It is positive, so the righthand side must also be positive. This means that P2 > Pi!! What this says is that as you climb a mountain the air gets thicker, contrary to experience. What kind of nonsense is this? Results like this remind me of the story"1 of the great physicist Arnold Sommerfeld, who had written a series of books on various topics in physics. When asked why he hadn't written one on thermodynamics, he is supposed to have said It's a funny subject. The first time you go through it you don't understand it at all. The second time through you think you do except for one or two minor points. The third time you know you don't un derstand it, but by then you are so used to it, it doesn't bother you. At the time he was killed in an accident, the physicist was in the middle of writing a book on ... guess what? Yesthermodynamics! To get back to the problem, thoughwhere is the error? Please help me straighten out this curious conclusion. REFERENCE 1. Angrist, S.W., and L.G. Helper, Order and Chaos, Ba sic Books, page 215 (1967) This gem of a book is unique, contains only three equations, and makes thermo al most fun. The author welcomes comments and solutions to this problem. A later issue of CEE will list those who have saved thermodynamics from disgrace. 207 LEARNING THROUGH DOING A Course on Writing a Textbook Chapter PHILLIP C. WANKAT Purdue University West Lafayette, IN 47907 People learn best when they become involved in the process of doing something.[1] While actually working on a project, there is great motivation to learn those things that are needed to finish the project.[2' Properly organized projects which allow students to function as engineers and to re ceive feedback are an excellent teaching method. In the course described in this paper, graduate students completed projects which required them to perform one of the functions of a chemical engineer ing professorwriting an advanced textbook chap ter. The idea for a seminar course in this form came from a book by Eble,[31 and the result was a course wherein the students worked harder and learned more than the professor. This is in stark contrast to a "normal" course where the professor works harder and learns more than the students. THE COURSE The course was titled "Seminar in Separation Re views," but the methodology can be used for any technical topic. The prerequisite for the course, an advanced class in ChE separations, ensured that time did not have to be spent teaching basics. Since this was a graduatelevel elective, it was not necessary to cover a specific body of material, and the students could pick their own topic. This proce dure has the advantage that the students cannot later blame the instructor if their topic proves to be difficult for them. The seminar was advertised to all students who met the prerequisites, and four students eventually registered. Two other students were interested but could not take the course because of schedule conflicts. A larger class could easily be taught (see "Possible Course Modifications" appearing at the end of this article). The students were told to produce a professional quality textbook chapter on an advanced topic in separations. To make sure that writing was done for this course, the topic could not be on the subject of their thesis research. This requirement meant that everyone started with a very modest knowledge base of the chosen topic. This mimics industrial practice where engineers are often assigned projects in areas outside of their expertise. The topic had to come from a list of over fifty separations, the chapter was to be written at the graduate level, and the students were to work in teams of two. The course grade was based on this project. During the first class meeting I introduced the course objectives and rules and presented an over view of separations. In the second class, the stu dents analyzed the structure of a separations text book to determine what is typically included in a textbook chapter. They concluded (with my help) that the following sections are necessary: introduc tion; body, with appropriate figures and tables; examples, including some for real systems; sum mary; notation; references; and homework, with a separate solution manual. In the third class the students critiqued a recent paper from the literature. Fortunately, the paper chosen by the professor had several flaws, and a lively discussion developedthe flaws made it clear that not all papers are created equal. The students were then given a list of journals which included papers on separations, and they were told to skim through several to obtain topic ideas. They came to class with a list of three topics. We spent much of the fourth class period in team ing up students who had an interest in working Chemical Engineering Education Phil Wankat received his BSChE from Purdue and his PhD from Princeton. He is currently a professor of chemical engineering at Purdue University. He is interested in teaching and coun seling, has won several teaching awards at Purdue, and is Head of Freshman Engineering. His research interests are in the area of separa tion processes, with particular emphasis on cy clic separations, adsorption, preparative chro matography, and simultaneous fermentation and separation. Copyright ChE Division ofASEE 1993 together, and this was eventually accomplished to everyone's satisfaction. The remainder of the period was consumed by a minilecture on the different work styles for doing big projects. For example, some engineers prefer to do the work serially by first collecting all the information, then doing cal culations, and then writing the report. Others pre fer parallel processing and mix their work on the different aspects. A librarian from the engineering library gave three lectures on manual and computer library search methods. To get started, the teams worked with the librarian on performing computer searches using Dialog. The groups were required to do a patent search and to include patents in their bib liographies. Once they had learned how to do computer searches, the students did their searches independently. We spent much of the remainder of the semester in individual group meetings. I met with each group for twentyfive minutes during the regularly scheduled class meetings, and since each group met with me three times during the week, procrastination was not a problem. On a few occasions the students told me that they had not had time to do any work since the previous meeting, but this never happened twice in a row. I used the group meetings to discuss tech nical points and work habits. One work habit that both groups needed assis tance with was how to efficiently read journal ar ticles. The students had a tendency to try to read all of the papers thoroughly in an effort to completely understand each article. So we had a discussion on how all papers are not of equal importance. I illus trated the concept of triage to themthat through skimming, papers can quickly be classified into three piles: important, possibly important, and unimpor tant. Since only the important papers need to be read carefully, triage can save considerable time. Later in the semester I used the group meetings to discuss the outlines, the written sections, the ex amples, and the homework problems. On occasion, when I felt the students were overwhelmed, the group sessions became pep talks. This kind of support fa cilitates learning.[1,21 I dispersed other class activities throughout the semester. Once the students had read a reasonable number of articles, I critiqued their notes on the articles. I found that, almost invariably, the stu dents were not keeping complete enough reference citations. Each group presented two informal progress reports to the class during the semester. In addition to serving as informal communication practice, these Fall 1993 reports forced the students to integrate their progress and see what else had to be done. After midterm break and shortly before the chap ter outlines were due, I gave a lecture on organizing papers and writing, following the ideas of Peter El bow.14' Briefly stated, Elbow's idea is that writers should do the first draft as quickly as possible, and then rewrite and rewrite. Toward the end of the semester a technical communication expert gave a lecture on common mistakes in written English and a lecture on oral presentations. I gave a mini lecture on critiqueing papers after the students turned in their first drafts. In addition to the two informal progress reports, I used a series of partial assignments on the project in an effort to prevent procrastination. A couple of weeks after the midterm break the teams turned in a detailed outline of their chapters which I quickly returned to them with extensive comments on what could be deleted and what should be added. Then a first draft of the entire chapter (without homework) was turned in and was critiqued by both myself and the other student teamI told the students to read the chapter and to respond as students who were trying to learn the material. The teams then com pleted a final version of the chapter which corrected the rough draft. The final draft was due on the last class day of the semester, and during finals period each group gave a formal oral presentation. THE PROFESSOR'S DUTIES In this class, the professor's duties differ from those in a normal lecture class. The professor must Develop the class schedule and arrange for the guest lecturers Present three of the eight lectures Lead the discussion on book chapters, critique the literature article, and critique the first drafts Develop an extensive list of acceptable topics and set the criteria for acceptable projects Serve as a facilitator for selection of groups and topics Read and grade the first drafts and the final chapter plus the solution manual Listen to and grade the oral reports Serve as a consultant and listen, question, encour age, and prod during the remaining thirty class periods (Perhaps the most important) Set the tone that the students could and would produce a professional quality chapter. Since little preparation time was needed, during most of the semester I averaged about four hours a week on this course. This number increased, how ever, during the two weeks that reports were graded. Overall, the professor's workload in a class of this type is so low as to be almost sinful. Yet, the stu dents learned a lot and the class was very success ful! Student learning depends much more on how hard the student works than on how hard the pro fessor works. Since I was able to focus most of my attention on the students instead of on the material, they received much more personal atten tion than normal. This class was also fun to teach. The students all worked hard in a positive and en couraging atmosphere. The professor's technical knowledge plays a defi nite role, but it is not as obvious as it is in a lecture class. An experienced professor can quickly tell when the students are getting bogged down on relatively unimportant points; he can look at their chapters and evaluate how a student who did not know the material would react to it; he can see when the students are developing reasonable knowledge struc tures and including most of the important material; he can understand the text material, the examples, and the homework problems and thus can evaluate them even though he may not have read many of the cited papers. In my opinion, it would be extremely difficult to teach a class like this if the professor is not an expert in the general topic. THE STUDENT REACTIONS The students all became very involved in this course. They invested too much time on their projects and had to work to keep the chapters manageable. They thought that learning how to do library searches was extremely useful and ex pressed the wish that they had learned how to do this sooner. The following quote from Quarderer is appropriate: "Four to six weeks in the lab can save you an hour in the library.""