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1 THE ROLE OF SURFACE MICROSTRUCTURE AND TOPOGRAPHY IN POOL BOILING HEAT TRANSFER By BRADLEY BON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE D EGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2011
2 2011 Bradley Bon
3 To m y p arents
4 ACKNOWLEDGMENTS I would like to acknowledge Professor James F. Klausner, my Ph. D. advisor, for dedicating his time to many in depth thought prov oking discussions. His dedication to quality research and meticulous theoretical development have instilled in me the qualities to be a successful Mechanical Engineer. I would also like to extend my gratitude to my supervisory committee Professors Renwei M ei, David Worthington Hahn and Jason F. Weaver whose additional guidance and expertise facilitated the development and completion of this research. I would like to thank my colleague Edward McK enna for his time and effort in the development of this resea rch. I would also like to extend my gratitude to m y fellow graduate students who turned the otherwise arduous task of doctoral research into an enlightening and enjoyable experience. I would like to thank my parents, whose commitment and sacrifice through out my life have always assured that I receive the best education possible. Certainly without their encouragement I would not be where I am today. Special thanks are given to Nicole Kurthausen. H er patience, love and support have kept me motivated througho ut this entire process.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 9 LIST OF ABBREVIATIONS ................................ ................................ ........................... 15 ABSTRACT ................................ ................................ ................................ ................... 18 CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW ................................ ..................... 20 1.1 Boiling Heat Transfer ................................ ................................ .................. 20 1.2 The Boiling Curve ................................ ................................ ....................... 24 1.3 What Affects Boiling Heat Transfer? ................................ ........................... 30 1.3.1 Pressure ................................ ................................ ............................ 31 1.3.2 Subcooling ................................ ................................ ........................ 31 1.3.3 Dissolved Gases ................................ ................................ ............... 31 1.3.4 Forced Convection ................................ ................................ ............ 32 1.3.5 Surface Roughness ................................ ................................ .......... 32 1.3.6 Surface Size and Gravity ................................ ................................ .. 36 1.3.7 Surface Orientation ................................ ................................ ........... 36 1.3.8 Surface Geometry ................................ ................................ ............. 37 1.3.9 Surface Wettability ................................ ................................ ............ 39 1.3.10 Surface Modification ................................ ................................ ........ 41 1.4 Thermodynamics of Metastable Liquids ................................ ..................... 46 1.5 Fundamentals of Nucleation Theory ................................ ........................... 52 1.6 Dissertation Outline ................................ ................................ .................... 61 2 EXPERIMENTAL FACILITY ................................ ................................ ................... 63 2.1 Substrate Heater ................................ ................................ ........................ 63 2.2 Pool Boiling Chamber ................................ ................................ ................. 67 2.3 Data Acquisition ................................ ................................ ......................... 69 2.4 Image Acquisition ................................ ................................ ....................... 69 2.5 Experimental Procedure ................................ ................................ ............. 70 2.6 Data Post Processing ................................ ................................ ................. 71 2.7 Image Analysis for Determining Nucleation Site Density on Structured Surfaces ................................ ................................ ................................ ........ 82 3 POOL BOILING ON SMOOTH SURFACES ................................ ........................... 85 3.1 Nucleation and Heat Transfer on Smooth Surfaces ................................ ... 85
6 3.2 Pool Boiling Results for Smooth Surfaces ................................ .................. 92 3.2.1 Experiment Series 1 ................................ ................................ .......... 92 3.2.2 Visual Observations for Series 1 ................................ ....................... 98 3.2.3 Experiment Series 2 ................................ ................................ ........ 102 3.3 Discussion of Heat Transfer Results ................................ ........................ 107 3.3.1 Experiment S eries 1 ................................ ................................ ........ 107 3.3.2 Experiment Series 2 ................................ ................................ ........ 115 3.4 Concluding Remarks on Boiling Heat Transfer of Smooth Surfaces ........ 123 4 POOL BOILING ON CYLINDRICAL CAVITY ARRAYS ................................ ........ 125 4.1 Introduction to Cylindrical Cavity Arrays ................................ ................... 125 4.2 Surface Fabrication ................................ ................................ .................. 128 4.3 Cylindrical Cavity Array Boiling Heat Transfer Results ............................. 130 4.4 Discussion and Concluding Remarks o n Cylindrical Cavity Arrays .......... 154 5 POOL BOILING ON HOODOO STRUCTURE ARRAYS ................................ ...... 157 5.1 Introduction to Hoodoos ................................ ................................ ........... 157 5.2 Hoodoo Surface Fabrication ................................ ................................ ..... 164 5.3 Hoodoo Array Pool Boiling Results ................................ .......................... 165 5.3.1 Hoodoo Size an d Spacing ................................ ............................... 165 5.3.2 Hoodoo Physical Attributes ................................ ............................. 172 5.3.3 Fluid Property Effects on Hoodoo Boiling Heat Transfer ................. 176 5.4 Discussion and Concluding Remarks on Hoodoo Surface Structures ...... 195 6 RECOMMENDATIONS FOR FUTURE RESEARCH ................................ ............ 200 6.1 The Mitigation of Edge Boiling ................................ ................................ .. 200 6.2 Modified Heterogeneous Nucleation Theory ................................ ............ 201 6.3 Parametric Surface S tructure Studies ................................ ...................... 202 APPENDIX A HEATER DESIGN FOR THE MITIGATION OF EDGE BOILING ......................... 203 B TABULATED POOL BOILING DATA ................................ ................................ .... 217 LIST OF REFERENCES ................................ ................................ ............................. 240 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 249
7 LIST OF TABLES Table page 2 1 Fitting coefficients for the calibration curves generated for heaters 1 and 2. Statistical parameters are included to verify accuracy. ................................ ....... 66 3 1 Thermophysical proper ties of the different heating surfaces used. ..................... 88 3 2 Planar structure and planar density for an FCC crystal. The crystal planes shown are those that were tested. ................................ ................................ ...... 89 3 3 Crystal structure of five different crystal planes of Silicon. Atoms colored black are those that are at the topmost layer of the crystal. ............................... 90 3 4 Thermophysical property comparison of hexane and perfluorohexane. ............. 91 4 1 Facilities used for surface fabrication. ................................ .............................. 129 4 2 Measured nucleation site de nsity for the shallow cylindrical cavities with varying cavity spacing and diameter at different heat fluxes. (Pool boiling of FC 72) ................................ ................................ ................................ .............. 138 4 3 Measured nucleation site density for the deep cylindr ical cavities with varying cavity spacing and diameter at different heat fluxes. (Pool Boiling of FC 72) ... 139 4 4 The number of cylindrical cavities on a given surface as a function of cavity spac ing. ................................ ................................ ................................ ............ 140 B 1 Pool boiling data for three crystal plane orientations of silicon with FC 72 as the working fluid. ................................ ................................ ............................... 217 B 2 Pool Boiling d ata for three crystal plane orientations of silicon with hexane as the working fluid. ................................ ................................ ............................... 218 B 3 Pool boiling data for five different crystal planes of silicon with FC 72 as the working fluid. ................................ ................................ ................................ ..... 219 B 4 Pool boiling data for five different crystal planes of silicon with hexane as the working fluid. ................................ ................................ ................................ ..... 220 B 5 Pool boiling data for diff erent crystal plane orientations of copper with FC 72 as the working fluid. ................................ ................................ .......................... 221 B 6 Pool boiling data for different crystal plane orientations of copper with hexane as the working fluid. ................................ ................................ .......................... 222 B 7 Pool boiling data for different crystal plane orientations of aluminum with FC 72 and hexane as the working fluids. ................................ ............................... 223
