Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 17.6.3 - Studies on chemical reactions in liquid phase by applying flat micro reactors for the model-based determination of inherent kinetics
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 Material Information
Title: 17.6.3 - Studies on chemical reactions in liquid phase by applying flat micro reactors for the model-based determination of inherent kinetics Reactive Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Warnecke, H.-J.
Berth, G.
Waschke, S.
Bothe, D.
Zrenner, A.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: fluid phase
chemical reactions
kinetics
micro reactor
 Notes
Abstract: Flow based mixing procedures are of great importance in many chemical processes. Realizable mixing times range from a few milliseconds to seconds, whereas the entire homogenization can often not be guaranteed. If the mixing process is not determined, chemical reactions of this time scale are masked by the mixing procedure and do not reflect the inherent chemical kinetics. Aim of this work is the application and validation of a method for defining the inherent kinetics of chemical reactions in liquid phases. Therefore a flat micro reactor operated under stationary and laminar conditions is applied. The pursued strategy is based on the mechanical modelling of the amount of moles considering convection, diffusion and reaction and the determination of kinetic parameters by adjusting the model to experimentally obtained concentration fields. Therefore, reliable kinetic data is required to design and intensify chemical reaction processes. In this work the applied device is realized as a flat micro reactor (FMR) with a constant channel depth of 10 μm, therefore the 3-dimensional problem is transformed to a 2-dimensional one. This enables time reduction concerning the CDR model based calculations with respect to the experimental data (less computationally intensive evaluation). We report on the validation of the anticipated depth homogenization and the quantification of concentration fields by confocal laser induced fluorescence (LIF) microscopy. Furthermore results concerning the data- and model-based determination of kinetic parameters for a prototype process are presented.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Resource Identifier: 1763-Warnecke-ICMF2010.pdf

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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Studies on chemical reactions in liquid phase by applying flat micro reactors
for the model-based determination of inherent kinetics


H.-J. Warnecke1, G. Berth2, S. Waschke1, D. Bothe3 and A. Zrenner2

1University of Paderbor, Faculty of Science, Department of Chemistry, Institute of Polymer Materials and Processes
Warburger Str. 100, Paderbor, 33098, Germany
waschke@mail.uni-paderborn.de

'mi in\ ci -u of Paderborn, Faculty of Science, Department of Physics, Center for Optoelectronics and Photonics Paderborn
Warburger Str. 100, Paderbom, 33098, Germany

3Technical University Darmstadt, Faculty of Science, Department of Chemistry, Cluster of Smart Interfaces
Petersenstr. 32, Darmstadt, 64287, Germany


Keywords: fluid phase, chemical reactions, kinetics, micro reactor




Abstract

Flow based mixing procedures are of great importance in many chemical processes. Realizable mixing times range from a few
milliseconds to seconds, whereas the entire homogenization can often not be guaranteed. If the mixing process is not
determined, chemical reactions of this time scale are masked by the mixing procedure and do not reflect the inherent chemical
kinetics. Aim of this work is the application and validation of a method for defining the inherent kinetics of chemical reactions
in liquid phases. Therefore a flat micro reactor operated under stationary and laminar conditions is applied. The pursued
strategy is based on the mechanical modelling of the amount of moles considering convection, diffusion and reaction and the
determination of kinetic parameters by adjusting the model to experimentally obtained concentration fields. Therefore, reliable
kinetic data is required to design and intensify chemical reaction processes. In this work the applied device is realized as a flat
micro reactor (FMR) with a constant channel depth of 10 gmn, therefore the 3-dimensional problem is transformed to a
2-dimensional one. This enables time reduction concerning the CDR model based calculations with respect to the experimental
data (less computationally intensive evaluation). We report on the validation of the anticipated depth homogenization and the
quantification of concentration fields by confocal laser induced fluorescence (LIF) microscopy. Furthermore results
concerning the data- and model-based determination of kinetic parameters for a prototype process are presented.