[5 The students also thought that writing was useful, but difficult. The difficulty involved in developing good homework and example problems surprised them. They found that writing a problem requires better understanding than they could get from merely reviewing the literature. The students chose to write on Reactive Distilla tion and on Supercritical Fluid Extraction of Solids. The first topic was almost ideal for this course. There are enough references, but not so many as to over whelm the students. The material is not covered in any depth in existing distillation texts, but is of considerable industrial and academic interest. As pen Plus was used to develop example and home work problems and solutions. The second topic was much more of a challenge, mainly because of the huge number of references (almost 19,000 were identified in the computer search). This team had more difficulty in limiting their chapter and in finding appropriate data for examples and homework. They eventually decided to focus on coffee decaffeination since it is the most important industrial process and since there is more information available on this process than on others. They also wrote their own computer programs to solve some of the examples and homework problems. The reports were excellent as student papers and would be acceptable, but not outstanding, as profes sional contributions. After one semester of studying a topic, the students' knowledge base remained thin. This was evident from their inability to critically evaluate the work they were reporting on and from their difficulty in writing good examples. Student evaluations showed that half the students agreed, and half strongly agreed, with the statement that this was among the best courses they had ever taken. Three of the students strongly agreed, while one student was undecided, about the statement that this instructor was among the best teachers they had known. Since the professor did not teach in the traditional sense, it is difficult to interpret this result. In general, the students thought the course was intellectually fulfilling, that it contributed signifi cantly to their professional growth, and it provided a good background for further study. They also put a lot of effort into the class, were satisfied with their accomplishments, and thought they had done well. POSSIBLE COURSE MODIFICATIONS By putting the students into groups of three, one professor could handle up to twelve students. Group meetings with the instructor every other class meeting (that is, three times every two weeks) for twentyfive minutes should be sufficient. With three people in the group, students would still receive significant individual attention. The effort required to grade projects would double with four groups, but grading only occurred twice during the semester. The basic format should be retained with this num ber of students, including the checkpoints used to minimize procrastination. The students suggested requiring, or strongly en couraging, all new students to take this course dur ing their second semester. At this point in their studies, new students have chosen a thesis project and a major professor, so the textbook chapters could be written on their thesis topics. Because of the Chemical Engineering Education broad range of topics involved, however, one profes sor could not teach the course without assistance. The professor in charge could serve as a course coor dinator and could present the lectures, while other professors would be involved in working with the groups containing their new students. This proce dure would structure the process of learning how to do library research, it would give the students a chance to get a good start on understanding the literature in their research area, and it would pro vide an early opportunity to improve communication skills. During the process of developing their chap ters (particularly the examples and the homework) most students will obtain a good picture of what needs to be done in a given area, and the net effect should be a faster start in research. The difficulties of a teamtaught course include ensuring uniformity in the group meetings and in grading. In addition, students who have not had a graduatelevel course in the general area of their topic may have extreme difficulty reading the litera ture. They would either have to delay taking the course or get extra help from their major professor. COMMENTS This course was unusual as a graduate course in chemical engineering since the focus was on learn ing the processes of doing library research and writ ing a book chapter instead of on learning specific knowledge. Since the students found their own sources and charted their own paths, there was very little structure for the technical material. But there was quite a bit of structure and support for the processes of doing library research and in develop ing a book chapter. This structure (deadlines, lec tures, and continual meetings) is probably necessary to prevent procrastination. Obviously, the students learned technical content in addition to the process. The content learned was in one narrow area, but with significant depth. A normal lecturehomeworktest course could probably cover at least twice as much content, but it is doubt ful that the students would learn the material as well, and they certainly would not learn howto learn as well as they did in this course. The original course plan was to ask students to write critical reviews. Discussions in the graduate committee convinced me, however, that this was inappropriate since the students did not have enough expertise to critically evaluate papers. So the course plan was changed to have the students write textbook chapters. In addition, the students would have to develop example and homework problems. Developing problems stretched the stu dents and forced them to learn material they might otherwise only half learn. Including problems also forced the students to write computer programs or to use simulation programs. Overall, asking the stu dents to write a textbook chapter is an excellent pedagogical approach. The students had to work in teams, and this, of course, follows normal industrial practice. In addi tion, the projects were too big to be done by a single student within a reasonable period of time, so the team members encouraged each other when the task appeared overwhelming (as it did midway through the semester). The members of one team worked very well together. Their chapter meshed well and it was not obvious which student wrote which section. The other team, however, needed significant encour agement to work together. For much of the semes ter, the group meetings with the professor served as this team's only point of contact. Their chapter showed a seam where the two parts were glued together. Of course, the presence of seams in multi author textbooks is not unusual. SUMMARY In this seminar course, the students became in volved in the processes of doing a literature search and in writing a textbook chapter. As a result of learning these processes, in the future they will be able to learn more efficiently on their own. The pro fessor functioned as a consultant rather than a lec turer, and the net result was that most of the effort and learning was done by the students. ACKNOWLEDGMENT The assistance of the engineering librarian, Ms. Jean Poland, and the technical communication ex pert, Dr. Frank Oreovicz, in teaching this course is gratefully acknowledged. Discussions with Profes sor Nick Delgass were crucial to the course design. The enthusiasm and participation of the students made the course a success. REFERENCES 1. Wankat, P.C., and F.S. Oreovicz, Teaching Engineering, McGrawHill, New York, Chaps. 1 and 15 (1993) 2. Rogers, C.R., Freedom To Learn, Charles E. Merrill, Colum bus, OH, Chap. 7 (1969) 3. Eble, IKE., The Craft of Teaching, 2nd ed., JosseyBass, San Francisco, CA, p. 102 (1988) 4. Elbow, P., Embracing Contraries: Explorations in Learning and Teaching, Oxford University Press, New York, Chaps. 2 and 3 (1986) 5. Felder, R.M. "Random Thoughts," Chem. Eng. Ed., 27(2) (1993) 0 Fall 1993 THE DU PONT TEACHING FELLOWSHIP PROGRAM 1991 Teaching Experiences Editorial Note: The DuPont Teaching Fellows Program was initiated in 1990 to complement the objectives of the DuPont Fellowship Program in chemical, mechanical, and electrical engineering. The Teaching Fellows Program was initiated to encourage highquality students to obtain PhD degrees and enter academia.. There were six DuPont Teaching Fellowships awarded in chemical engineering in 1991: Linda J. Broadbelt, Gregory S. Fisher, Walter M. Hart, Michael L. Luyben, Steven A. McCluney, and Ronald D. Shaver. DuPont teaching fellows were required to have responsibility for one undergraduate course. The following article describes the teaching experience of five of these students, written by the students themselves. We thank Professor TW Fraser Russell, who provided the inspiration, advice, and compilation of the material for this presentation. NAME: Steven A. McCluney DEPARTMENT: Chemical Engineering UNIVERSITY: Texas A&M University COURSE TAUGHT: "Chemical Engineering Reactor Design/Kinetics" NUMBER OF STUDENTS: 24 TEXT USED: Fundamentals of Chemical Reaction Engineering, by Charles D. Holland and Rayford G. Anthony; Prentice Hall Book Company, Publisher FACULTY MENTOR: Dr. Rayford Anthony NUMBER OF YEARS OF GRADUATE EDUCATION COMPLETED: 6 THESIS TOPIC: Modeling AC Impedance Behavior of Coated Electrodes THESIS ADVISOR: Dr. Ralph White faculty mentor several times during the semester, but, in general, I was solely responsible for prepar ing each lecture, and my lectures were not moni tored. Since my mentor coauthored the course text book, I had a clear guideline of the material I was expected to cover. I was also given examples of ex ams and course notes from previous semesters. On an average, I spent one to two hours preparing each lecture, depending on its content. I also worked each homework assignment so I would be able to explain the concepts as clearly as possible to the students. In summary, teaching an undergraduate course was a rewarding experience. I now have a greater respect for professors who work hard to be good teachers in addition to researchers. I hope to eventu ally have a career which will allow me to teach collegelevel courseseither as a college professor or as a guest instructor from industry. O Chemical Engineering Education Teaching an undergraduate course was an ex tremely valuable and enjoyable experience for me. I feel that in many ways I learned as much as I taught, and I was surprised to find that I still remembered a lot of the material that I had not used for several years. I also discovered that teaching a subject is the best way to become thoroughly familiar with it, both through preparing lessons and through trying to answer students' often indepth questions. Finally, I learned that teaching involves dedication and patience. In order to teach well, one must be willing to put in the necessary time to carefully prepare a lesson and to try to anticipate any questions which may be raised. One must also be willing to take the time to explain a concept clearly and at the students' level. I was given almost complete freedom in teaching the course; I discussed my teaching plans with my NAME: Ronald D. Shaver DEPARTMENT: Chemical Engineering UNIVERSITY: Oklahoma State University COURSE TAUGHT: "Introduction to Chemical Process Engineering" NUMBER OF STUDENTS: 24 TEXT USED: Elementary Principles of Chemical Processes, 2nd ed.; by Richard M. Felder and Ronald W. Rousseau; John Wiley & Sons, Inc., Publisher FACULTY MENTOR: Dr. Ruth Erbar NUMBER OF YEARS OF GRADUATE EDUCATION COMPLETED: 3.5 THESIS TOPIC: Equation of State Development for Equilibrium Predictions THESIS ADVISOR: Dr. KA.M. Gasem Having the opportunity to serve as a 199192 DuPont Teaching Fellow gave me some valuable insights into teaching at the college level. The course I taught was the sophomorelevel "Introduction to Chemical Process Engineering." Traditionally, chemical engineering attracts only the best students, and this course represents the first challenging course that most of them take. This