8 B 8 Pool boili ng data for polycrystalline nickel and titanium with FC 72 and hexane as the working fluids. ................................ ................................ ........... 224 B 9 Pool boiling data for shallow cylindrical cavity arrays with 3 m and 9 m diameter at 300 m spacing with FC 72 as the working fluid. .......................... 225 B 10 Pool boiling data for shallow cylindrical cavity arrays with 27 m diameter at 75, 150 and 300 m spacing with FC 72 as the working fluid. ......................... 226 B 11 Pool boiling data for shallow cylindrical cavity arrays with 75 m diameter at 300 and 600 m spacing with FC 72 as the working fluid. ............................... 227 B 12 Pool boiling data for deep cylindrical cavity arrays with 3 m and 9 m diameter at 300 m spacing with FC 72 as the working fluid. .......................... 228 B 13 Pool boili ng data for deep cylindrical cavity arrays with 27 m diameter at 75, 150 and 300 m spacing with FC 72 as the working fluid. ............................... 229 B 14 Pool boiling data for deep cylindrical cavity arrays with 75 m diameter at 300 and 600 m spacing with FC 72 as the working fluid. ............................... 230 B 15 Pool boiling data for deep cylindrical cavity arrays with 9 m diameter at 75 and 150 m spacing with FC 72 and he xane as the working fluids. ................. 231 B 16 Pool boiling data for different Hoodoo sizes with FC 72 as the working fluid (wafer 1). ................................ ................................ ................................ .......... 232 B 17 Pool boiling data for different Hoodoo spacing with FC 72 as the working fluid. ................................ ................................ ................................ .................. 233 B 18 Pool boiling data for hoodoo attribute variation with FC 72 as the working fluid. (Standard, Short, Less U ndercut) ................................ ............................ 234 B 19 Pool boiling data for hoodoo attribute variation with FC 72 as the working fluid. (No undercut, Thick top, Copper coating) ................................ ................ 235 B 20 Pool boiling data for 10 and 20 m hoodoo with FC 72 as the working fluid. (wafer 2) ................................ ................................ ................................ ........... 236 B 21 Pool boiling data for 40 and 80 m hoodoo with FC 72 as the working fluid. (wafer 2) ................................ ................................ ................................ ........... 237 B 22 Pool boiling data for 10 and 20 m hoodoo with hexane as the working fluid. (wafer 2) ................................ ................................ ................................ ........... 238 B 23 Pool boiling data for 40 and 80 m hoodoo with hexane as the working fluid. (w afer 2) ................................ ................................ ................................ ........... 239
9 LIST OF FIGURES Figure page 1 1 Bubble ebullition cycle. ................................ ................................ ....................... 25 1 2 Boiling curve for controlled heat flux. ................................ ................................ .. 26 1 3 Conceptual depiction of the potential energy surface. ................................ ........ 49 1 4 Generic pressure volume diagram. ................................ ................................ .... 51 1 5 Classical heterogeneous bubble nucleation model. ................................ ............ 57 2 1 Substrate heating block assembly. ................................ ................................ ..... 63 2 2 Calibration of heater 1. ................................ ................................ ....................... 65 2 3 Calibration of heater 2. ................................ ................................ ....................... 65 2 4 Pool boiling facility. ................................ ................................ ............................. 68 2 5 Apparent heat flux and wall superheat time histories during an incipience event. ................................ ................................ ................................ .................. 73 2 6 Time history of the apparent heat flux determined from equatio n 2 18. .............. 76 2 7 Relationship between the time till the maximum in apparent heat flux and thermal diffusivity. ................................ ................................ ............................... 77 2 8 Apparent heat flux and wall superheat time histories for CHF. ........................... 80 2 9 Variation of apparent heat flux following CHF. ................................ .................... 81 2 10 Wall temperature change foll owing CHF. ................................ ........................... 81 2 11 Mask image taken of surface before boiling. ................................ ...................... 82 2 12 Image taken at steady state for a given heat flux. ................................ .............. 83 2 13 Subtraction of mask image from target image. ................................ ................... 83 2 14 Conversion of target image from RGB to gray scale. ................................ ......... 83 2 15 Application of built in MATLAB function for contrast limited adaptive histogram equalization. ................................ ................................ ....................... 84 3 1 Boiling curves for perfluorohexane on all the polycrystalli ne and single crystal <111> orientation surfaces. ................................ ................................ ................ 93
10 3 2 Boiling curves for hexane on all the polycrystalline and single crystal <111> orientation surfaces. ................................ ................................ ........................... 93 3 3 Boiling curves for perfluorohexane on two different crystal plane orientations of Aluminum. ................................ ................................ ................................ ....... 95 3 4 Boiling curves for hexane on two different crystal plane orientati ons of Aluminum. ................................ ................................ ................................ ........... 96 3 5 Boiling curves for perfluorohexane on two different crystal plane orientations of copper. ................................ ................................ ................................ ........... 96 3 6 Boiling curve s for hexane on two different crystal plane orientations of copper. ................................ ................................ ................................ ............... 97 3 7 Boiling curves for perfluorohexane on three different crystal plane orientations of Silicon. ................................ ................................ ........................ 97 3 8 Boiling curves for hexane on three different crystal plane orientations of Silicon. ................................ ................................ ................................ ................ 98 3 9 Time series of film boiling transition at incipience for hexane on Si<110> ........ 100 3 10 Time series of film boiling transition for perfluorohexane on Si<110> ............. 100 3 11 Time series of transient film boi ling at incipience for hexane on Al<100> ....... 101 3 12 Time series of incipience for hexane on Al<111> surface ............................... 101 3 13 Boiling curves fo r pool boiling heat transfer of FC 72 on five different crystal planes of single crystal Silicon. ................................ ................................ ......... 105 3 14 Boiling curves for pool boiling heat transfer of hexane on five different crystal planes of single crystal Silicon. ................................ ................................ ......... 105 3 15 Boiling curves for pool boiling heat transfer of FC 72 on three different crystal planes of single crystal Copper. ................................ ................................ ........ 106 3 16 Boiling curves for pool boiling heat transfer of hexane on three different crystal planes of single crystal Copper. ................................ ............................ 106 3 17 Different regions of the microlayer under a bubble. ................................ .......... 111 3 18 Bubble radius time history for different fluid and heater combinations using the model of Chen et al. . ................................ ................................ ............ 117 3 19 Comparison of the effects heating block material on pool boiling of FC 72 on Si(111). ................................ ................................ ................................ ............. 118