Introduction

Chemical reactions require homogenous mixing of the
reactants on molecular scale. The time scale of flow based
mixing processes in liquid phase with an energy application
of up to 1 kW/kg ranges from 10-' to 10'1 s. Chemical
reactions that are not masked by mixing must not exceed
time scales of TR < 1 s to fulfill the condition TM << ZR.
Certainly if liquid-phase reactions exceed this time scale,
two methods can be adapted to determine their inherent
kinetics, which is not falsified due to imperfect mixing.
The experimental based approach is often not provable
under suitable experimental conditions, which have to be
arranged to fulfill the presupposition of Tm << T,. Therefore
a model-based method, which applies a 2-dimensional
convection-diffusion-reaction (CDR) model is taken into
consideration.
Measuring technologies, pursuing the absolute experimental
strategy, are the "stopped flow" and the "continuous flow"
method [3] with pre-mixing. In order to be able to study
chemical reactions in the named timescale, the "stopped


flow" method necessitates not only very small mixing times,
but also technologies for time-resolved (cycle frequency >
103 s-') simultaneous investigation on the concentration of
several components. The requirement of a high temporal
resolution can be overcome by "continuous flow" methods.
To reduce the pre-mixing time micro reactors have been
proved advantageous. First attempts to achieve
mixing-times in the scale of less than a millisecond by
chaotic advection, realized by engravings in the ground of
the micro reactor [4] or by pulsating volume currents [5] or
alternative by cross currents [6] are promising. But still the
achievement of an ideal mixture, cannot surely be
guaranteed in the time scale below 1 ms.
Additionally the processes of homogenization taking place
in the pre-mixer do not operate in the following measuring
channel. According to this the necessary homogeneity of the
profiles decreases by the interaction of chemical reaction
and aberration from the ideal "Plug-Flow". Therefore
preferentially the chemical kinetics were determined under
defined volume flow relations and after all calculated via
modelling.









Because of its miniaturized dimensions the micro channel
reactor was chosen [7-11] which enables time scales of
diffusion and reaction in the laminar current scale (Reynolds
number Re < 1) with moderate effort [6][12-14]. This
allows for examination of the kinetic parameters by
adjustment of CDR-models to the experimental obtained
concentration gradients. But still only few works on the
actual realization have been published. Thus Matthews et al.
[15] state the development of a three-dimensional finite
differences method (in kinetic evaluation), confirmed by
LIF experiments in the micro reactor. Wheat and Posner
[16] report on the application of the Ca2+/Fluo-4 equilibrium
reaction to determine the mixing quality. The kinetics of this
reaction have also been explored by Hoffmann et al. [17].
By quasi-stationary UV/VIS absorption, diffusion and
mixing processes were determined for the reaction-technical
interpretation of a micro reactor [18]. Kawamura et al. [19]
carried out numerical analyses for competitive consecutive
reactions in the micro reactor with the purpose of improving
the product yield.

Nomenclature

Re Reynolds number
Pe P6clet number
Dal Damk6hler number
Vm average flow velocity (m s-')
dh hydrodynamic diameter (m)
p pressure (N m 2)
h channel height (m)
b channel width (m)
L channel length (m)
d/2 dl: height diameter (m), d2: width diameter (m)
x variable, channel length (m)
y variable, channel width (m)
z variable, channel height (m)
w flow velocity depending on z, y (m s-')
k reaction rate constant (L mol-1 s-')
D diffusion coefficient (m2 s-')
c, concentration of species i (mol L 1)
V volume flow (tL/min)

Greek letters
7 dynamic viscosity (Pa s)
v kinematic viscosity (m2 s-')


Experimental Facility

For our experiments a T-shaped FMR (Borosilicate) with
rectangular profiles was adapted (Fig. 1). The micro reactor
consists of two inlets (width: 100 ntm, depth: 10 ntm) and the
mixing channel (width: 200 itm) with same depth.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

syringe pump (Harvard Apparatus), the pipe accessories
(with suitable filters) and the FMR installation module
(experimental setup adaptation). The syringe pump can be
equipped with two syringes, whose piston stroke is
generated by a mechanically conversed stepper motor. The
educts soluted in liquid phase are conveyed into the mixing
channel via two inlets.
To achieve well-defined flow conditions the FMR is
operated in steady state under terms of laminar flow. The
used flow velocities of vm = 2.1 x 10-4 m/s up to 8.3 x 10-2
m/s guarantee the laminar condition for this reactor
geometry (Re < 1).

Vm dH
Re = H (1)
U

Here u denotes the kinematic viscosity and dH the
hydrodynamic diameter. The hydrodynamic dwell-times and
the expected reaction times were chosen to be in the same
range which enables the monitoring of the reaction process
in axial direction.
For the given FMR geometry and the adjusted flow
properties the axial velocity component w(y, z) analytically
arises to:


w(y,z) = 16Ap sin sin y (2)
7L r / i j (i Z d Z + sin d 2 (2
7Ld dd, j dd, )


The simulated velocity field for a specific channel
cross-section (rectangular T-shaped), as shown in figure 2,
was obtained by the application of the incompressible
Navier-Stokes equation.