teaching experience taught me how to properly orga nize a fastpaced engineering course and how to recognize when students properly understand the necessary concepts, as well as when they do not. Daily preparation for the course required much more time than I had originally thought it would. I found that not only must the lectures be presented in an organized, logical manner, but also that every possible question that may be asked by someone being exposed to the material for the first time must be anticipated. Throughout the semester I had the privilege of being able to consult the late Dr. Ruth Erbar about details of course organization and how to structure some special projects to ensure that the students obtained the maximum benefit and preparation for later courses. We often talked about the students' reactions to various situations; for example, we both felt that in order for students to best learn the cov ered topics, they should be pushed to the limit of their abilities. Although many students were ini tially intimidated by exams that challenged even the best students in the class, several of them com mented at the end of the course that the material they best understood was the material they initially had the most trouble comprehending. Throughout the course I maintained an opendoor policy and encouraged the students to come discuss any problems they might be having with the course material. There is a wonderful satisfaction in seeing students' eyes light up when they first truly under stand a concept that they've been struggling with, and even more joy in seeing students become excited about a topic and excelling beyond that which is required or expected of them. Being a DuPont Teaching Fellow was a wonderful experience, and I fully intend to pursue university teaching at some future point in my career. 0 NAME: Greg Fisher DEPARTMENT: Chemical Engineering UNIVERSITY: Michigan State University COURSE TAUGHT:" Material and Energy Balances" NUMBER OF STUDENTS: 52 TEXT USED: Elementary Principles of Chemical Processes, 2nd edition; by Richard M. Felder and Ronald W. Rousseau; John Wiley & Sons, Inc., Publisher FACULTY MENTOR: Dr. Alec Scranton NUMBER OF YEARS OF GRADUATE EDUCATION COMPLETED: 5 THESIS TOPIC: The Effect of Interphase Composition on Adhesion in Polyphenylene Sulfide/Carbon Fiber Composites THESIS ADVISOR: Dr. Lawrence T. Drzal The time I spent as a DuPont Teaching Fellow was time well spent. The experience was overwhelm ingly positive, both as an introduction to college level lecturing and in organizing familiar material into a package that beginners could understand. I actually received instruction from my faculty men tor the term before I taught the course when I served as his teaching assistant. This enabled me to be completely on my own during the time I taught the course, heightening the experience even more for me. Teaching the course required approximately ten to fifteen hours a week. The help of a teaching assistant and two homework graders allowed me to concentrate on writing and giving lectures, on writ Fall 1993 ing exams, and on assigning grades. It was disappointing to discover that some stu dents expected a 3.0/4.0 grade "just for showing up," and that often the students who needed extra help the most were the very ones to request it too late. On the other hand, I was delighted to find that many students were eager to learn the material, that some of the students who struggled in the beginning worked hard and did well in the end, and that estab lishing a good rapport with most of the students was relatively easy. The most difficult part of teaching the course was designing a fair grading scale, and keeping as many of the students as possible involved in lectures pro vided another challenge. Working with the students to help them learn was the most rewarding aspect of teaching the course. I enjoyed the teaching experience a great deal and would like to pursue a career in teaching after gain ing some industrial experience. Since chemical engineering is such an applied field, I believe stu dents appreciate instructors who have actually worked in industry. I believe the DuPont Teaching Fellows program is a worthwhile program and truly appreciate the op portunity I had to participate in it. O NAME: Michael Luyben DEPARTMENT: Chemical Engineering UNIVERSITY: Princeton University COURSE TAUGHT: "Introduction to Chemical Engineering" NUMBER OF STUDENTS: 45 TEXT USED: Elementary Principles of Chemical Processes, 2nd ed., by Richard M. Felder and Ronald W. Rousseau; John Wiley & Sons, Inc., Publisher FACULTY MENTOR: Dr. S. Sundaresan NUMBER OF YEARS OF GRADUATE EDUCATION COMPLETED: 4 THESIS TOPIC: A MultiObjective Optimization Approach for Analyzing the Interaction of Design and Control THESIS ADVISOR: Dr. C.A. Floudas My service as a DuPont Teaching Fellow in 1991 at Princeton University provided a valuable oppor tunity for me to learn about teaching. The course I taught, "Introduction to Chemical Engineering," con tained material with some approaches, terminology, and jargon which were unfamiliar to the first and secondyear undergraduates, and it was important to remember and consider this when I was planning classes and answering questions. The course challenged me to communicate ideas as clearly and enthusiastically as possible, since suc cess in this respect usually engaged the students' intellectual curiosity and challenged them to think clearly and independently. Teaching involves not so much an imparting of information as it does training students' minds to think critically and teaching them to approach problems both systematically and creatively. Such a goal demands a lot of practical experience, and this opportunity to teach gave me that experience. The course culminated in a casestudy project which required the students to work in groups and to tie together all of the material they had learned in the course. This gave them a better perspective on the type of analysis used in chemical engineering and demanded more sophistication in applying general principles to a problem that was larger than the weekly homework assignments to which they were accustomed. The students seemed to think this was a helpful survey of the course material and it proved to be a valuable educational tool. I cannot make generalizations about how students learn since each of them is an individual. Some of them understand the subject quickly just by read ing the book, while some learn from doing the homework assignments and still others have to come by the office and ask questions to clarify the material. The real teaching challenge lies in finding an appropriate balance of difficulty in the course material. Many students have a lot of pressure on them with their coursework load, and it compounds the problem when universities place so much em phasis on research rather than on teaching. The DuPont Teaching Fellows Program contributes sig nificantly to support teaching ability and works to counteract this trend. The course required three to four hours a week of lecture preparation; I also spent quite a bit of addi tional time with the individual students, answering questions. The faculty mentor for the course occa sionally attended class while I taught, and at least once a week we discussed teaching, course material, and overall plans. I would like to again thank DuPont for providing this opportunity for me to gain undergraduate teach ing experience. I found that I greatly enjoy teaching Chemical Engineering Education and want to pursue it as a career. I feel it will be a challenging and rewarding occupation. DuPont has generously provided the support and encouragement for me and for other graduate students in chemical engineering to consider careers in teaching through their Teaching Fellows Program. 0 NAME: Linda J. Broadbelt DEPARTMENT: Chemical Engineering UNIVERSITY: University of Delaware COURSE TAUGHT: "Chemical Engineering Kinetics" NUMBER OF STUDENTS: 20 TEXT USED: Chemical Reaction Engineering, 2nd ed., by Octave Levenspiel; John Wiley & Sons, Publisher FACULTY MENTOR: Dr. TW Fraser Russell NUMBER OF YEARS OF GRADUATE EDUCATION COMPLETED: 3 THESIS TOPIC: Thermal Degradation of High Performance Polymers and Integration of Structure, Reactivity, and Property THESIS ADVISOR: Dr. Michael T. Klein The experience I had as a DuPont Teaching Fellow was extremely positive and reinforced my desire to pursue a teaching career. It also forced me to in crease my knowledge of reaction engineering and kinetics. Most importantly, it revealed to me that it is quite different to be up in front of the class teach ing a course than it is to sit at a desk and listen! Teaching style is directly related to an individual's personality. I found I was most comfortable when I did not try to adopt someone else's style and just acted naturally. I learned a great deal, however, from watching and listening to Drs. Russell and Orbey when they taught. I found that inclass problem sessions were invalu able. The problems generated excellent class discus sion and dramatically reinforced learning while at the same time providing ample opportunity for stu dentteacher interaction. It also prevented a mo notonous, longwinded monologue at the blackboard. I had the benefit of sitting in Dr. Orbey's lecture in advance of mine. The course was taught in two 20 student sections. This allowed me to improve my own grasp of the material, and more importantly, to assess the students' responses to the various facets of the lecture. Dr. Russell sat in on most of my lectures and gave me excellent feedback about my style and the students' reactions. He was also an invaluable resource during a lecture, providing knowledge and insight from his years of experience. Having such an active and interested mentor was the most crucial element in making my teaching experience so rewarding and successful. I also received invaluable feedback from the stu dents. It was not hard to determine when a certain approach was successfulthe students were not afraid to participate in discussions or to voice their frustrations when they had them. They enjoyed the inclass problems and felt they were beneficial to learning the material. They also voiced appreciation of any extra effort I expended, such as long office hours, help sessions, etc., and took advantage of any help I offered. I found that one of the most important elements of establishing good rapport with the stu dents was knowing and calling them by name. A more negative facet was that teaching reminded me what it was like to be an undergraduate student, when the end goal was not necessarily the learning or the acquired knowledge, but the grade received. Students frustratingly begged for additional points, asked for extensions on their homework, com plained about unfair or difficult exams, or lamented the poor choice of a textbook. I had to remind myself that only hard work earns a high grade and that learning is always the ultimate goal. I found assign ing grades at the end of the course to be the most difficult part of teaching. It was hard not to let an element of subjectivity to creep into the grade of a student with whom I had significant personal inter action. While there is room in the grading system for effort expended and class participation to be consid ered along with reliance on numerical analysis of exams and homework, I tried not to let personal feelings cloud my judgment. The time commitment involved was immense and involved preparing lectures, exams, and interesting homework in addition to studentteacher interaction outside of class. I had the benefit of two excellent mentors who made all the tasks much easier and less time consuming. I estimate that we spent two or three hours a week discussing lecture preparation, class material, exam preparation and grading, and teaching style. I feel very fortunate to have been a part of the DuPont Teaching Fellows program. My mentors were exceptional and contributed greatly to making the experience so rewarding. 