11 3 20 Comparison of the effects heating block material on pool boiling of hexane on Si(111). ................................ ................................ ................................ ............. 118 3 21 Comparison of the effects heating block material on pool boiling of FC 72 on Si(100). ................................ ................................ ................................ ............. 119 3 22 Comparison of the effects heating block ma terial on pool boiling of hexane on Si(100). ................................ ................................ ................................ ............. 119 3 23 Comparison of the effects heating block material on pool boiling of FC 72 on Si(110). ................................ ................................ ................................ ............. 120 3 24 Comparison of the effects heating block material on pool boiling of hexane on Si(110). ................................ ................................ ................................ ............. 120 3 25 Comparison of the effects heating block material on pool boiling of FC 72 on Cu(100) ................................ ................................ ................................ ........... 121 3 26 Comparison of the effects heating block material on pool boiling of hexane on Cu(100). ................................ ................................ ................................ ........... 121 4 1 Effect of cavity diameter on the boiling heat transfer of FC ................................ ................................ ........................ 131 4 2 Effect of cavity diameter on heat transfer coefficient of FC ................................ ................................ .................. 132 4 3 Effect of cavity diameter on the boiling heat transfer of FC ................................ ................................ ................ 133 4 4 Effect of cavity diameter on heat transfer coef ficient of FC ................................ ................................ ................ 134 4 5 Images taken at q=0.96 W/cm 2 for the various cylindrical cavity surfaces with ................................ ................................ ................................ ..... 135 4 6 Images taken at q=0.96 W/cm 2 for the various cylindrical cavity surfaces with ................................ ................................ ................................ ....... 137 4 7 d FC 72 as the working fluid. ................................ ................................ ............... 140 4 8 depth with FC 72 as the working fluid. ................................ .............................. 141 4 9 with FC 72 as the working fluid. ................................ ................................ ........ 141
12 4 10 Effect of cavity spacing on heat transfer coeffi depth with FC 72 as the working fluid. ................................ .............................. 142 4 11 FC 72 as the working fluid. ................................ ................................ ............... 143 4 12 depth. ................................ ................................ ................................ ............... 144 4 13 .... 145 4 14 depth. ................................ ................................ ................................ ............... 145 4 15 boiling heat transfer performance of FC 72. ................................ ..................... 151 4 16 cal cavities, on the boiling heat transfer coefficient for FC 72. ................................ ........................ 152 4 17 cavity spacing on pool boiling heat transfer. ................................ ..................... 152 4 18 boiling heat transfer performance of hexane. ................................ ................... 153 4 19 boiling heat transfer coefficient for hexane. ................................ ...................... 153 4 20 Variation of bubble departure diameter with wall superheat f or FC 72 and ................................ ............... 154 5 1 Pit containing a small array of hoodoo surface structures. ............................... 158 5 2 Diagram depicting the relevant geometric parameters for calculating the characteristic length scale of the hoodoo surface structure. ............................. 160 5 3 ......... 161 5 4 ................... 162 5 5 Feature spacing shown are 6um, 12um, 24um, and 48um. .............................. 163 5 6 e to show the lower hoodoo structure. ................................ ................................ .................... 163 5 7 Diagram of the fabrication process used to create the hoodoo surfaces. ......... 164
13 5 8 Effect of hoodoo size on the pool boiling of FC 72. ................................ .......... 168 5 9 Effect of hoodoo size on the pool boiling heat transfer coefficient of FC 72. .... 169 5 10 Effect of Hoodoo size on CHF enhancement for pool boiling of FC 72. ........... 169 5 11 Effect of hoodoo spacing on the pool boiling of FC 72. ................................ .... 170 5 12 Effect of hoodoo spacing on the pool boiling heat transfer coefficient of FC 72. ................................ ................................ ................................ .................... 171 5 13 Effect of hoodoo spacing on CHF enhancement for pool boiling of FC 72. ...... 171 5 14 Effect of physical attribute variations of the hoodoo surface feature on pool boiling heat transfer of FC 72. ................................ ................................ .......... 174 5 15 Comparison of CHF enhancement for physical attribute variation. ................... 175 5 16 Effect of copper coating on pool boiling heat transfer of FC 72 on the hoodoo surface. ................................ ................................ ................................ ............. 175 5 17 Effect of copper coating on pool boiling heat transfer coefficient of FC 72 on hoodoo surface. ................................ ................................ ................................ 176 5 18 The effect of hoodoo size on the pool boiling heat transfer performance of with FC 72 as the working fluid. ................................ ................................ ........ 178 5 19 The effect of hoodoo size on pool boiling heat transfer performance with hexane as the working fluid. ................................ ................................ ............. 178 5 20 The effect of hoodoo size on the pool boiling heat transfer coefficient of FC 72.. ................................ ................................ ................................ ................... 179 5 21 The effect of hoodoo size on the pool boiling heat transfer coefficient with hexane as the wor king fluid. ................................ ................................ ............. 179 5 22 Comparison of the measured CHF enhancement for pool boiling of FC 72 and hexane on surfaces with different hoodoo sizes. ................................ ....... 183 5 23 Variation of the characteristic length scale of the hoodoo surface structure with hoodoo size. ................................ ................................ .............................. 184 5 24 Images taken of holes present in the vapor film on a hoodoo surface. ............. 184 5 25 Plot of CHF enhancement versus non dimensional parameter .................... 187 5 26 Predicted CHF enhancement due to capillary action as predict ed by the modified lift off model for working fluids FC 72 and hexane. ............................ 187
1 4 5 27 Time series showing the subsurface liquid front motion from a droplet of ................................ ................ 189 5 28 Measured relative liquid front motion for a hexane droplet on the 10 m and 30 m hoodoo surfaces at 25C. ................................ ................................ ....... 190 5 29 Capillar y front profiles near the point of displacement measurement. Data is ................................ ........... 191 5 30 Measured radius of curvature variation for the capillary liquid front Data is for hexane at 25C on the 10 m hoodoo surface. ................................ ................ 192 5 31 Dependence of wetted fraction of subsurface structure on hoodoo size. ......... 192 5 32 Comparison of the measured CHF enhancement for pool boiling of FC 72 on different hoodoo surfaces for different batches of surfaces. ............................. 194 A 1 Wall superheat variation for a circular he ating surface with a/R = 0.5, h = 100 W/m 2 K, H = 0.510 3 m, k = 110 W/m K, and T sat = 30 C. ............................ 206 A 2 Wall superheat variation for a circular heating surface with a/R=0.25, h=100 W/m 2 K, H=0.510 3 m, and T sat =30 C. ................................ .......................... 207 A 3 Wall superheat variation for a circular heating surface with a/R=0.5, h=100 W/m 2 K, H=0.510 3 m, and T sat =30 C. ................................ .......................... 207 A 4 Wall superheat variation for a circular heating surface with a /R=0.75, h=100 W/m 2 K, H=0.510 3 m, and T sat =30 C. ................................ .......................... 208 A 5 The dependence of the temperature difference between the center and the edge of the surface on applied wall superheat for different va lues of thermal conductivity. ................................ ................................ ................................ ...... 209 A 6 Wall superheat variation for a square heating surface with a/L=0.5, h=100 W/m 2 K, H=0.510 3 m, k=110 W/m K, and T sat =30 C. ................................ .. 212 A 7 Wall superheat variation for a square heating surface with a/L=0.25, h=100 W/m 2 K, H=0.510 3 m, and T sat =30 C. ................................ .......................... 213 A 8 Wall superheat variation for a square heating surface with a/L=0.5, h=100 W/m 2 K, H=0.510 3 m, and T sat =30 C. ................................ .......................... 213 A 9 Wall superheat variation for a circular heating surface with a/L=0.75, h=100 W/m 2 K, H=0.5 10 3 m, and T sat =30 C. ................................ .......................... 214 A 10 Variation of the center edge temperature difference with applied wall superheat for different values of heating surface thermal conductivity. ............ 215