./ /. /


SI.
1.5 2.0
y ( o-04)
Figure 2: Simulated velocity field under laminar flow
condition inside the FMR (volume flow: 0.2 tL/min).

According to Hagen-Poiseuille an approximately parabolic
velocity profile arises as a function of the depth (z axis),
whereas perpendicular to the main flow direction (y axis) a
"Plug-Flow" profile develops in respectable approximation
(Fig. 3).


10 pm
100 pm


FMR:
laminar + steady state 200 pm
Figure 1: Scheme of the reactor geometry.

Furthermore the reactor instrumentation includes the


a) y (104m) b) z(10-5m)
Figure 3: FMR velocity profiles for laminar flow
condition (volume flow: 0.2 gl/min) in a) y-direction
(width) and b) z-direction (depth). Here the ratio between
channel width and depth is 20:1.






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Due to the low dimension of the channel depth a quick
homogenization is anticipated.
For analysis of the reaction processes inside the micro
channel several non-invasive measurement techniques can
be applied like fluorescence microscopy and Raman
spectroscopy [12, 13]. In the confocal mode detection light
which does not derive from the focal plane is faded out by a
confocal pinhole placed in front of the detection unit. Thus a
spatial filtering and an additional depth discrimination can
be achieved which allows for a 3-dim determination of
concentration fields [20]. The experimental analyses
presented here are performed by a modular confocal LIF
setup (Fig. 4). Here the generation of the detection signal
occurs directly by excitation of the species or via activity
quenching of a fluorophore respectively.

Pinhole-Module, BS FS


Figure 4: Schematic illustration of the modular-engineered
experimental setup for confocal LIF microscopy.

Several paths are implemented into the system for sample
excitation thus measurements in transmission and reflection
mode can be performed. Focussing of the excitation light
and collimation of the detection signals is realized by
utilization of an infinity-corrected objective. Here lateral
sample positioning is accomplished by a positioning system
with respect to a fixed laser focus. For spectral filtering
appropriate fluorescence filters are integrated in the
detection path. Thus solely fluorescence light is registered
by the detector. Operation in the quasi-stationary mode
increases the sensitivity of the system which enables
detection of acutely low material concentrations.


Results and Discussion

System parameters and validation:


The experimental determination of the kinetic parameters is
based on the transformation from a temporal resolution (z =
1 s ... 1 ms) into a spatial one, which requires stationarity of
the system. Thus the local concentration variation can be
measured by appropriate analysis methods and the temporal
ones can be derived. Additionally the assumption of vertical
homogenization within the system is of much importance. In
order to validate the steady state, two records of adjacent
FMR areas (same confocal plane) were recorded with a
temporal delay, whereas the spatial development of the
pH-value in the neutralization-reaction NaOH-H2CO3 was
observed (Fig. 5).


t NaOH
4


t t,=30 min
t.t-


0 t 1000 1500 2000 2500 3000
HCO X (pm)
Figure 5: Assembly of two images (I. and II.) of adjacent
areas inside the FMR, recorded with a time delay of 30
minutes (volume flow: 10 tL/min). Here the scan
increment was 5 gtm in y-direction and 20 gtm in
x-direction.

The assembly of recorded images proves a sufficient steady
state regime. Furthermore the correlation of the particular
intensity levels demonstrates the long-term stability of this
measuring method (temporal constancy of the signal
intensity).
To ensure the 2-dimensional interpretation of concentration
profiles, the working hypothesis of homogeneous profiles in
vertical direction has been proved by computational
simulation and experimental investigation. The development
of the segregated concentration profiles in flow direction (x)
is shown in figure 6.








Figure 6: Cross section plots (y/z-planes) of normalized
concentration fields along flow direction derived from
numeric calculation (diffusion coefficient: 6.5 x 10-10 m2/s;
volume flow: 0.2 gL/min).

Due to the short diffusion paths the concentration in vertical
direction is already homogenized. Corresponding
simulations also were done for different segregated entrance
profiles (e.g. triangular), whereby the concentration is
depth-homogenized in each case.
The experimental validation of the anticipated depth
homogenization was done by measuring concentration
profiles for different depths via confocal LIF microscopy.
Exemplarily such profiles resulting from the reaction system
CaGreen/CaC12 are depicted in figure 7.


0 100 200
v (m)
Figure 7: Normalized concentration profiles (transverse to
the flow direction) for different depths (z) at a distance
(Ax) of 50 pm away from the T-junction.