0 a Fal19 1 215 Fall 1993 n The 0Wjzv;271tY DEPARTMENT OF CHEMICAL ENGINEERING GRADUATE PROGRAM Graduate assistant stipends for teaching and research start at $7,800. Industrially sponsored fellowships available up to $17,000. In addition to stipends, tuition and fees are waived. Ph.D. students may get some incentive scholarships. The deadlinefor assistantship applications is February 15th. FACULTY RESEARCH INTERESTS G. A. ATWOOD1 G. G. CHASE H. M. CHEUNG S. C. CHUANG J.R. ELLIOTT L. G. FOCHT K. L. FULLERTON M. A. GENCER2 H. L. GREENE' L.K.JU S. LEE D. MAHAJAN2 J. W. MILLER2 H. C. QAMMAR C. K. RIEW2 R. W. ROBERTS1 N.D. SYLVESTER M. S. WILLIS Digital Control, Mass Transfer, Multicomponent Adsorption Multiphase Processes, Heat Transfer, Interfacial Phenomena Colloids, Light Scattering Techniques Catalysis, Reaction Engineering, Combustion Thermodynamics, Material Properties Fixed Bed Adsorption, Process Design Fuel Technology, Process Engineering, Environmental Engineering Biochemical Engineering, Environmental Biotechnology Oxidative Catalysis, Reactor Design, Mixing Biochemical Engineering, Enzyme and Fermentation Technology Fuel and Chemical Process Engineering, Reactive Polymers, Waste CleanUp Homogeneous Catalysis, Reaction Kinetics Polymerization Reaction Engineering Hazardous Waste Treatment, Nonlinear Dynamics Reactive Polymer Processing Plastics Processing, Polymer Films, System Design Environmental Engineering, Flow Phenomena Multiphase Transport Theory, Filtration, Interfacial Phenomena 'Professor Emeritus 2 Adjunct Faculty Member Cooperative Graduate Education Program is also available. For Additional Information, Write * 216 Chemical Engineering Education FIAT LUX o1870 CHEMICAL ENGINEERING PROGRAMS AT THE UNIVERSITY OF ALABAMA The University of Alabama, located in the sunny South, offers excellent programs lead ing to M.S. and Ph.D. degrees in Chemical Engineering. Our research emphasis areas are concentrated in environmental studies, reaction kinetics and catalysis, alternate fuels, and related processes. The faculty has extensive indus trial experience, which gives a distinctive engineering flavor to our programs. For further information, contact the Director of Graduate Studies, Department of Chemi cal Engineering, Box 870203, Tuscaloosa, AL 354870203; (2053486450). FACULTY G. C. April, Ph.D. (Louisiana State) D. W. Arnold, Ph.D. (Purdue) W. C. Clements, Jr., Ph.D. (Vanderbilt) R. A. Griffin, Ph.D. (Utah State) W. J. Hatcher, Jr., Ph.D. (Louisiana State) I. A. Jefcoat, Ph.D. (Clemson) A. M. Lane, Ph.D. (Massachusetts) M.D. McKinley, Ph.D. (Florida) L. Y. Sadler III, Ph.D. (Alabama) V. N. Schrodt, Ph.D. (Pennsylvania State) RESEARCH INTERESTS Biomass Conversion, Modeling Transport Processes, Thermodynamics, CoalWater Fuel Development, Process Dynamics and Control, Microcomputer Hardware, Catalysis, Chemical Reactor Design, Reaction Kinetics, Environmental, Synfuels, Alternate Chemical Feedstocks, Mass Transfer, Energy Conversion Processes, Ceramics, Rheology, Mineral Processing, Separations, Computer Applications, and Bioprocessing. An equal employment/equal educational opportunity institution. Fall 1993 THE UNIVERSITY OF ARIZONA STUCSON, AZ The Chemical and Environmental Engineering Department at the University of Arizona offers a wide range of research opportunities in all major areas of chemical engineering and environmen tal engineering, and graduate courses are offered in most of the research areas listed below. The department offers a fully accredited undergraduate degree as well as MS and PhD graduate degrees. Strong interdisciplinary programs exist in bioprocessing and bioseparations, microcontamination in electronics manufacture, and environmental process modification. Finan cial support is available through fellowships, government and industrial grants and contracts, teaching and research assistantships. THE FACULTY AND THEIR RESEARCH INTERESTS ROBERT ARNOLD, Associate Professor (Caltech) Microbiological Hazardous Waste Treatment, Metals Speciation and Toxicity JAMES BAYGENTS, Assistant Professor (Princeton) Fluid Mechanics, Transport and Colloidal Phenomena, Bioseparations, Electrokinetics MILAN BIER, Professor (Fordham) Protein Separation, Electrophoresis, Membrane Transport CURTIS W. BRYANT, Associate Professor (Clemson) Biological Wastewater Treatment, Industrial Waste Treatment WILLIAM P. COSART, Associate Professor (Oregon State) Heat Transfer in Biological Systems, Blood Processing EDWARD FREEH, Adjunct Professor (Ohio State) Process Control, Computer Applications JOSEPH GROSS, Professor Emeritus (Purdue) Boundary Layer Theory, Pharmacokinetics, Microcirculation, Biorheology ROBERTO GUZMAN, Assistant Professor (North Carolina State) Protein Separation, Affinity Methods BRUCE E. LOGAN, Associate Professor (Berkeley) Bioremediation, Biological Wastewater Treatment, Fixed Film Bioreactors Tucson has an excellent climate and many recreational opportuni ties. It is a growing modern city of 450,000 that retains much of the old Southwestern atmosphere. For further information, write to Chairman, Graduate Study Committee Department of Chemical and Environmental Engineering University of Arizona Tucson, Arizona 85721 The University of Arizona is an equal opportunity educational institution/equal opportunity employer. Women and minorities are encouraged to apply. KIMBERLY OGDEN, Assistant Professor (Colorado) Bioreactors, Bioremediation, Organics Removal from Soils THOMAS W. PETERSON, Professor and Head (CalTech) Aerosols, Hazardous Waste Incineration, Microcontamination ALAN D. RANDOLPH, Professor (Iowa State) Crystallization Processes, Nucleation, Particulate Processes THOMAS R. REHM, Professor (Washington) Mass Transfer, Process Instrumentation, Computer Aided Design FARHANG SHADMAN, Professor (Berkeley) Reaction Engineering, Kinetics, Catalysis, Reactive Membranes, Microcontamination RAYMOND A. SIERKA, Professor (Oklahoma) Adsorption, Oxidation, Membranes, Solar Catalyzed Detox Reactions JOST 0. L. WENDT, Professor (Johns Hopkins) CombustionGenerated Air Pollution, Incineration, Waste Management DON H. WHITE, Professor Emeritus (Iowa State) Polymers, Microbial and Enzymatic Processes DAVID WOLF, Visiting Professor (Technion) Fermentation, Mixing, Energy, Biomass Conversion Chemical Engineering Education ARIZONA STATE UNIVERSITY CHEMICAL, BIO, AND MATERIALS ENGINEERING Sa a r aO CHEMICAL SC,,40 L aRTIFICIAL B10 *SE 0.0 * o * *0 Ir CROSS nDISCi INARY RESEA RCH 0 ] o * 0 .p C . .4 . SQe Graduate Research in a High Technology Environment Chemical Engineering Beckman, James R., Ph.D., U. of Arizona Crystallization and Solar Cooling Bellamy, Lynn, Ph.D., Tulane Process Simulation Berman, Neil S., Ph.D., U. of Texas, Austin Fluid Dynamics and Air Pollution Burrows, Veronica A., Ph.D., Princeton Surface Science, Semiconductor Processing Cale, Timothy S., Ph.D., U. of Houston * Catalysis, Semiconductor Processing Garcia, Antonio A., Ph.D., U.C., Berkeley AcidBase Interactions, Biochemical Separation, Colloid Chemistry Henry, Joseph D., Jr., Ph.D., U. of Michigan Biochemical, Molecular Recognition, Surface and Colloid Phenomena Kuester, James L., Ph.D., Texas A&M * Thermochemical Conversion, Complex Reaction Systems Raupp, Gregory B., Ph.D., U. of Wisconsin Semiconductor Materials Processing, Surface Science, Catalysis Rivera, Daniel, Ph.D., Cal Tech Process Control and Design Sater, Vernon E., Ph.D., Illinois Institute of Tech Heavy Metal Removal from Waste Water, Process Control Torrest, Robert S., Ph.D., U. of Minnesota Multiphase Flow, Filtration, Flow in Porous Media, Pollution Control Zwiebel, Imre, Ph.D., Yale Adsorption of Macromolecules, Biochemical Separations Bioengineering Dorson, William J., Ph.D., U. of Cincinnati Physicochemical Phenomena, Transport Processes Guilbeau, Eric J., Ph.D., Louisiana Tech * Biosensors, Physiological Systems, Biomaterials Kipke, Daryl R., Ph.D., University of Michigan Computation Neuroscience * Machine Vision, Speech Recognition, Robotics Neural Networks Pizziconi, Vincent B., Ph.D. Arizona State Artificial Organs, Biomaterials, Bioseparations Sweeney, James D., Ph.D., CaseWestern Reserve Rehab Engineering, Applied Neural Control Towe, Bruce C., Ph.D., Penn State * Bioelectric Phenomena, Biosensors, Biomedical Imaging Yamaguchi, Gary T., Ph.D., Stanford * Biomechanics, Rehab Engineering, ComputerAided Surgery Materials Science & Engineering Alford, Terry L., Ph.D., Cornell U. Elec tronic Materials Physical Metallurgy * Electronic Thin Films Surface/Thin Film Dey, Sandwip K., Ph.D., NYSC of Ceramics, Alfred U. Ceramics, SolGel Processing Hendrickson, Lester E., Ph.D., U. of Illinois Fracture and Failure Analysis, Physical and Chemical Metallurgy Jacobson, Dean L., Ph.D., UCLA * Thermionic Energy Conversion, High Temperature Materials Krause, Stephen L., Ph.D., U. of Michigan Ordered Polymers, Electronic Materials, Electron Xray Diffraction, Electron Microscopy Mayer, James, Ph.D., Purdue *Thin Film Processing Ion Bean Modification of Materials Stanley, James T., Ph.D., U. of Illinois * Phase Transformations, Corrosion For more details regarding the graduate degree programs in the Department of Chemical, Bio, and Materials Engineering, please call (602) 9653313 or (602) 9653676, or write to: Dr. Eric Guilbeau, Chair of the Graduate Committee, Department of Chemical, Bio, and Materials Engineering, Arizona State University, Tempe, Arizona 852876006. Fall 1993 21 BRIGHAM YOUNG UNIVERSITY T H E W O R L D I S O U R C A M P U S GRADUATE S in Biomedical Engineering Chemical Propulsion Coal Combustion & Gasification Computer Simulation Electrochemistry Thermodynamics Fluid Mechanics STUDIES IN CHEMICAL the beautiful Rocky Mountains of ENGINEERING Utah Kinetics & Catalysis Mathematical Modeling Materials Transport Phenomena Molecular Dynamics Process Design Process Control For additional information write to: Graduate Coordinator Department of Chemical Engineering, 350 CB Brigham Young University Provo. Utah 84602 Tel: (801) 3782586 Asa7 . ' a7 U DEPARTMENT OF CHEMICAL AND M N PETROLEUM ENGINEERING TM THE The Department offers graduate programs leading to the M.Sc. and UNIVERSITY Ph.D. degrees in Chemical Engineering (fulltime) and the M.Eng. OF CALGARY degree in Chemical Engineering or Petroleum Reservoir Engineering (parttime) in the following areas: FACULTY R. G. Moore, Head (Alberta) A. Badakhshan (Birmingham, U.K.) L. A. Behie (Western Ontario) J. D. M. Belgrave (Calgary) F. Berruti (Waterloo) P. R. Bishnoi (Alberta) R. M. Butler (Imperial College, U.K) A. Chakma (UBC) R. A. Heidemann (Washington U.) A. A. Jeje (MIT) N. Kalogerakis (Toronto) A. K. Mehrotra (Calgary) E. Rhodes (Manchester, U.K) P. M. Sigmund (Texas) J. Stanislav (Prague) W. Y. Svrcek (Alberta) E. L. Tollefson (Toronto) M. A. Trebble (Calgary) Biochemical Engineering & Biotechnology Biomedical Engineering Environmental Engineering Modeling, Simulation & Control Petroleum Recovery & Reservoir Engineering Process Development Reaction Engineering/Kinetics Thermodynamics Transport Phenomena Fellowships and Research Assistantships are available to all qualified applicants. For Additional Information Write * Dr. A. K. Mehrotra Chair, Graduate Studies Committee Department of Chemical and Petroleum Engineering The University of Calgary Calgary, Alberta, Canada T2N 1N4 The University is located in the City of Calgary, the Oil capital of Canada, the home of the world famous Calgary Stampede and the 1988 Winter Olympics. The City combines the traditions of the Old West with the sophistication of a modern urban center. Beautiful Banff National Park is 110 km west of the City and the ski resorts of Banff, Lake Louise,and Kananaskis areas are readily accessible. In the above photo the University Campus is shown with the Olympic Oval and the student residences in the foreground. The Engineering complex is on the left of the picture. Fall 1993 221 THE UNIVERSITY OF CALIFORNIA AT 6 BERKELEY... RESEARCH INTERESTS BIOCHEMICAL ENGINEERING ELECTROCHEMICAL ENGINEERING ELECTRONIC MATERIALS PROCESSING ENERGY UTILIZATION FLUID MECHANICS KINETICS AND CATALYSIS POLYMER SCIENCE AND TECHNOLOGY PROCESS DESIGN AND DEVELOPMENT SEPARATION PROCESSES