15 LIS T OF ABBREVIATIONS CAP Capillary CHF Critical Heat Flux DFT Density Functional Theory FBI Film Boiling Incipience FCC Face Centered Cubic HET Heterogeneous HOM Homogeneous NSD Nucleation Site Density SAT Saturated NOMENCLATURE T Superheat ( C) x Thermocouple spacing A Surface area (m 2 ), Aspect ratio a Heating zone length scale C P Heat capacity (J/kg K) d Hoodoo size ( m) D Bubble departure diameter, Hoodoo region size E Interaction energy (J), CHF enhancement g Gravity (m/s 2 ), Hoodoo gap spacing ( m) h Hoodoo height ( m) H Surface Height J Nucleation rate (1/cm 3 s) k Thermal conductivity (W/m K)
16 k B Boltzmann constant L Length (m) L* Hoodoo characteristic length scale ( m) m mass per molecule N Number distribution n number of mo lecules P Pressure (N/m 2 ) q Heat Flux (W/cm 2 ) R Surface radius r Radius (m), Radial coordinate R Universal gas constant S Spacing ( m) SA Surface area ( m 2 ) T Temperature ( C) u Undercut ( m) V Hoodoo region volume ( m 3 ) v specific volume (m 3 /kg), Vapor ve locity x,y,z Cartesian Greek Letters Thermal diffusivity (m 2 /s), Molecular evaporation rate, z eigenvalue Molecular condensation rate Standard thermocouple error Non dimensional x,r coordinate
17 Non dimensional z coordinate Contact angle Curvat ure x,r eigenvalue Chemical potential Density (kg/m 3 ) Surface tension (N/m) Free energy, Non dimensional heat flux Subscripts b Bubble c Capillary e Equilibrium fg Liquid vapor h Heater L,l Liquid p Hoodoo post V,v Vapor w Wall
18 Abstract of Dis sertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THE ROLE OF SURFACE MICROSTRUCTURE AND TOPOGRAPHY IN POOL BOILING HEAT TRANSFER By Br adley Bon December 2011 Chair: James F. Klausner Cochair: Renwei Mei Major: Mechanical Engineering B oiling heat transfer is an integral part of industrial processes of all scales. The capability to predict boiling heat transfer rates is dependent upon t he ability to predict the active nucleation site density. However, subtle changes in surface structure and topography can produce significant variations in the active nucleation site density resulting in considerably different boiling heat transfer rates Determining the salient structural and topograph ical characteristics of the surface and their effects on boiling heat transfer requires surfaces that can be easily characterized. Three unique surfaces were used for a systematic investigation of the effects of surface microstructure on pool boiling heat transfer: Single crystal surfaces, Cylindrical Cavity arrays, and Hoodoo arrays. Pool boiling on metallic and non metallic single crystal surfaces has revealed that different crystal structures can yield not iceable changes in boiling heat transfer. Inherent differences in the molecular nature of the crystals result in different dependencies on crystal structure. These results confirm that in the absence of nucleation sites molecular structure can have profoun d effects on boiling heat transfer. Silicon cylindrical cavity
19 arrays with different cavity diameters, spacings, and depths have revealed the effects of controlled nucleation site density on different regimes of pool boiling. For low wall superheats accura te nucleation site density measurements have been made using image processing techniques to facilitate the investigation of controlled nucleation site density. Nucleation site activation performance was observed to vary significantly with cavity diameter a nd depth. At larger superheats, increased nucleation site density exacerbates heat transfer degradation due to local dry out of the heating surface. T he Hoodoo, a new surface enhancement structure for boiling heat transfer, was developed and parame trically studied. The unique hoodoo structure produces a variety of newly observed pool boiling phenomena: staggered nucleation site activation film boiling holes, and most notably critical heat flux enhancement Critical heat flux enhancement was observed to vary from 5% to 67% with varying hoodoo size and spacing for FC 72 and hexane A newly developed critical heat flux (CHF) model was extended to incorporate the effects of hemi wicking to predict the amount of CHF enhancement for the Hoodoo surface structure. Conclusively, s urface micro structure and topography c an greatly influence nucleate boiling heat transfer. The various p hysical attributes employed with the structured surfaces further reve aled the profound influence of surface topogr aphy on enhancing boiling heat transfer O n the atomic scale it is seen that even differences in crystal structure can also produce noticeable v ariations in the boiling heat transfer rate
20 CHAPTER 1 INTRODUCTION AND LITERATURE REVIE W 1.1 Boiling Heat Transfer From statistical to classical thermodynamics, lamin ar to turbulent flow and including all modes of heat transfer, boiling heat transfer can appear to be a complex dynamical process that is extremely difficult to explain from first principles However, a meticulous and methodical investigation will explicat e the most difficult to understand phenomena. In a review presented by Lienhard  he essentially poses the question to this day this is a formidable question. A majority of the fundamental and empirical boiling heat transfer knowledge we possess today is an assemblage of the pioneering work conducted over the last 50 years. The more recent developments in the field have moved into the realm of micro and nano scale thermal transport. Rapid advancements in computing technology and the demand for even greater comp uting power have shrunk the size of high powered computing Th e drastic decrease in the size of computing techno logy demands more innovative means of thermal management. Yet, application s of boiling heat transfer are not limited to the smallest of devices Boiling heat transfer is a crucial and intricate part of nuclear reactor facilities. A thorough knowledge of al l aspects of bo iling heat transfer is essential in thermal management of devices of all length scales From microchips to nuclear reactors, pool boiling is an essential mode of heat transfer for many industrial and technological applications. Although it is widely used in industrial practice a fundament al understanding is lacking. The current predictive capability relies on a surplus of empirical correlati ons with stringent usage criterions that produce reasonable pre d ic tions. At present a general empiric al understanding of the
21 influence of different variables such as pressure, subcooling, liquid thermoph y sical properties, surface roughness, surface orientation and surface material has been gained Even with this knowledge, pre dictive capabilities of heat transfer are limited to accura cies to with in 30%. A significant discrepancy among researchers is most typically associated with experimental facility variability and extraneous contaminants that are generally uncontrollable (i.e. impurities in the liquid Liquid impurities and surface contamination are generally very difficult to control and even the smallest level of contamination can significantly alter the nucleation rate. It is then clearly evident that the surface fluid in teraction is one of the most important factor s in a boiling process. Despite this, a comprehensive multi scale model for boiling heat transfer capable of linking molecular scales to continuum level phenomena remains elusive. A fundamental understanding of any physical phenomena inherently requires a first principles analysis from the molecular scale to the macro scale. Continuum mechanics is thoroughly capable of providing an empirical description of a majority of macro and meso scale phenomena. It is only at very small length scales where the applicability of continuum mechanics is questionable and whether the introduction of statistical and probabilistic methods is useful For instance, viscosity is a property that is completely understoo d from the perspec tive of Newtonian fluid flow and can therefore be accurately measured This level of understanding is sufficient for engineering purposes. However, a more detailed understanding of the molecular origins of viscosity requires a great deal of mathematical a nd theoretical rigor. A succinct and rudimentary explanation proceeds by considering that the fluid contains simple spherical molecules