This axial homogenization also was verified for additional
measuring points along flow direction (Ax). The excellent
correspondence of the concentration profiles originating
from different depths proves the assumed depth
homogenization. Therefore the restriction of the model-
based analysis on the horizontal and axial transport
mechanisms is justified.
Furthermore the homogenization in depth was validated
experimentally by mapping of confocal slices (x/y-planes)
of different depths (z), whereby the slice distance was fitted
to the depth discrimination of the optical system. In any
confocal plane, the development of the concentration profile
along the current direction (x) shows the expected shape of
the reaction wedge.

Model-based Interpretation:

The interpretation of recorded concentration profiles is
based on a "first-principles" model and performed by
adaptation of its kinetic parameters to the experimentally
determined species fields. Due to the stationary flow, the
modelling is reduced to transport equations for the chemical
species.

A simple reaction is of the type:

A+B >P (3)

This leads to following equations (incl. chem. reaction):

8cA
w(z, y) = DAACA k CAC (4)
8x
9c
w(z,y) = DBAc, -kcAc, (5)
ax

w(z,y)- = DpAcp +k CAc, (6)
ax

for -- 2 2 2 ~ 2

Here k is the reaction rate constant, c, the molar
concentration of the chemical species i, D, their diffusion
coefficient and w(z,y) the axial velocity component. L, h, b,
represent the length, height and width of the mixing channel.
The diffusion in flow direction (x) can be disregarded:


Ac = + (8)


Due to the height independent concentration profiles a
concentration change only occurs in y-direction:

h/2
C,(y)= Jc,(z,y)dz (9)
h/2


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Equations (4) (6) and the approximately ideal
"Plug-Flow" profile in y-direction lead to the final equations
after integration of height. In non-dimensional phrase these


c*A 1 2cA b
Ox* Pe a 2 L

S1-__ c -Da cac,
x* Pe y 82 L
acp 1 02Cp b *
+ DaICACB
x* Pep y*2 L
1 1 L
For -- 2 2 b


with y* = x*
b=


z bW kcrefL
, Pe = Da, -r
b D, W


The mathematical model (10)-(12) is completed by
following boundary conditions:


9c 1
- = 0 at y c, =c,,,,
wy 2
with x*= 0 for i= A,B,P


This results in a system of partial differential equations in
only one space variable, which allows for a time efficient
numerical calculation and therefore enables the
parameter-adaptation by nonlinear regression. For the
determination of one specific diffusion coefficient the
system of equations is reduced to a component equation
without reaction term.

Determination of Parameters:

For the in principle validation of the FMR method Ca2
sensing in aqueous solutions was chosen. Here the
considered reaction represents the complexation of calcium
by appropriate fluorophores (Fluo-4). The resulting
complexes exhibit a specific fluorescence ("Off/On
-system") and therefore the system is adaptable to
LIF-microscopy.


Ca2+ + Fluo-4 = [Ca-Fluo-4]2


For the excitation of Fluo-4/Ca2+-complex a diode pumped
solid state Laser (473 nm) was used, whereby the emitted
wavelength (473 nm) is within in the absorption band of
Fluo-4 (absorption maximum: 493 nm). The calibration
procedure has been carried out on the reactor system in
confocal mode (detection volume approx. 0.5 unm3).
As depicted in figure 8, within the relevant concentration
range (1 x 10-9 mol/L to 1 x 10-6 mol/L) a linear correlation
between the [Ca-Fluo4] +-concentration and corresponding
fluorescence intensity ensues.












30k o 10k

'F 20k- 1E-9 1E-8 1E-7 1E-6
c Concentration (molL
10k
S| Adj. R-Square: 0,997
0
0 3x107 6x107 9x10-7
Concentration (mol/L)
Figure 8: Calibration curve: Plot of the fluorescence
intensity versus [Ca-Fluo4]2+-concentration.

Based on this functional correlation corresponding
concentration fields are assigned to the determined local
intensity distribution. To ensure a stable neutral pH-value
Tris(hydroxymethyl)-aminomethan was used as a buffer.