SURFACE AND COLLOID SCIENCE THERMODYNAMICS ... offers graduate programs leading to the Master of Science and Doctor of Philosophy. Both programs involve joint facultystudent research as well as courses and seminars within and outside the department. Students have the opportunity to take part in the many cul tural offerings of the San Francisco Bay Area and the recreational activities of California's northern coast and mountains. FACULTY ALEXIS T. BELL HARVEY W. BLANCH ELTON J. CAIRNS ARUP K. CHAKRABORTY DOUGLAS S. CLARK MORTON M. DENN (CHAIRMAN) ALAN S. FOSS SIMON L. GOREN DAVID B. GRAVES ENRIQUE IGLESIA JAY D. KEASLING C. JUDSON KING SCOTT LYNN ROYA MABOUDIAN SUSAN J. MULLER JOHN S. NEWMAN JOHN M. PRAUSNITZ CLAYTON J. RADKE JEFFREY A. REIMER DAVID S. SOANE DOROS N. THEODOROU PLEASE WRITE: DEPARTMENT OF CHEMICAL ENGINEERING UNIVERSITY OF CALIFORNIA BERKELEY, CALIFORNIA 947209989 Chemical Engineering Education UNIVERSITY OF CALIFORNIA RVI NE Graduate Studies in Chemical and Biochemical Engineering for Chemical Engineering, Engineering, and Science Majors PROGRAM Offers degrees at the M.S. and Ph.D. levels. Research in frontier areas in chemical engineering, including biochemi cal engineering, biotechnology and materials science and engineering. Strong molecular biology, biochemistry, mi crobiology, and other engineering and science research groups on campus. LOCATION The 1,510acre UC Irvine campus is in Orange County, five miles from the Pacific Ocean and 40 miles south of Los Angeles. Irvine is one of the nation's fastest growing resi dential, industrial, and business areas. Nearby beaches, mountain and desert area recreational activities, and local cultural activities make Irvine a pleasant city in which to live and study. FACULTY Nancy A. Da Silva (California Institute of Technology) G. Wesley Hatfield (Purdue University) Juan Hong (Purdue University) James T. Kellis, Jr. (University of California, Irvine) Henry C. Lim (Northwestern University) Martha L. Mecartney (Stanford University) Betty H. Olson (University of California, Berkeley) Frank G. Shi (California Institute of Technology) Thomas K. Wood (North Carolina State University) RESEARCH AREAS Bioreactor Engineering Bioremediation Environmental Chemistry Environmental Engineering Interfacial Engineering Materials Processing Metabolic Engineering Microstructure of Materials Optimization Process Control Protein Engineering Recombinant Cell Technology Separation Processes SolGel Processing Water Pollution Control For further information and application forms, contact Biochemical Engineering Program School of Engineering University of California Irvine, CA 927172575 Fall 1993 CHEMICAL ENGINEERING AT UIA RESEARCH AREAS * Thermodynamics and Cryogenics * Process Design, Dynamics, and Control * Polymer Processing and Transport Phenomena * Kinetics, Combustion, and Catalysis * Surface and Interface Engi neering * Electrochemistry and Corrosion * Biochemical Engineering * Aerosol Science and Technology * Air Pollution Control and Environmental Engineering FACULTY D. T. Allen Y. Cohen T. H. K. Frederking S. K. Friedlander R. F. Hicks E. L. Knuth (Prof Emeritus) V. Manousiouthakis H. G. Monbouquette K. Nobe L. B. Robinson (Prof Emeritus) S. M. Senkan O. Smith W. D. Van Vorst (Prof. Emeritus) V. L. Vilker A. R. Wazzan PROGRAMS UCLA's Chemical Engineering Department of fers a program of teaching and research linking fundamental engineering science and industrial prac tice. Our Department has strong graduate research programs in environmental chemical engineering, biotechnology, and materials processing. With the support of the Parsons Foundation and EPA, we are pioneering the development of methods for the de sign of clean chemical technologies, both in gradu ate research and engineering education. Fellowships are available for outstanding ap plicants in both M.S. and Ph.D. degree programs. A fellowship includes a waiver of tuition and fees plus a stipend. Located five miles from the Pacific Coast, UCLA's attractive 417acre campus extends from Bel Air to Westwood Village. Students have ac cess to the highly regarded science programs and to a variety of experiences in theatre, music, art, and sports on campus. CONTACT 224 Chemical Engineering Education UNIVERSITY OF CALIFORNIA SANTA BARBARA * FACULTY AND RESEARCH INTERESTS * L. GARY LEAL Ph.D. (Stanford) (Chairman) Fluid Mechanics; Suspension and Polymer Physics. ERAY S. AYDIL Ph.D. (University of Houston) Microelectronics Materials Processing SANJOY BANERJEE Ph.D. (Waterloo) TwoPhase Flow, Chemical & Nuclear Safety, Computational Fluid Dynamics, Turbulence. BRADLEY F. CHMELKA Ph.D. (U.C. Berkeley) Guest/Host Interactions in Molecular Sieves, Dispersal of Metals in Oxide Catalysts, Molecular Structure and Dynamics in Polymeric Solids, Properties of Partially Ordered Materials, SolidState NMR Spectroscopy. GLENN H. FREDRICKSON Ph.D. (Stanford) Electronic Transport, Glasses, Polymers, Composites, Phase Separation. OWEN T. HANNA Ph.D. (Purdue) Theoretical Methods, Chemical Reactor Analysis, Transport Phenomena. JACOB ISRAELACHVILI Ph.D. (Cambridge) Surface and Interfacial Phenomena, Adhesion, Colloidal Systems, Surface Forces. FRED F. LANGE Ph.D. (Penn State) Powder Processing of Composite Ceramics; Liquid Precursors for Ceramics; Superconducting Oxides. GLENN E. LUCAS Ph.D. (M.I.T.) (Vice Chairman) Mechanics of Materials, Radiation Damage. DIMITRIOS MAROUDAS Ph.D. (M.I.T.) Structure and Dynamics in Heterogeneous Materials. ERIC McFARLAND Ph.D. (M.I.T.) M.D. (Harvard) Biomedical Engineering, NMR and Neutron Imaging, Transport Phenomena in Complex Liquids, Radiation Interactions. DUNCAN A. MELLICHAMP Ph.D. (Purdue) Computer Control, Process Dynamics, RealTime Computing. G. ROBERT ODETTE Ph.D. (M.I.T.) High Performance Structural Materials DALE S. PEARSON Ph.D. (Northwestern) Rheological and Optical Properties of Polymer Liquids and Colloidal Dispersions. PHILIP ALAN PINCUS Ph.D. (U.C. Berkeley) Theory of Surfactant Aggregates, Colloid Systems. A. EDWARD PROFIO Ph.D. (M.I.T.) Biomedical Engineering, Reactor Physics, Radiation Transport Analysis. ROBERT G. RINKER Ph.D. (Caltech) Chemical Reactor Design, Catalysis, Energy Conversion, Air Pollution. ORVILLE C. SANDALL Ph.D. (U.C. Berkeley) Transport Phenomena, Separation Processes. DALE E. SEBORG Ph.D. (Princeton) Process Control, Computer Control, Process Identification. PAUL SMITH Ph.D. (State University ofGroningen, Netherlands) High Performance Fibers; Processing of Conducting Polymers; Polymer Processing. T. G. THEOFANOUS Ph.D. (Minnesota) Nuclear and Chemical Plant Safety, Multiphase Flow, Thermalhydraulics. W. HENRY WEINBERG Ph.D. (U.C. Berkeley) Surface Chemistry; Heterogeneous Catalysis; Electronic Materials JOSEPH A. N. ZASADZINSKI Ph.D. (Minnesota) Surface and Interfacial Phenomen, Structure of Microemulsions. PROGRAMS AND FINANCIAL SUPPORT The Department offers M.S. and Ph.D. degree programs Financial aid, including fellowships, teaching assistantships, and research assis tantships, is available. THE UNIVERSITY One of the world's few seashore cam puses, UCSB is located on the Pa cific Coast 100 miles northwest of Los Angeles. The student enrollment is over 18,000. The metropolitan Santa Barbara area has over 150,000 residents and is famous for its mild, even climate. For additional information and applications, write to Chair Graduate Admissions Committee Department of Chemical and Nuclear Engineering University of California Santa Barbara, CA 93106 Fall 1993 Chemical Engineering at the yTuo CALIFORNIA 891 1z INSTITUTE \OF N OF TECHNOLOGY "At the Leading Edge" Frances H. Arnold John F. Brady Mark E. Davis Richard C. Flagan George R. Gavalas Konstantinos P. Giapis Julia A. Kornfield Manfred Morari C. Dwight Prater (Visiting) John H. Seinfeld Nicholas W. Tschoegl (Emeritus) ZhenGang Wang Aerosol Science Applied Mathematics Atmospheric Chemistry and Physics Biocatalysis and Bioreactor Engineering Bioseparations Catalysis Chemical Vapor Deposition Combustion Colloid Physics Fluid Mechanics Materials Processing Microelectronics Processing Microstructured Fluids Polymer Science Process Control and Synthesis Protein Engineering Statistical Mechanics of Heterogeneous Systems For further information, write Professor Mark E. Davis Chemical Engineering 21041 California Institute of Technology Pasadena, California 91125 Chemical Engineering Education )h Cm Joh L. Anderson Loen Blee * Pa l DiSll Mihe M. oac Ufias goin on Igai E. UGro ssmann S Uila S. 5 Ha mc Oinnt M. Jacobson 5 Ayun S. S . *_m n 1 Ko 3ar J. Powers  )eni C. S U  Je nie L. Sinclair* *u J. Sd s 6oer D. Tilton 0 Chemical Engineering in the 21st Century? Diamond crystals synthesized by graduate student C. Kovach. For more information contact: The Graduate Coordinator Department of Chemical Engineering Case Western Reserve University Cleveland, Ohio 44106 Want to learn what the future holds for chemical engineers? Consider graduate study at CASE WESTERN RESERVE UNIVERSITY Opportunities for Innovative Research in Advanced Energy Conversion * Chemical/Biological Sensors Intelligent Control * Micro and NanoMaterials * Novel Separations/Processing * Faculty and Specializations John C. Angus, Ph.D. 1960, University of Michigan Diamond and diamondlike films, redox equilibria Coleman B. Brosilow, Ph.D. 1962, Polytechnic Institute of Brooklyn Adaptive inferential control, multivariable control, coordination algorithms Robert V. Edwards, Ph.D. 1968, Johns Hopkins University Laser anemometry, mathematical modeling, data acquisition Donald L. Feke, Ph.D. 1981, Princeton University Colloidal phenomena, ceramic dispersions, fineparticle processing Nelson C. Gardner, Ph.D. 1966, Iowa State University Highgravity separations, sulfur removal processes Uziel Landau, Ph.D. 1975, University of California (Berkeley) Electrochemical engineering, current distributions, electro deposition AN ChungChiun Liu, Ph.D. 1968, Case Western Reserve University Electrochemical sensors, electrochemical synthesis, electrochemistry related to electronic materials J. Adin Mann, Jr., Ph.D. 1962, Iowa State University Interfacial structure and dynamics, light scattering, Langmuir Blodgett films, stochastic processes Philip W. Morrison, Jr., Ph.D. 1987, University of California (Berkeley) Materials synthesis, semiconductor processing, insitu diagnostics Syed Qutubuddin, Ph.D. 1983, CarnegieMellon University Surfactant and polymer solutions, metal extraction, enhanced oil recovery Robert F. Savinell, Ph.D. 1977, University of Pittsburgh Applied electrochemistry, electrochemical system simulation and _optimization, electrode processes CASE WESTERN RESERVE UNIVERSITY Chemical Engineering Education The UNIVERSITY OF CINCINNATI ILJL Opportunities for GRADUATE STUDY in Chemical Engineering M.S. and PhD Degrees in Chemical Engineering SFinancial Aid Available * Faculty The city of Cincinnati is the 23rd largest city in the United States, with a greater metropolitan population of 1.7 million. The city offers numerous sites of architec tural and historical interest, as well as a full range of cultural attractions, such as an outstanding art museum, botanical gardens, a worldfamous zoo, theaters, symphony, and opera. The city is also home to the Cincinnati Bengals and the Cincinnati Reds. The business and industrial base of the city includes pharmaceu tics, chemicals, jet engines, autoworks, electronics, printing and publishing, insur ance, investment banking, and health care. A number of Fortune 500 companies are located in the city. Amy Ciric Joel Fried Stevin Gehrke Rakesh Govind David Greenberg Daniel Hershey SunTak Hwang Robert Jenkins YuenKoh Kao SoonJai Khang Jerry Lin Glenn Lipscomb Neville Pinto Sotiris Pratsinis n Air Pollution Modeling and design of gas cleaning devices and systems, source apportionment of air pollutants. a Biotechnology (Bioseparations) Novel bioseparation techniques, chromatography, affinity separations, biodegradation of toxic wastes, controlled drug delivery, twophase flow, suspension rheology. 