22  Assuming that the mole cules are instantaneously arranged in a lattice structure there will be a certain number of voids present; these voids are small volumes that are present because of an absent fluid molecule. Molecules adjacent to the void can move into it but must overcome a potential energy barrier that is produced by molecules in closer proximity to the void. The energy minimums of the potential energy function are equal in magnitude due to the absence of an external force. However in the presence of an external force, th e force acts to reduce the energy required to move the molecule into the void if the force is in the direction of the void. Once a molecule is in the activated state, at the peak of energy barrier, movement into the void is guaranteed since it is energetic ally unfavorable to return to the initial position. Continuing along this line of reasoning it is shown that the viscosity takes a form similar to a unimolecular reaction rate type equation. It is found that the viscosity is proportional to the exponential of the Gibbs free energy of activation of the motion. It can further be presumed that the relative motion of molecules from one site to the next requires the breaking of intermolecular bonds. This breaking of intermolecular bonds is the same process by wh ich liquid vapor phase change occurs. Therefore the activation energy for relative molecular motion should be proportional to the energy required for vaporization. Hirschfelder et al.  do indeed show that the viscous activation energy is proportional to the internal energy of vaporization. The constant of proportionality in this case comes out to be approximately 0.408, which implies that the void volume required for molecule displacement is only a fraction of the actual molecular volume. The authors continue by noting that shape and type of molecule have drastic effects on the activation of viscous motion at the molecular scale due to the dependency of the heat o f vaporization on
23 these two molecular parameters. It is at this point where further fundamental understanding is inundated by the mathematical and theoretical rigor required to account for all the degrees of freedom associated with molecules, especially as temperature is increased. This example demonstrates that a fluid property as simple as viscosity can be very complex when analyzed at the molecular scale (from first principles) Further considering surface effects and fluid composition effects would o nly exacerbate the theoretical description of the phenomena. Boiling heat transfer falls into the category of physical phenomena whose ab initio understanding is not complete. This arises from two very general difficulties that hinder the detailed developm ent of a first principles model A complete understanding of the interaction at the solid liquid interface is the first hindrance. Surface structure and heterogeneity are some of the many characteristics of the heating surface that have an influence on the wetting dynamics at the solid liquid interface. This dynamic interaction between the solid and the liquid plays an important role throughout the entire boiling process from incipience to film boiling. However, merely saying that wetting is a controlling f actor is an understatement. The wetting characteristics can vary from hydrophobic to hydrophilic. Both extremes can show markedly different behaviors for different regimes of boiling heat transfer. S urface structure and heterogeneity can further complicate the complete description of the wetting dynamics. Surface structures, depending on their size, can drastically alter wetting affinity as well a s two phase flow dynamics Surface heterogeneity can create hydrophobic or hydrophilic regions with either stoch astic or periodic structure. Aside from altering the wetting ability larger scale
24 heterogeneity can alter the local temperature field if the two regions differ significantly in thermal properties. This is just a mere glimpse of the total complexity involv ed in accurately describing the underlying physics of the liquid solid interaction during boiling heat transfer. Furthermore, the second general hindrance to an accurate description of boiling heat transfer is the lack of a first principles understanding o f the molecular dynamics of phase change. We can assign a temperature at which boiling should occur, however when normally attempting to boil a liquid the temperature of the heating surface required to initiate boiling can be many degrees above the known b oiling point. The question that arises from this situation is what is happening in the liquid that the temperature must exceed that of the known boiling temperature? The simplest explanation typically begins by noting that the phenomenon of liquid vapor ph ase change is the result of breaking intermolecular bonds. However, as will be shown later on, a more complete thermodynamic description of fluids at temperatures in excess of their boiling temperatures is available. 1.2 The Boiling Curve Any comprehensive int roduction to boiling heat transfer begins by outlining the classical understanding of the bubble ebullition cycle, which is comprised of bubble nucleation, growth and departure. The diagram shown in Figure 1 1 depicts the various stages of the bubble ebullition cycle. In stage 1, vapor or non condensable gas is trapped in a pre existing cavity on the surf ace. Internal pressure decreases with increasing radius of curvature as a result of liquid vaporization and non condensable gas e xpansion resulting in bubble growth. At stage 2, the three phase line is initially pinned at the cavity mouth. For stage 3, furth er vaporization and bubble growth forces the three phase contact line to expand beyond the cavity mouth; the b ubble volume
25 cont inues to increase due to heat transfer and latent heat conversion. In stage 4, the increased buoyancy force begins to increase tension in the bubble interface. Bubble necking ensues and results in bubble departure, stage 5. Upon bubble departure a small po rtion of vapor remains within the cavity. The departing bubble also entrains fluid as a result of the wake generated. A short waiting time is generally observed before the cycle starts over. Bubble departure frequency and size are generally functions of th e local wall temperature and bulk fluid temperature. Figure 1 1 Bubble ebullition cycle: (1) Vapor trapped in cavity. (2) Bubble grows till interface is pinned at cavity mouth. (3) Bubble grows beyond ca vity mouth. (4) Bubble volume continues to increase due to vaporization. (5) Bubble departure resulting from rupture of interface due to excess buoyancy. The c onventional assessment of boiling heat transfer performance is characterized using a boiling curv e. Typically expressed as heat flux versus wall superheat this simple curve can capture all the salient heat transfer phenomena for a given boiling system. Figure 1 2 shows the generic boiling curve for a heat flux controlled surf ace. Moving from points A to B heat transfer from the surface occurs by natural convection. On approach to point B the thermal boundary layer becomes increasingly superheated. As will be discussed further in section 1.4 increa sed metastability increases the likelihood of phase change. At some given heat flux the surface superheat is enough for
26 Figure 1 2 Boiling curve for controlled heat flux. (Red Arrow Increasing Heat Flux Blue Arrow Decreasing Heat Flux) the rapid nucleation of vapor bubbles on the surface. The spontaneous generation of vapor results in high heat transfer due to latent heat conversion and therefore a significant drop in surface temperature occurs Alter natively, for a temperature controlled surface, the heat flux increases at incipience. Either way the resultant rapid latent heat conversion is apparent from the thermal energy expenditure observed from the heating surface. Upon reaching steady state at th e specified heat flux the state point resides at point C, which is now on the nucleate boiling curve. This phenomenon at incipience is most commonly referred to as temperature overshoot or temperature
27 hysteresis Temperature overshoot at incipience occurs because matter of any phase can exist in a metastable state (i.e. in states in excess of the equilibrium conditions). In the absence of ready centers for nucleation inc ipience is by its very nature a stochastic process. Skripov  reported that experimental measurements of the time to nucleation in a su perheated liquid were capable of being described by a Poisson distribution. The Poisson distribution is a discrete probability distribution used to describe the probability of number of events occurring in a fixed period of time with a known rate of occurr ence. Additionally, events are assumed to be independent of the time since the last event. The Poisson distribution is most applicable to events that rarely occur but have numer ous opportunities to occur, such as nucleation events. In You et al.  and You et al.  nucleate boiling heat transfer of highly wetting dielectric fluids as well as boiling incipience was investigated Multi run tests with FC 72 and R 113 showed a wide variation in the measured superheats. However when the recorded incipience data is recast to account for the number of occurrences in a given temperature range they find that heterogeneous incipience event s can likewise be described in a probabilistic manner. Surface energy, microstructure and material properties were also found to effect heat transfer but these effects will be further discussed in section 1.3 Continuing on, t h e line connecting points C and D comprises the nucleate boiling curve. The lower portion of the curve is generally referred to as the isolated bubble regime because of the low density of bubbles on the heating surface. In this regime thermal and convective communication between adjacent sites is minimal and therefore total heat transfer can be closely approximated by the additive contribution of single