For determination of the inherent kinetics of chemical
reactions a definite knowledge of the diffusion processes is
required. Here the parameters result from experimental
quantified concentration fields adjusted by fitting to the
model. Concerning the complexation of Ca2+ via Fluo-4 the
diffusion of the complex was examined. Therefore two
aqueous solutions of CiCl Fluo-4 (Fluo-4: 1.08 x 10-7
mol/L) and of CaC12 respectively with equal
Ca2-concentrations (10-2 mol/L) were injected into the
inlets of the micro reactor. Under these conditions the
resulting fluorescence image is solely based on the diffusion
of the [Ca-Fluo-4]2+-complex. The diffusion wedge of the
complex occurs at the contact line of both solutions (Fig.9)
whereby its shape is predominantly affected by the flow
conditions and the diffusion parameters.


experiment:
200


0mm


simulation:


200
100


2.6x10 8

5.1xlO8

M 1.0xli'7


ck= 1,0-10-7 mol/L
V= 0,2 pL/min
Re= 0,03
k= [Ca-Fluo4]2+


Figure 9: Concentration field based on experimental data
caused by the diffusion of [Ca-Fluo4]2 (above) and
appropriate result by simulation (below).

Experimental data were obtained by measurements at a
volume flow of 0.2 [tL/min (Re = 0.03). The depicted
concentration field shows the specific increase and decrease
of the [Ca-Fluo4]2+-complex on the opposite channel halves.
The determined concentration fields are based on the initial
concentrations and volume flows. Here the model-based
numeric adjustment of the diffusion parameter to the
experimental data yields a diffusion coefficient for the
Ca-Fluo-4 complex of Dca-Fluo-4 = (6.5 0.6) x 10-10 ms1.

For reaction analysis the complexation of Calcium by
Fluo-4 was examined. Therefore on one side (inlet A) of the
FMR a Fluo-4-solution completely reacted with Ca2
(Fluo-4: 1.0 x 10-7 mol/L, Ca2+: 1.0 x 10-2 mol/L) was


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

induced. A solution of equal Fluo-4 concentration with a
basic complex concentration due to the Ca2+ impurities of
the solvent was filled into the second inlet (inlet B). The
diffusion of the exceeded Ca2 causes the complexation and
therefore imaging of the resulting concentration field
becomes possible (Fig. 10). Additionally our measuring
method allows for quantitative determination of the Ca2
background concentration.

Fluo4 (1,0x 10-7mol/L) V = 0.2 pL/min
200 4.6x10
~100 7.5x10 8
S1.Ox107
t X(pm)
Fluo4 (1,0x107 mol/L)
Ca2+(1,0xl02 mol/L)
Figure 10: Confocal image of the recorded [Ca-Fluo-4]2
concentration field resulting from the reaction of Ca2+ and
Fluo-4 (Volume flow: 0.2 [tL/min, Scan increment: Ay = 2
[um, Ax = 20 [tm).

For the determination of the reaction rate-constant a spatial
high-resolved measurement (Ay = 250 nm) has been
performed on this system, to enable the mathematical
adaption at a low wedge expansion. Via CDR-model
adaption a value of k = (7 1.2) x 108 L mol1- s- was
obtained for the reaction rate-constant. The determined
values for the diffusion constant D and the reaction
rate-constant k suit well to the values given in the literature
[16].


Conclusions

This work represents a fundamental study on inherent
kinetics of chemical reactions in liquid phase. Here the
determination of the kinetic parameters is realized by
adjustment of a convection-diffusion-reaction model to
concentration fields quantified by confocal LIF-microscopy
under laminar and stationary conditions. It was shown, that
the applied method is appropriate for the determination of
kinetic parameters.
An essential condition is the steady state of the FMR, which
was validated by successive time-delayed mapping of
adjacent concentration fields. Both, numeric calculations
and depth resolved analyses confirm the anticipated depth
homogenization. Here the measured concentration profiles
perpendicular to the main flow direction show a nearly
congruent run for different depths. Furthermore confocal
slices of the concentration fields show approximately an
identical spatial distribution. The FMR method was
validated by Ca2+ sensing in aqueous solutions under
application of appropriate flourophores. A linear correlation
between fluorescence intensity and corresponding complex
concentrations was found in the relevant range (103 10-9
mol/L). For both, diffusion and reaction processes
corresponding concentration fields were quantified. We
found a good qualitative and quantitative agreement
between simulation and experiment. Furthermore kinetic
results for the Ca2+ complexation via Fluo-4 as a prototype
process were presented. Overall within this work we have
established our method as an appropriate technique for
determination of inherent kinetics in liquid phase.


B N~m


R 1UU____


>1


E


I









Acknowledgements

The authors would like to acknowledge support by the DFG
(PAK119). Furthermore the authors thank Prof. Dr. T. Meier
(University of Paderbom) for his valuable support and Prof.
Dr. M. Schliiter (Technical University of Hamburg-Harburg)
for useful discussions on fluorescence microscopy.


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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


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