0 Chemical Reaction Engineering and Heterogeneous Catalysis Modeling and design of chemical reactors, deactivation of catalysts, flow pattern and mixing in chemical equipment, laser induced effects. o Coal Research New technology for coal combustion power plant, desulfuriza tion and denitritication. 0 Material Synthesis Man ufacture of advanced ceramics, opticalfibers and pigments by aerosol processes. 0 Membrane Separations Membrane gas separations, membrane reactors, sensors and probes, equilibrium shift, pervaporation, dynamic simulation of membrane separators, membrane preparation and characteri zation for polymeric and inorganic materials. a Polymers Thermodynamics, thermal analysis and morphology of polymer blends, hightemperature polymers, hydrogels, polymer processing. a Process Synthesis Computeraided design, modeling and simulation of coal gasifiers, activated carbon columns, process unit operations, prediction of reaction byproducts. For Admission Information * Director, Graduate Studies Department of Chemical Engineering, # 0171 University of Cincinnati Cincinnati, Ohio 452210171 Fall 1993 229 I EU.L LUUI I** Graduate Study in CHEMICAL ENGINEERING AT CLARKSON * CENTER FOR ADVANCED MATERIALS PROCESSING * NASA CENTER FOR THE DEVELOPMENT OF COMMERCIAL CRYSTAL GROWTH IN SPACE INSTITUTE OF COLLOID AND SURFACE SCIENCE For details, please write to: Dean of the Graduate School Clarkson University Box 5625 Potsdam, New York 136995625 Clarkson University is a nondiscriminatory, equal opportunity, affirmative action educator and employer. Chemical Engineering Education Clemson University No matter where you do your graduate work, your nose will be in your books and your mind on your research. But at Clemson University, there's something for you when you can stretch out for a break. Like enjoying the beautiful mountain scenery. Or fishing, swimming, sailing, and water skiing in the clean lakes. Or hiking in the nearby Blue Ridge Mountains. Or in Chmia Engneein driving to South Caro lina's famous beaches for a weekend. Some thing that can really relax you. All this and a top notch Chemical Engineering Depart ment, too. With active research and teaching in poly mer processing, com posite materials, pro cess automation, ther modynamics, catalysis, and membrane applica tions what more do you need? I I The University Photo Courtesy of Patrick Wright The University Clemson, the landgrant university of South Carolina, offers 72 undergraduate and 70 graduate fields of study in its nine academic colleges. Present oncampus enrollment is about 17,000 students, onethird of whom are in the College of Engineering. There are about 4,100 graduate students. The 1,400acre campus is located on the shores of Lake Hartwell in South Carolina's Piedmont, and is midway between Charlotte, N.C., and Atlanta, Ga. The Faculty Charles H. Barron, Jr. James M. Haile Amod A. Ogale John N. Beard Douglas E. Hirt Richard W. Rice Dan D. Edie Stephen S. Melsheimer Mark C. Thies Charles H. Gooding Joseph C. Mullins Programs lead to the M.S. and Ph.D. degrees. Financial aid, including fellowships and assistantships, is available. For further information and a descriptive brochure, contact: Graduate Coordinator, Department of Chemical Engineering Clemson University Clemson, South Carolina 296340909 (803) 6563055 CLEMSON UNIVERSITY College of Engineering Fall 1993 231 UNIVERSITY OF COLORADO BOULDER Graduate students in the Department of Chemical Engineering may also participate in the popular, interdisciplinary Biotechnology Training Program at the University of Colorado and in the interdisciplinary NSF Industry/University Cooperative Research Center for Separations Using Thin Films. FACULTY CHRISTOPHER N. BOWMAN Assistant Professor Ph.D., Purdue University, 1991 DAVID E. CLOUGH Professor Ph.D., University of Colorado, 1975 ROBERT H. DAVIS Professor and Chair, CoDirector of Colorado Institute for Research in Biotechnology W Ph.D., Stanford University, 1983 JOHN L. FALCONER James and Catherine Patten Professor Ph.D., Stanford University, 1974 YURIS O. FUENTES Assistant Professor Ph.D., University of WisconsinMadison, 1990 R. IGOR GAMOW Associate Professor Ph.D., University of Colorado, 1967 HOWARD J. M. HANLEY. Professor Adjoint Ph.D., University of London, 1963 DHINAKAR S. KOMPALA Associate Professor Ph.D., Purdue University, 1984 WILLIAM B. KRANTZ Professor and President's Teaching Scholar, CoDirector of NSF I/UCRC Center for Separations Using Thin Films Ph.D., University of California, Berkeley, 1968 RICHARD D. NOBLE Professor CoDirector of NSF I/UCRC Center for Separations Using Thin Films Ph.D., University of California, Davis, 1976 W. FRED RAMIREZ Professor Ph.D., Tulane University, 1965 THEODORE W. RANDOLPH Associate Professor Ph.D., University of California, Berkeley, 1987 ROBERT L. SANI Professor Director of Center for Lowgravity Fluid Mechanics and Transport Phenomena Ph.D., University of Minnesota, 1963 EDITH M. SEVICK Assistant Professor Ph.D., University of Massachusetts, 1989 KLAUS D. TIMMERHAUS Professor and President's Teaching Scholar Ph.D., University of Illinois, 1951 RESEARCH INTERESTS Biotechnology and Bioengineering Bioreactor Design and Optimization Mammalian Cell Cultures Protein Folding and Purification Chemical Environmental Engineering Global Change Pollution Remediation Materials Science and Engineering Catalysis and Surface Science Colloidal Phenomena Polymerization Reaction Engineering Membrane Science Chemically Specific Separations Membrane Transport and Separations Polymeric Membrane Morphology Modeling and Control Expert Systems Process Control and Identification Thermodynamics Cryogenics Statistical Mechanics Supercritical Fluids Transport Phenomena Fluid Dunamics and Suspension Mechanics Materials Processing in LowG PAUL W. TODD Research Professor Ph.D., University of California, Berkeley, 1964 RONALD E. WEST Professor Ph.D., University of Michigan, 1958 FOR INFORMATION AND APPLICATION, WRITE TO Director, Graduate Admissions Committee Department of Chemical Engineering University of Colorado, Boulder Boulder, Colorado 803090424 *FAX (303) 4924341 Chemical Engineering Education COLORADO OF O SCHOOL OF MINE S 1874 THE FACULTY AND THEIR RESEARCH R. M. BALDWIN, Professor and Head; Ph.D., Colorado School of Mines. Mechanisms and kinetics of coal liquefaction, catalysis, oil shale process ing, fuels science. A. L. BUNGE, Professor; Ph.D., University of California, Berkeley. Mem brane transport and separations, mass transfer in porous media, ion exchange and adsorption chromatography, in place remediation of con taminated soils, percutaneous absorption. J.R. DORGAN, Assistant Professor; Ph.D., University of California, Berke ley. Polymer science and engineering. J. F. ELY, Professor; Ph.D., Indiana University. Molecular thermodynamics and transport properties of fluids. J. H. GARY, Professor Emeritus; Ph.D., University of Florida. Petroleum refinery processing operations, heavy oil processing, thermal cracking, visbreaking and solvent extraction. J.O. GOLDEN, Professor; Ph.D., Iowa State University. Hazardous waste processing, polymers, fluidization engineering M.S. GRABOSKI, Research Professor; Ph.D., Pennsylvania State University. Fuels Synthesis and evaluation, engine technology, alternate fuels :1, A A. J. KIDNAY, Professor and Graduate Dean; D.Sc., Colorado School of Mines. Thermodynamic properties of gases and liquids, vaporliquid equi s libria, cryogenic engineering. J.T. McKINNON, Assistant Professor; Ph.D., Massachusetts Institute of Tech nology. High temperature gas phase chemical kinetics, combustion, haz ardous waste destruction. R. L. MILLER, Associate Professor; Ph.D., Colorado School of Mines. Liq uefaction coprocessing of coal and heavy oil, low severity coal liquefac tion, particulate removal with venturi scrubbers, interdisciplinary educa tional methods M. S. SELIM, Professor; Ph.D., Iowa State University. Heat and mass transfer with a moving boundary, sedimentation and diffusion of colloidal suspensions, heat effects in gas absorption with chemical reaction, en trance region flow and heat transfer, gas hydrate dissociation modeling. E. D. SLOAN, JR., Professor; Ph.D. Clemson University. Phase equilibrium measurements of natural gas fluids and hydrates, thermal conductivity of coal derived fluids, adsorption equilibria, education methods research. J. D. WAY, Research Professor; Ph.D. University of Colorado. Novel separa tion processes, membrane science and technology, membrane reactors, ceramic and metal membranes, biopolymer adsorbents for adsorption of heavy metals. V. F. YESAVAGE, Professor; Ph.D., University of Michigan. Vapor liquid equilibrium and enthalpy of polar associating fluids, equations of state for highly nonideal systems, flow calorimetry. For Applications and Further Information on M.S. and Ph.D. Programs, Write Chemical Engineering and Petroleum Refining Colorado School of Mines Fall 1993 J university ol nnecticul Graduate Study in Chemical Engineering M.S. and Ph.D. Programs for Scientists and Engineers FACULTY RESEARCH AREAS Luke E.K. Achenie, Ph.D., Carnegie Mellon University Modeling and Optimization, Neural Networks, Process Control Thomas F. Anderson, Ph.D., University of California, Berkeley Modeling of Separation Processes, FluidPhase Equilibria James P. Bell, Sc.D., Massachusetts Institute of Technology StructureProperty Relations in Polymers and Composites, Adhesion Carroll 0. Bennett, Professor Emeritus, Ph.D., Yale University Catalysis, Chemical Reaction Engineering Douglas J. Cooper, Ph.D., University of Colorado Process Control, Neural Networks, Fluidization Technology Robert W. Coughlin, Ph.D., Cornell University Biotechnology, Biochemical and Environmental Engineering, Catalysis, Kinetics, Separations, Surface Science Michael B. Cutlip, Ph.D., University of Colorado Kinetics and Catalysis, Electrochemical Reaction Engineering, Numerical Mett Anthony T. DiBenedetto, Ph.D., University of Wisconsin Composite Materials, Mechanical Properties of Polymers James M. Fenton, Ph.D., University of Illinois, UrbanaChampaign Electrochemical and Environmental Engineering, Mass Transfer Processes, Electronic Materials, Energy Systems Suzanne (Schadel) Fenton, Ph.D., University of Illinois Computational Fluid Dynamics, Turbulence, TwoPhase Flow Robert J. Fisher, Ph.D., University of Delaware Biochemical Engineering and Environmental Biotechnology G. Michael Howard, Ph.D., University of Connecticut Process Systems Analysis and Modeling, Process Safety, Engineering Educatic Herbert E. Klei, Professor Emeritus, Ph.D., University of Connecticut Biochemical Engineering, Environmental Engineering Jeffrey T. Koberstein, Ph.D., University of Massachusetts Polymer Blends/Compatibilization, Polymer Morphology, Polymer Surface and Interfaces Harold R. Kunz, Ph.D., Rensselaer Polytechnic Institute Fuel Cells, Electrochemical Energy Systems Montgomery T. Shaw, Ph.D., Princeton University Polymer Rheology and Processing, Polymersolution Thermodynamics Richard M. Stephenson, Professor Emeritus, Ph.D., Cornell University Mutual Solubility Measurements, LiquidLiquid Equilibrium Donald W. Sundstrom, Professor Emeritus, Ph.D. University of Michigan Environmental Engineering, Hazardous Wastes, Biochemical Engineering Robert A. Weiss, Ph.D., University of Massachusetts Polymer StructureProperty Relationships, IonContaining and Liquid Crystal Polymers, Polymer Blends FOR MORE INFORMATION Graduate Admissions, 191 Auditorium Road University of Connecticut, Storrs, CT 062693222 Tel. (203) 4864020 CHEMICAL ENGINEERING CORNELL UNIVERSITY At Cornell University students have the flexibility to design interdisciplinary research programs that draw upon the resources of many excellent departments and NSFsponsored interdisciplinary centers such as the Biotechnology Center, the Cornell National Supercomputing Center, the National Nanofabrication Facility, and the Materials Science Center. Degrees granted include the Master of Engineering, Master of Science, and Doctor of Philosophy. All MS and PhD students are fully funded with attractive stipends and tuition waivers. Situated in the scenic Finger Lakes region of New York State, the Cornell