28 bubble heat transfer. Increasing the heat flux beyond point C, more sites activate and the surface density of bubbles increases. Thermal and convective communication between adjacent bubbles now becomes a strong influence on bubble growth and departure. Additionally, bubble coalescence, both on the surface and for departing bubbles, becomes another important f actor in the heat transfer in this high heat flux regime. On approach to point D the high wall superheat begins to vaporize more of the liquid in contact with the surface. The high vapor generation rate produces columns of vapor from the nucleation sites. Vapor column coalescence induced by interfacial instability results in localized regions of superheated liquid that soon after dry out. Complete surface dry out then leads to the formation of a vapor film on the surface. The low thermal conductivity of the vapor film essentially insulates the surface and the lo cal heat transfer coefficient is dramatically reduced. Subsequently the surface temperature increases dramatically to accomodate the set heat flux. The heat flux at which this transition from nucleate boiling to film boiling occurs is referred to as the critical heat flux (CHF). A physical understanding of CHF has been attempted and many of the present models are mechanistic in nature which precludes a complete explanation of the physical mechanisms Likewise, bubble incipience and the many factors that influence its dynamics are also incompletely understood. Consider that on approaching point D the heat flux is decreased so as to return to point C. In this situation the state of the system would res ide on curve C D. However surfaces with complex surface structures do exhibit some hysteresis in the nucleate boiling regime, and this is generally attributed to the surfaces effectiveness at sustaining active nucleation. Boiling would persist upon decreas ing the heat flux below that at point
29 C moving towards point E. As mentioned above liquids can exist in metastable states and therefore to initiate boiling the temperature excess must be great enough to perturb the metastable state into a resulting phase transition. However, once the two phases are present this metastability impediment is no longer present. Boiling therefore continues because the bubbles are already present and their continued presence on the surface is controlled by the heat flux. Moving past point E the applied heat flux is no longer sufficient to sustain boiling, bubble collapse ensues and natural convection heat transfer becomes the sole thermal dissipative mechanism. Further decrease s in heat flux moves the state point along the natur al convection curve. However, further increasing the heat flux may result in a reduced superheat for incipience. Going below point E guarantees that bubbles are no longer present but remnant uncondensed vapor may be present in microscopic inclusions in the surface. Site reactivation from a previous cycle of boiling depends on how low of a surface temperature is reached before reheating is commenced. Buchholz et al.  and Luttich et al.  investigated local heat transfer mechanisms for different regimes of pool boiling using a microthermocouple probe, micro optical probe as well as an array of microthermocouples imbedded in a copper heater. The use of all these micro sensors provided excellent spatial and temporal resolution. Vapor temperature inside the departing bubbles was observed to increase with increasing superheat. In the low heat flux regime vapor temperatures were marginally higher than the saturation temperature where as in film boiling vapor temperatures far exceeded the saturation temperature. Temperature fluctuations indicative of the growth and departure of bubble s was observed with the micro
30 thermocouple array. Additional use of the other two micro sensors revealed that the superheated liquid layer above the sur face during boiling is subject to low frequency temperature fluctuations. The authors report that the th ickness of the superheated layer above the surface during boiling decreases with increasing superheat. It is also noted that in the low heat flux region the low number of active sites results in convection being the dominant contributing factor to the tot al heat flux. In the high heat flux regime, near critical heat flux, temperature excursions were observed in both the surface temperature and the departing vapor. The authors attribute this occurrence to periodic local dry out of the surface. Heat transfer mechanisms are further elucidated for the transition and film boiling regimes. 1.3 What Affects Boiling Heat Transfer? The preceding introduction to the boiling curve is just a glimpse of the underlying complexity inherent in two phase flow. There are a numbe r of controlling factors that can have marked effects on the boiling heat transfer rate. Some of these factors are related to system control parameters like pressure and liquid subcooling. Others pertain to surface related characteristics like surface roug hness, orientation, geometry, size and wettability. Even surface thermal properties can have an effect on boiling heat transfer  Many of these surface factors can occur simultaneously ; however a distinct understanding of their individual contribution is overshadowed by the inherent complexity involved in studying two phase flow s. Pioro et al.  provide a review of some of the common effects of surface parameters on boiling heat transfer. What proceeds here i s a small portion of the large amount of available literature on boiling heat transfer.
31 1.3.1 Pressure Significant changes in the system pressure can drastically alter the heat transfer. Increasing system pressure raises the boiling temperature and reduces the l atent heat of vaporization. However, the increased pressure also reduces the bubble size due to the compressibility of the vapor. As a result of the reduced bubble size there is a higher density of nucleating bubbles on the surface as well as a higher depa rture frequency. Thus an increase in heat transfer wi ll result in a leftward horizontal shift of the boiling curve for heat flux controlled experiments 1.3.2 Subcooling Increasing the subcooling of the bulk liquid increases the temperature difference which driv es the convective process and there for e natural convection is enhanced. As for the nucleate boiling regime a smaller portion of the thermal boundary layer is superheated, depending on the level of subcooling. Bubble growth is limited to this small region within the boundary layer. Despite this subcooling has a marginal effect on the nucleate boiling regime. Increases in CHF with respect to subcooling have been observed experimentally and this occurrence is due to the reduced impediment of liquid flow to t he surface. Bubbles that depart from the surface immediately begin to collapse because of the subcooled liquid. This in turn allows more fluid to reach the surface prolonging the film boiling transition (CHF). 1.3.3 Dissolved Gases The presence of dissolved gase s promotes nucleation site activation. Qi and Klausner  compared nucleation site densities in pool boiling and gas nucleation for both Water and Ethanol. For Water, moderately wetting, the nucleation site density as a result of gas nucleation is observed to be greater than that produc ed during pool boiling.
32 However for Ethanol, highly wetting, the nucleation site density observed during pool boiling is greater than that induced by gas nucleation. The behavior seen in the presence of dissolved gases is as expected due to the highly wett ing nature of the fluid, resulting in flooded cavities. However the anomalous low superheat measured, which resulted in much greater nucleation site densities put to question the convectional theory behind nucleation site activation. You et al.  earlier investigated the effect of dissolved gas content on pool boiling heat transfer and bubble incipience. High gas concen trations resulted in reduced incipient superheats and conversely low concentrations still required excessive surface temperatures to induce bubble nucleation. Furthermore, with low concentrations boiling hysteresis in the nucleate boiling regime was also o bserved. 1.3.4 Forced Convection The presence of forced convection enhances heat transfer in the natural convection regime. However, the reduced thickness of the boundary layer suppresses bubble nucleation to higher temperatures. Therefore a slope change in the natural convection portion of the boiling curve is observed with an additional elongation due to the increased incipient superheat. For the nucleate boiling regime the strong convective flows induced by the two phase flow minimize the enhancement of forced convection, especially in the high heat flux region. Yet CHF has been observed to increase in the presence of forced convection. 1.3.5 Surface Roughness Measuring surface roughness using one of the many methods available typically gives little descriptive infor mation about its boiling heat transfer performance. Any method used to measure surface roughness will produce several statistical metrics such
33 as average roughness, skew, kurtosis, maximum roughness, minimum roughness, etc. Little knowledge is available th at can correlate surface morphology and h eat transfer performance. T he presence of surface roughness on any boiling surface introduces two effects to boiling heat transfer, altered surface wettability and enhanced vapor trapping capability. Both effects ca n result in an enhancement in heat transfer. Most correlations that include surface roughness use the average or root mean squared (RMS) roughness. While the use of this metric has been shown to most strongly capture the effects of surface roughness, predi ctability is still limited and most correlations fall within a range of 30% uncertainty. However, the g eneral effect is a horizontal shift in the boiling curve and a reduction in the incipient superheat. Berenson  conducted a series of experiments to determine the e ffects of surface roughness, surface material and cleanliness on pool boiling heat transfer. His data showed that roughness had a significant effect on the heat transfer. However he notes that RMS roughness is not the sole parameter that can gauge a surfac es heat transfer performance. A comparison amongst the various methods of producing surface finishes of differing roughness further confirms his argument of loose applicability of RMS roughness. Tests were conducted with a variety of metallic surfaces with similar finishes. Roughness was observed to have a significant effect on heat transfer for all surfaces tested. Additionally, thermal properties of the surface also had significant effects on heat transfer. The author notes that although the surfaces may have had the same surface treatment the distribution and size of cavities present on the surface would depend on the hardness of the surface material. This can be attributed to the method used to apply the surface finishes. All surfaces were polished using lapping
34 compound, which is a suspension of abrasive particles. The polishing capability of the compound is dependent on the relative hardness of the surface compared to that of the abrasive particle. Film boiling heat transfer was also studied; roughness had no effect on heat transfer. The author cites that in the transition boiling regime roughness has an effect on the location of the critical heat flux. It is further argued that during transition boiling the surface wetting properties are very important and can produce significant differences in the boiling dynamics. Berenson et al.  observed c ritical heat flux to be unaffected by the surface material, cleanliness and roughness. However, this is not generally true. Luke  presented an analysis of the preparation and measurement of the microstructure of evaporator surfaces. Her analysis surveys all of the available meth ods for surface characterization. The salient measurements produced from the latest surface characterization methods are further analyzed to assess their influence on boiling heat transfer. Intricacies of the microstructure created using industrial methods of surface preparation are also elucidated. Bon et al.  conducted pool boiling experiments on smooth metallic surfaces with RMS roughness ranging from 30 365 nm. Pentane and Butane were used as the testing fluids. The heating surfaces tested were brass, unpolished and electropol ished stainless steel. The test fluids used in conjunction with the metallic surfaces produce a favorable wetting situation. This would further imply that any cavities present on the surface would be flooded. However despite the favorable wetting condition low incipient superheats were observed. A comparison with the known homogeneous superheats for the two test fluids showed that the observed incipient superheats were only 15 30% of
35 the homogeneous limit. Roughness was noted to have varying effects on the heat transfer depending on the surface material. Jones et al.  investigated the influence of surface roughness on pool boiling heat transfer. They used two fluids, FC 77 and water, along with surfaces with varying degrees of micron and submicron roughness. The authors noted tha t heat transfer coefficient increased with increasing roughness. A trend which the authors observed followed a power law relationship. The micron scale roughness showed no improvement in critical heat flux, although the authors cite that their facility was not able to proceed towards critical heat flux for the rougher surfaces due to the condensers inability to compete with the excess vapor production. They also note that the power law dependence of the heat transfer coefficient with roughness is more appar ent with FC 77 than with water. Presumably this dependence is associated with the wetting ability of the fluorinert liquid as compared to deionized water. Jung et al.  investigate d the effects of sub micron scale roughness on pool boiling heat transfer. Treated silicon surfaces were heated under pool boiling conditions in a subcooled pool of FC 72. Two different methods of surface preparation were used to create two surfaces with s ub micron roughness with distinguishingly different surface topographies, as confirmed by atomic force microscopy. The data obtained by the shows that small changes in even sub micron roughness leads to noticeable changes in heat transfer. Additio nally they note that the measured CHF for the treated surfaces increased linearly with the effective boiling area. The effective boiling area refers to the additional area created by the surface morphology.
36 1.3.6 Surface Size and Gravity The magnitude of the cha racteristic dimension of the heating surface can have a significant effect on the measured boiling curve. Generally, the smaller surface s display greater disparity from the typically observed boiling curve. Boiling from thin wires, thin heating strips and MEMS heaters are just some examples of typical applications of small heating elements. The influence of gravity has its applications in aerospace technologies. The effects of surface size and gravity can be directly correlated with the capillary length sca le Raj and Kim  investigated the effects of heater size and gravity on pool boiling heat transfer. From their results they were able to generate a boiling regime map that demarcates the regions dominated by buoyancy and by surface tens ion, respectively. The defining criterion depends on the ratio of the heater side length and the capillary length scale When this ratio exceeds a value of 2.1 then the region is buoyancy dominated and heater size independent and conversely below the critical value it is surface te nsion dominated and heater size dependent. Th e critical value i s observed to be valid for low and high gravity. They the in terface of the bubble, which typically is negligible for terrestrial gravity situations, can contribute substantially to surface tension dominated regimes. 1.3.7 Surface Orientation Kaneyasu et al.  and Priarone  studied t he effect of surface orientation on nucleate boiling and critical heat flux. Measuring the angle of inclination with respect to the horizontal orientation three distinct regions show up in the boiling curves. In the low
37 heat flux region of the nucleate boi ling curve increasing the angle of inclination was observed to increase heat transfer due to agitation of the thermal boundary layer from bubble movement parallel to the surface. For moderate heat fluxes the inclination was observed to have no effect on he at transfer. In the high heat flux region, near CHF, increase in the angle of inclination was observed to decrease heat transfer due to the accumulation of vapor on the surface. 1.3.8 Surface Geometry Most industrial applications of boiling heat transfer typical ly occur inside and outside tubes. Other surface geometries such as vertical and horizontal plates and discs are usually for very specific applications or fundamental research. The geometry of the boiling surface as well as its orientation, as mentioned pr eviously, can alter both the shape and magnitude of the boiling curve. For a horizontal surface bubble departure during nucleate boiling results in an induced on flow of liquid. Departing bubbles never make any additional contact with the surface so heat t ransfer is solely produced by the ebullition cycle. Conversely, boiling on the outer surface of a tube, bubble incipience occurs at the bottom and top portions of the surface. Bubbles that form on the lower portion of the tube do not leave the surface but instead slide along the surface and depart once they have passed the lower half of the tube. As a result of the bubble sliding heat transfer along the lateral portions of the tube is enhanced. Boiling from the top of the tube proceeds just as that in boili ng from a horizontal surface and overall heat transfer on a horizontal tube is observed to be greater than that on a horizontal surface. Aside from the most apparent variations in heater geometry (i.e. tube, sphere, plate), a mere change in the plan form g eometry of a horizontal plate can also alter boiling performance and two phase flow dynamics.
38 Al Arabi and El Reidy  studied natural convection from isothermal horizontal plates of di fferent shapes. The measured local heat transfer coefficients for square, rectangular and circular plates show a negligible contribution of the corner regions of the surfaces to heat transfer. Although a distinct decrease in heat transfer was observed near the leading edge of the boundary layer. Lewandowski et al.  conducted a similar set of experiments concerning natural convection from polygonal horizontal isothermal surfaces. They present an analytical treatment of the boundary layer flow along with experimental confirmation of their model. Visual observations confirm their hypotheses regarding the flow structure. Additionally the use of the diameter of an inscribed circle in the polygon a s t he characteristic length collapses the recorded data to one curve with an uncertainty of 20%. Conclusively, polygonal surfaces show interesting visual differences in flow structure and the effects of boundary layer interaction. The visual observations o f Lewandowski et al.  confirm that the boundary layer structur e is markedly different from on e surface to the next, respectively dependent on the number of sides. The general characteristic that can be observed on natural convection from any polygonal horizontal plate is the convergence of boundary layers from each of the respective sides of the plate. Subsequently natural convection from a circular horizontal disc shows no convergence region s. This prominent feature of convection from a polygonal surface was additionally observed in our present experiments on square single crystal substrates. Upon reaching CHF film boiling ensued, the number of bubbles departing from the surface and their re spective locations was observed to correspond to the four distinct regions that are formed on the surface by the converging boundary layers.