campus is one of the most beautiful in the ID 111111 country. Students enjoy sailing, skiing, fishing, hiking, bicycling, Boating, winetasting and many more activities in this popular vacation region. Distinguished Faculty ... A. Brad Anton Robert P. Merrill H Paulette Clancy William L. Olbricht Claude Cohen A. Panagiotopoulos T. Michael Duncan Ferdinand Rodriguez ... With Research In James R. Engstrom Biochemical Engineering Polymer Science Keith E. Gubbins Michael L. Shuler Applied Mathematics Fluid Dynamics Computer Simulation Rheology and Biorheology Daniel A. Hammer Paul H. Steen Environmental Engineering Process Control Kinetics and Catalysis Molecular Thermodynamics Peter Harriott William B. Street Surface Science Statistical Mechanics Donald L. Koch John A. Zollweg Heat and Mass Transfer ComputerAided Design For Further Information, Write: Graduate Field Representative Cornell University Olin Hall of Chemical Engineering Ithaca, NY 148535201 Fall 1993 Chemical En gneerin at The Faculty Giovanni Astarita Mark A. Barteau Antony N. Beris Kenneth B. Bischoff Douglas J. Buttrey Stuart L. Cooper Costel D. Denson Prasad S. Dhurjati Henry C. Foley Eric W. Kaler Michael T. Klein Abraham M. Lenhoff Roy L. McCullough Arthur B. Metzner Jon H. Olson Michael E. Paulaitis T. W. Fraser Russell Stanley I. Sandler Jerold M. Schultz Annette D. Shine Norman J. Wagner Androew L.Zydney he University of Delaware offers M.ChE and Ph.D. degrees in Chemical Engineering. Both degrees involve research and course work in engineering and related sciences. The Delaware tradition is one of strong interdisciplinary research on both fundamental and applied problems. Current fields include Thermodynamics, Separation Processes, Polymer Science and Engineering, Fluid Mechanics and Rheology, Transport Phenomena, Materials Science and Metallurgy, Catalysis and Surface Science, Reaction Kinetics, Reactor Engineering, Process Control, Semiconductor and Photovoltaic Processing, Biomedical Engineering, Biochemical Engineering, and Colloid and Surfactant Science. For more information and application materials, write: Graduate Advisor Department of Chemical Engineering University of Delaware Newark, Delaware 19716 I The Universi Delawa ty of ire Chemical Engineering Education Modern Applications of Chemical Engineering at the University of Florida Graduate Study Leading to the MS and PhD FACULTY. TIM ANDERSON Semiconductor Processing, Thermodynamics IOANNIS BITSANIS Molecular Modeling of Interfaces SEYMOUR S. BLOCK Biotechnology OSCAR D. CRISALLE Electronic Materials, Process Control RICHARD B. DICKINSON Biomedical Engineering RAY W. FAHIEN Transport Phenomena, Reactor Design ARTHUR L. FRICKE Polymers, Pulp & Paper Characterization GAR HOFLUND Catalysis, Surface Science LEW JOHNS Applied Design, Process Control, Energy Systems DALE KIRMSE Computer Aided Design, Process Control HONG H. LEE Semiconductor Processing, Reaction Engineering FRANK MAY ComputerAided Learning RANGA NARAYANAN Transport Phenomena, Semiconductor Processing MARK E. ORAZEM Electrochemical Engineering, Semiconductor Processing CHANGWON PARK Fluid Mechanics, Polymer Processing DINESH 0. SHAH Surface Sciences, Biomedical Engineering SPYROS SVORONOS Process Control, Biochemical Engineering GERALD WESTERMANNCLARK Electrochemical Engineering, Bioseparations For more information, please write: Graduate Admissions Coordinator Department of Chemical Engineering University of Florida Gainesville, Florida 32611 or call (904) 3920881 Fall 1993 237 Reeac an Srdut S tde in Chmia EngSnS erinS Adane Maeral (Ceramic, Clod, an Polymers 3 *fPiifi Iili 3 Cheica Vaor epoito Fa u t Composite material Comp lex Fluids Pedro 3 *ii Ph.D. Phase Transitions Purdue University, 1990 13*3** Ph3e33mena Ravi*3hell Ph.D. Mo^romolecular Transport in.Polymer Gel Media Univ eity o fM a tts,198 4333 Processing Se iod3 trad*3ecodco Prcssn Da.. Edlo P. D. Throynmc Yal Unvesiy 41949 Biegnern .a i 333etai 3h.D. 3i~ ta i Conl 3*vesiy 31389* 43.eartin Pee 3ils hD Bioinformati~~~~s Ohi SaeU ivest,1 6 Prcs Sytei an Coto 33 Li3 333.D.' No ina Prcs Control Rochste Univer3 ty,3 198 Prcs .Optimization Exer Sytm Bruc Lok Ph.D.3 5 Surface~~~~~~~~ ~ ~ ~ ~ ~ ~ ScecCtlssan3nrai3'ei! sNrhCrln taeUiest,18 Fli M caic fCrsa Got 3rnia 3* an i P. D.4 Kineti~~~~~~s an o bu3o niest o i 'ga ,1 9 Hetrogno CtalsisandRecto Dei3 Mihe Pe 3r Ph.D Molecular~~~~~ ~ ~ ~ ~ ~ ~ Trnsor Mehnc3nMtra einhoSaeUiest,18 Fo Inor ato Wrt so Jorg Vifl Ph.D. 'DYO, CHEMICAL ENGINEERING The Faculty and Their Research Heterogeneous catalysis, surface chemistry, reaction kinetics Pradeep K. Agrawal Process design and control, spoutedbed reactors Microelectron ics, polymer processing itrup Molecular thermo dynamics, chemical kinetics, separations arles A. Eckert W Reactor design, catalysis 1lliam R. Ernst E Molecular modeling of polymeric materials ,ter J. Ludovice w Mechanics of aerosols, buoyant plumes and jets LarryJ. Forney Aerocolloidal systems, interfacial phenomena, fineparticle technology Michael J. Matteson Heat transport phenomena, fluidization )rton Polymer engineering, energy conservation, economics John D. Muzzy EPulp and paper Jeffrey S. Hsieh Biomechanics, mammalian cell structures Robert M. Nerem Photochemical processing, chemical vapor deposition M Emulsion polymeriza tion, latex technology Gary W. Poehlein Optimal process design and scheduling atthewJ. Realff Reactor engineering, process control, polymeriza tion, reactor dynamics Joseph Schork Catalysis, kinetics, reactor design ark G. White M, Biochemical engineering, mass transfer, reactor design Ronnie S. Roberts Mass transfer, extraction, mixing, non Newtonian flow A. H. Peter Skelland Biochemical engineering, cellcell interactions, biofluid dynamics Timothy M. Wick i Separation processes, crystallization Ronald W. Rousseau SProcess design and simulation Jude T. Sommerfeld Electrochemical engineering, thermodynam ics, air pollution control Jack Winnick Biochemical engineering, microbial and animal cell cultures Athanassios Sambanis Process synthe sis and simula tion, chemical separation, waste manage ment, resource recovery D. William Tedder Biofluid dynamics, rheology, transport phenomena Ajit P. Yoganathan Polymer science and engineering Robert J. Samuels Thermody namic and transport properties, phase equilibria, supercritical gas extraction Amyn S. Teja For more information, contact: Professor Ronald Rousseau, Director School of Chemical Engineering Georgia Institute of Technology Atlanta, Georgia 303320100 (404) 8942867 Polymer science and engineering S. Abhiraman What do graduate students say about the University of Houston Department of Chemical Engineering? "It's great!" "Houston is a university on the move. The chemical engineering department is ranked among the top ten schools, and you can work in the specialty of your choice. The choice of advisor is yours, too, and you're given enough time to make the right decision. You can see your advisor almost anytime you want because the studenttoteacher ratio is low." If you'd like to be part of this team, let us hear from you! AREAS OF RESEARCH STRENGTH Biochemical Engineering Chemical Reaction Engineering Electronic and Ceramic Materials Multiphase Flow Environmental Remediation Nonlinear Dynamics Improved Oil Recovery Polymer & Macromolecular Systems FACULTY Neal Amundson Ernest Henley Vemuri Balakotaiah John Killough Abe Dukler Dan Luss Demetre Economou Kishore Mohanty Richard Pollard Jay Schieber William Prengle Cynthia Stokes Raj Rajagopalan Frank Tiller Jim Richardson Richard Willson Frank Worley For an application, write: Dept. of Chemical Engineering, University of Houston, 4800 Calhoun, Houston, TX 772044792, or call 713/7434300. The University is in compliance with Title IX. o0 Chemical Engineering Education U The University of Illinois at Chicago I Department of Chemical Engineering MS and PhD Graduate Program * FACULTY Irving F. Miller Ph.D., University of Michigan, 1960 Professor and Head John H. Kiefer Ph.D., Cornell University, 1961 Professor G. Ali Mansoori Ph.D., University of Oklahoma, 1969 Professor Sohail Murad Ph.D., Cornell University, 1979 Professor Ludwig C. Nitsche Ph.D., Massachusetts Institute of Technology, 1989 Assistant Professor John Regalbuto Ph.D., University of Notre Dame, 1986 Associate Professor Satish C. Saxena Ph.D., Calcutta University, 1956 Professor Stephen Szepe Ph.D., Illinois Institute of Technology, 1966 Associate Professor Raffi M. Turian Ph.D., University of Wisconsin, 1964 Professor Bert L. Zuber Ph.D., Massachusetts Institute of Technology, 1965 Professor RESEARCH AREAS Transport Phenomena: Slurry transport, multiphase fluid flow and heat transfer, fixed and fluidized bed combustion, indirect coal liquefaction, porous media. Thermodynamics: Transport properties of fluids, statistical mechanics of liquid mixtures, bioseparations, superficial fluid extraction/retrograde condensation, asphaltene characterization. Kinetics and Reaction Engineering: Gassolid reaction kinetics, diffusion and adsorption phenomena, energy transfer processes, laser diagnostics, combustion chemistry, environmental technology, surface chemistry, optimization, catalyst preparation and characterization, structure sensitivity, supported metals. Bioengineering: Membrane transport, pulmonary deposition and clearance, biorheology, physiological control systems, bioinstrumentation. For more information, write to Director of Graduate Studies Department of Chemical Engineering University of Illinois at Chicago Box 4348 Chicago, IL 60680 (312) 9963424 Fall 1993 Chemical Engineering at the University of Illinois at UrbanaChampaign The combination of distinguished fac ulty, outstanding facilities and a di versity of research interests results in exceptional opportunities for graduate education. The chemical engineering department A offers graduate programs leading to the M.S. and Ph.D. degrees. ON Richard C. Alkire Electroche OF Richard D. Braatz Advanced Thomas J. Hanratty Fluid Dyn Jonathan J. L. Higdon Fluid Mec CE Douglas A. Lauffenburger Cellular Bi Richard I. Masel Fundamen Semiconc Anthony J. McHugh Polymer Si William R. Schowalter Mechanics Edmund G. Seebauer Laser Stud Mark A. Stadtherr Chemical I Optimiza Frank B. van Swol Computer K. Dane Wittrup Biochemic Charles F. Zukoski IV Colloid an mical Engineering Process Control amics hanics and Transport Phenomena oengineering ital Studies of Catalytic Processes and luctor Growth science and Engineering Sof Complex Fluids ies of Semiconductor Growth Process Flowsheeting and tion Simulation and Interfacial Studies al Engineering d Interfacial Science For information and application forms write: Department of Chemical Engineering University of Illinois at UrbanaChampaign Box C3 Roger Adams Lab 600 S. Mathews Ave. Urbana, Illinois 618013792 Chemical Engineering Education TRADITI EXCELLENT GRADUATE STUDY IN CHEMICAL ENGINEERING AT Illinois Institute of Technology THE UNIVERSITY * Private, coeducational and research university * 4800 undergraduate students * 5400 graduate students * 3 miles from downtown Chicago and 1 mile west of Lake Michigan * Campus recognized as an architectural landmark THE CITY * One of the largest cities in the world * National and international center of business and industry * Enormous variety of cultural resources * Excellent recreational facilities * Industrial collaboration and job opportunities THE DEPARTMENT * One of the oldest in the nation * Approximately 40 fulltime and 40 parttime graduate students * M.Ch.E., M.S., and Ph.D. degrees * Financially attractive fellowships and assistant ships available to outstanding students THE FACULTY * HAMIDARASTOOPOUR (Ph.D., IIT) Multiphase flow and fluidization, flow through porous media, and powder and material processing * RICHARD A. BEISSINGER (D.E.Sc., Columbia) Transport processes in chemical and biological systems, rheology of polymeric and biological fluids * BARRY BERNSTEIN (Ph.D., Indiana University) Rheology, nonnewtonian flows, mechanical behavior of polymers * ALl CINAR (Ph.D., Texas A & M) Chemical process control, distributed parameter systems, expert systems * DIMITRI GIDASPOW (Ph.D., IIT) Hydrodynamics of fluidization, multiphase flow, separations processes * HENRY R. LINDEN (Ph.D., IIT) Energy policy, planning, and forecasting * SATISHJ. PARULEKAR (Ph.D., Purdue) Biochemical engineering, chemical reaction engineering * J. ROBERT SELMAN (Ph.D., CaliforniaBerkeley) Electrochemical engineering and electrochemical energy storage * FYODOR A. SHUTOV (Ph.D., Institute for Chemical Physics, Moscow) Polymer composite materials and plastic recycling * FOUAD TEYMOUR (Ph.D., University of Wisconsin, Madison) S.C. Johnson Polymer Assistant Professor Polymerization reaction engineering, and dynamic system analysis * DAVID C. VENERUS (Ph.D., Pennsylvania State U) Polymer rheology and processing, and transport phenomena * DARSH T. WASAN (Ph.D., CaliforniaBerkeley) Interfacial phenomena, separation processes, enhanced oil recovery * APPLICATIONS * Dr. A. Cinar Graduate Admissions Committee Department of Chemical Engineering Illinois Institute of Technology I.. T. Center Chicago, IL 60616 Fall 1993 Looking for a graduate program that's right for you? Since 1929, 1404 determined students have graduated from the Institute of Paper Science and Technology. Of those 1404 alumni, 963 are still actively working. Of those 963 individuals, 27% are CEOs, COOs, Presidents, Vice Presidents, Technical Directors, or Mill Managers of major paper companies. These numbers do not include those dedicated, welleducated alumni who are on their way to becoming the pulp and paper leaders of the future. BE A STATISTIC. Institute of Paper Science and Technology A Unique, Multidisciplinary Graduate Program for Engineers and Scientists The Institute of Paper Science and Technology offers a unique, multidisciplinary program at the graduate level for highly qualified students with a B.S. degree in chemical or mechanical engineering, chemistry, paper science, biology, or other physical sciences. The IPST academic program provides a broad technical education in engineering and science topics relevant to the paper industry. This broad perspective enables graduates to manage complex technical issues of importance to the industry. Students who are citizens of North America receive full tuition scholarships and graduate fellowships of $15,000 or $17,000 per year (12month basis), depending on the degree program. Opportu nities also exist for summer employment in the industry, providing income, as well as exposure to the challenges of the paper industry. For more information, contact the Office of Academic Affairs at 4048539556, or write to the Institute of Paper Science and Technology, Office of Academic Affairs, 500 10th Street, NW, Atlanta, GA 303185794. GRADUATE PROGRAM FOR M.S. & PH.D. DEGREES IN CHEMICAL AND BIOCHEMICAL ENGINEERING FACULTY GREG CARMICHAEL Chair; U. of Kentucky, 1979, Global Change/ Supercomputing RAVI DATTA UCSB, 1981 Reaction Engineering/ Catalyst Design DAVID MURHAMMER U. of Houston, 1989 Animal Cell Culture J. KEITH BEDDOW U. of Cambridge, 1959 Particle Morphological Analysis JONATHAN DORDICK MIT, 1986, Biocatalysis and Bioprocessing DAVID RETHWISCH U. of Wisconsin, 1984 Membrane Science/ Catalysis and Cluster Science AUDREY BUTLER U. of Iowa, 1989 Chemical Precipita tion Processes DAVID LUERKENS U. of Iowa, 1980 Fine Particle Science V.G.J. RODGERS Washington U., 1989 Transport Phenomena in Bioseparations For information and application write to: GRADUATE ADMISSIONS Chemical and Biochemical Engineering The University of Iowa Iowa City, Iowa 52242 3193351400 THE UNIVERSITY OF IOWA IOWA STAm OF SCIENCE ANDr!4 a i Impop A For additional information, please write Graduate Office Department of Chemical Engineering Iowa State University Ames, Iowa 50011 or call 515 2947643 EMail Seagrave@IASTATE.EDU U Biochemical and Biomedical Engineering Charles E. Glatz, Ph.D., Wisconsin, 1975. Carole A. Heath, Ph.D., R.P.I., 1988. PeterJ. Reilly, Ph.D., Pennsylvania, 1964. Richard C. Seagrave, Ph.D., Iowa State, 1961. Catalysis and Reaction Engineering L. K. Doraiswamy, Ph.D., Wisconsin, 1952. Terry S. King, Ph.D., M.I.T., 1979. Glenn L. Schrader, Ph.D.. Wisconsin, 1976. Energy and Environmental George Burnet, Ph.D., lowa State, 1951. Thomas D. Wheelock. Ph.D.. Iowa State, 1958. Materials and Crystallization Kurt R. Hebert, Ph.D., Illinois, 1985. Maurice A. Larson, Ph.D., Iowa State. 1958. Gordon R. Youngquist, Ph.D., Illinois, 1962. Process Design and Control Derrick K. Rollins, Ph.D., Ohio State, 1990. Dean L. Ulrichson, Ph.D., Iowa State, 1970. Transport Phenomena and Thermodynamics James C. Hill, Ph.D., Washington, 1968. Kenneth R. Jolls, Ph.D., Illinois, 1966. __~__ ___._._ ._ _I =~a Graduate Study and Research in Chemical Engineering TIMOTHY A. BARBARI MARK A. MCHUGH Ph.D., University of Texas, Austin Ph.D., University of Delaware Membrane Science HighPressure Thermodynamics Sorption and Diffusion in Polymers Polymer Solution Thermodynamics Polymeric Thin Films Supercritical Solvent Extraction W. MARK SALTZMAN MICHAEL J. BETENBAUGH Ph.D., Massachusetts Institute of Technology Ph.D., University of Delaware Transport in Biological Systems Biochemical Kinetics Polymeric Controlled Release Insect Cell Culture CellSurface Interactions Recombinant DNA Technology W. H. SCHWARZ Dr. Engr., The Johns Hopkins University MARC D. DONOHUE o Rheology Ph.D., University of California, Berkeley NonNewtonian Fluid Dynamics Equations of State Physical Acoustics and Fluids Statistical Thermodynamics Turbulence Phase Equilibria Phase Equilibria KATHLEEN J. STEBE JOSEPH L. KPh.D., The City University of New York Interfacial Phenomena Ph.D., University of Chicago Electropermeability of Biological Membranes Nucleation Surface Effects at FluidDroplet Interfaces Crystallization Flame Generation of Ceramic Powders DENIS WIRTZ Ph.D., Stanford University Phase Transitions and Critical Phenomena Polymer Systems Far from Equilibrium Pattern Selection in Convective Systems For further information contact: The Johns Hopkins University G. W.C. Whiting School of Engineering Department of Chemical Engineering Baltimore, MD 21218 (410) 5168480 E.O.E./A.A. 11 pn In Q~ Fall 1993 GRADUATE STUDY IN CHEMICAL AND PETROLEUM ENGINEERING GRADUATE PROGRAMS * M.S. degree with a thesis requirement in both chemical and petroleum engineering * Ph.D. degree characterized by moderate and flexible course requirements and a strong research emphasis * Typical completion times are 1618 months for a M.S. degree and 4 1/2 years for a Ph.D. degree (from B.S.) RESEARCH AREAS Catalytic Kinetics and Reaction Engineering Chemical Vapor Deposition Controlled Drug Delivery Corrosion Economic Evaluation Enhanced Oil Recovery Processes Fluid Phase Equilibria and Process Design Kinetics and Homogeneous Catalysis for Polymer Reactions Plasma Modeling and Plasma Reactor Design Phase Behavior Process Control Supercomputer Applications Supercritical Fluid Applications Waste Heat and Pollution of Combustion Processes FINANCIAL AID Financial aid is available in the form of fellowships and research and teaching assistantships ($13,000 to $16,000 a year) FACULTY Kenneth A. Bishop (Ph.D., Oklahoma) John C. Davis (Ph.D., Wyoming) Don W. Green (Ph.D., Oklahoma) Colin S. Howat (Ph.D., Kansas) Carl E. Locke, Jr., Dean (Ph.D., Texas) Russell D. Osterman (Ph.D., Kansas) Marylee Z. Southard (Ph.D., Kansas) Bala Subramaniam (Ph.D., Notre Dame) Galen J. Suppes (PH.D., Johns Hopkins) Brian E. Thompson (Ph.D., MIT) Shapour Vossoughi (Ph.D., Alberta, Canada) G. Paul Willhite, Chairman (Ph.D., Northwestern) RESEARCH FACILITIES Excellent facilities are available for research and instruction. Extensive equipment and shop facilities are available for research in such areas as enhanced oil recovery processes, fluid phase equilibria, catalytic kinetics, plasma processing, and supercritical fluid applications. The VAX 9000, along with a network of Macintosh personal computers and IBM, Apollo, and Sun workstations, support computational and graphical needs. For more information and application material, write or call Th* TT;nivrs;it .f I na st .111 vI L oIALY V ILalIa THE UNIVERSITY The Graduate Adviser Department of Chemical and Petroleum Engineering The University of Kansas is the largest and most comprehensive 4006 Learned Hall university in Kansas. It has an enrollment of more than 28,000 and Lawrnc KS Lal660452 almost 2,000 faculty members. KU offers more than 100 bachelors', nearly ninety masters', and more than fifty doctoral programs. The main campus is in Lawrence, Kansas, with other campuses in Kansas City, Wichita, Topeka, and Overland Park, Kansas. Chemical Engineering Education THE UIRTOK S Durland Hall Home of Chemical Engineering M.S. and Ph.D. Programs * Chemical Engineering * Interdisciplinary Areas of Systems Engineering * Food Science * Environmental Engineering Financial Aid Available Up to $17,000 Per Year For More Information Write To Professor B.G. Kyle Durland Hall Kansas State University Manhattan, KS 66506 Areas of Study and Research Transport Phenomena Energy Engineering Coal and Biomass Conversion Thermodynamics and Phase Equilibrium Biochemical Engineering Proces Dynamics and Control Chemical Reaction Engineering Materials Science Catalysis and Fuel Synthesis Process System Engineering and Artificial Intelligence Environmental Pollution Control Fluidization and Solid Mixing Hazardous Waste Treatment Fall 1993 Ic~ni KCANSAS STATE 9TRIVERSrT tAtxjw' 249 Far From An Ordinary Ball Research with advanced materials (carbon fibers, nitride catalysts, supercon ducting thin films, and liquid crystalline polymers) and with Buckyballs is ongoing here in Lexington. Anything But An Ordinary University At the University of Kentuckydesignated by the Carnegie Foundation as a Research University of the First Class, and included in the NSF's prestigious list ing of Top 100 research institutions in America CHOICESfor Chem. E. grad OK uate students are anything but ordinary. There are joint projects with Pharmacy, the Medical School, the Markey Cancer Center, and Chemistry researchers. And abundant opportu nities for intense interaction with extraordinary faculty, as well as access to stateoftheart facilities and equipment, including an IBM ES 3900/600J Supercomputer. With OutOfThe Ordinary Chem. E. Specialties Aerosol Chemistry and PhysicsWeighing picogram particles in electrodynamic balance, measuring monolayer adsorption, data with seven significant figures. Cellular BioengineeringRheological and transport properties of cell membranes; cell adhesion, cancer research, transport of drugs across membranes, and membrane biofouling. Computational EngineeringModeling turbulent diffusion in atmospheric convective boundary layers; modeling growth of multi component aerosol systems. Environmental Engineering EPAapproved analytical labora tory; global atmospheric transport models; atmospheric photochemistry; control of heavy metals and hazardous organic; water pollution research. Membrane ScienceDevelopment of low pressure charged membranes; thin film composite membranes; development of bio functional synthetic membranes. From A Uniquely UnOrdinary Faculty Recent national awards won by our faculty include: Larry K. Cecil AIChE Environmental Division; AIChE Outstanding Counselor Award, 1983, 1991; ASM Henry Marion Howe Medal; AAAR Kenneth T. Whitby Memorial Award; BMES Dr. Harold Lamport Award for a Young Investiga tor; and two NSFPresidential Young Investigators. Recent Universitywide awards by faculty include: Great Teacher; Research Professor; Excellence in Under graduate Education; and Alumni Professor. All Of Which Create Some Extraordinary Opportunities For You Doctoral incentives well worth your consideration: Up to $20,000 per year stipends plus tuition, books, research supplies, travel allowances. Interested in obtaining a degree of extraordinary worth? Contact Dr. K.W. Anderson, Department of Chemical Engineering, University of Kentucky, Lexington, KY 405060046 SUniversity of Kentucky Department of Chemical Engineering 6062574956 I Uilveisity of Kemucky I 
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