39 1.3.9 Surface Wettability Although surface roughness has an effect on the measured contact angle which can be indicative of surface wettability it is essentially its own entity mainly because of the many ways in which surface wettability can be altered aside from surface morphology. Kumar and Prabhu  provide a review of reactive and non reactive wetting. Nano coating surfaces with a thin layer of e ither a wetting promoting or inhibiting substance can remarkably enhance boiling heat transfer. Phan et al.  investigated the effect of surface wettability on subcooled pool boiling heat transfer by using various nanocoatings in order to control the wetting characteristics of the surface. Their study also took an in depth look at the effect of surface wet tability on bubble growth and nucleation. Using various deposition and coating methods they were able to vary the wettability from hydrophyllic to hydrophobic. The measured static contact angles for a water sessile drop on the test surfaces varied from 22 to 112. For the hydrophobic surfaces they observed low incipient superheats with minimal bubble departure. Hydrophobic surfaces also displayed early onset of film boiling due to bubble coalescence from the high density of undeparted bubbles. For the hydr ophyllic surfaces they observed that for increasing wettability bubble departure diameter increased and bubble departure frequency decreased. Overall heat transfer showed a parabolic trend with contact angle in the range from 0 to 90, with the best heat transfer occurring for highly wetting conditions. A dynamic contact angle approach is adopted by the authors in order to explain some of the anomalous behavior observed. The use of titanium dioxide (TiO 2 ) surfaces for the pool boiling of water have shown r emarkable performance due to ultraviolet induced superhydrophyllicity [24; 25] Nano particle deposition can also improve wettability of the surface resulting in an
40 increase in CHF [26; 27] Even low concentr ations of nano particles result in boiling heat transfer enhancement  Nano particle deposition of the heating surface is most commonly achieved by boiling a nanofluid with the desired particle species on the surface as a pretreatment. Deposition of the nano particles occurs as a result of microlayer dry out in t he ebullition process. The left over nano particles are thus adsorbed onto the surface. Chang et al.  investigated the pool boiling nucleation behavior of smooth surfaces immersed in highly wetting dielectric fluids. They observed a direct transition from natural convection to film boiling whe n the incipient heat flux was greater than the minimum heat flux. The appearance of this phenomenon is due solely to the smooth surface. Additionally they used a microporous coating to mitigate the occurrence of film boiling incipience. The authors further recommend that due to the enhanced nucleation performance and heat transfer that the microporous coating be used in direct immersion cooling processes. Cornwell  modified the conventional v apor trapping theory to account for contact angle hysteresis. Contact angle hysteresis is generally attributed to surface roughness and microscale heterogeneity. He further suggests that microroughness within the cavity can significantly alter its vapor tr apping ability by allow ing both convex and concave menisci within the cavity. He states that a substantial amount of experimental data supports his theory regarding the effects of contact angle hysteresis on bubble incipience. Tong et al.  also developed a new heterogeneous nucleation model for highly wetting fluids. Aside from the static contact angle, which can exhibit hysteresis
41 significantly reduce the incipience superheat required for activation. The supporting physics for their theory comes from the fact that adv ancing contact angles can be markedly greater than the measured static contact angle. This further implies that during initial wetting of the surface cavities that would of otherwise been classified as being flooded can in fact trap vapor because of the la rge advancing contact angle. A comparison of the classic activation criterion with the modified criterion shows a noticeable reduction in incipient superheat. It is further noted that static contact angle hysteresis can also influence bubble growth, howeve r this would be most observable for moderately wetting fluids. Surfactants and additives can also modify wetting conditions by reducing the surface tension of the host liquid. Surface tension is an important physical parameter that controls not only the bu bble nucleation rate but can significantly alter bubble growth and interfacial dynamics. Cheng et al.  provides a comprehensive revi ew of boiling heat transfer with surfactants and polymeric additives. 1.3.10 Surface Modification Increasing thermal power densities as a result of constant technological advancements creates a greater demand to develop more effective methods of thermal managemen t. Since boiling heat transfer is capable of removing heat at these higher power densities it is understandable that engineers would want to optimize their heat transfer surfaces to take advantage of this mode of heat transfer. Surface features have been f abricated at all length scales, from macroscopic features in the millimeter range to micro and nano sized features on the submicron scale. Depending on the chemical heterogeneity as well as geometry of the structur al features on a boiling surface many
42 of t he effects previously mentioned in this section c ould influence the boiling process and thereby result in anomalous boiling behaviors Khan et al.  provide a brief review of some of the surface features that have been developed for electronics cooling. Mitrovic  also provides a review of recent heat transfer enhancement methods, sfer enhancement are moving towards smaller scales. Ujereh et al.  investigated the use of carbon nanotube arra ys as a means of heat transfer enhancement in nucleate pool boiling. Carbon nanotube (CNT) arrays were tested on two different substrates with various array densities. Various surface patterns were adopted in order to observe the various effects of the CNT arrays. Pool boiling curves compared with bare silicon and copper surfaces showed significant improvements in incipience temperature, heat transfer and critical heat flux (CHF). The authors show that for the silicon substrate there is a monotonic increase in nucleate boiling heat transfer and CHF with increasing CNT coverage. Additionally there is a consistent decrease in incipience temperature with increasing CNT coverage. The fully covered silicon surface had a nearly constant wall superheat throughout t he entire boiling curve. The authors report similar results for the copper surfaces and propose that further research on the use of CNT arrays for surface enhancement in pool boiling be explored because of their anomalous thermal characteristics and ease o f production. Launay et al.  also used carbon nanotubes in addition to other micro and nano scale structured features. Carbon nanotubes enhanced heat transfer predominately in the low superheat region, CHF enhancement was observed for all the modified
43 surfaces. Close inspection of their reported data shows that the enhancement was greater for PF 5060 than for the deionized water. Honda et al.  studied pool boiling heat transfer of FC 72 on silicon chips with Micro Pin Fins and submicron scale roughness. In addition, varying degrees of subcooling as well as degassed and dissolved gas solutions were used. The authors report that both the micro pin fin surface and the surface with the submicron scale roughness improved the overall heat transfer and CHF over the smooth silicon surface. Their photographic studies revealed that upon bubble departure a small amount of vapor remains attached to the surface in the gap between pin fins. Additionally the micro pin fin surface with submicron scale roughness showed the greatest increase in heat transfer. They report that all the surfaces used showe d the same increasing trend of heat transfer with increase in subcooling, as well as, an increase in heat transfer in the low heat flux region with the presence of dissolved gas. The remarkable increase in CHF observed shows that augmenting the surface str ucture on the micron scale can drastically alter the heat transfer performance of the surface. Parker et al.  investigated subcooled and saturated pool boiling of FC 72 on copper and porous graphite surfaces. The porous graphite surface resulted in increased boiling performance along the entire boiling curve. CHF on the porous graphite surface increased in the range of 150% to 200% for increasing subcooling. Heat transfer was the exceptional boiling performance to the high volume porosity of the porous graphite surface. Which yield a high nucleation site density with cavities of all sizes of both the reentrant and normal type.
44 Reed et al.  took a novel approach to eliminating the excessive superheat generally observed when boiling highly wetting fluids. Using spheres in conta ct with a nucleation at superheats much lower than typically observed. Contact pressure was varied but later determined to have no significant effect. By additionally varying the sphere material and contact point material different aspects of the heat transfer were using an insulating sphere with a thermally conductive tip resulted in the best in cipience performance. However, the use of large structures in close proximity obs tructs the liquid flow on to the surface. This results in a decrease in CHF with increasing contact point density. Chen et al.  investigated pool boiling on a superhydrophilic surface with TiO 2 nanotube arrays. Pool boiling of water on a bare Titanium surface and one covered with TiO 2 nanotubes was conducted to observe the effect of hydrophilicity and surface microstructure. The surface with TiO 2 nanotubes showed better nucleation performance and heat transfer. The authors attribute this to the small bubble siz e and high departure frequency observed from the nanotube surface. The authors further hypothesize that the observed overall pool boiling enhancement can be attributed to the increased number of available sites and increased intrinsic area. Das et al.  developed a model to explain the effect of liquid intake on pool boiling heat transfer from structure d surfaces. The structured surfaces investigated in their stud y were tunnel and pore structures. They cite that subsurface communication between adjacent cavities has been shown to improve nucleate boiling heat transfer.
45 Their predictive model shows good agreement with experimental data and shows trends similar to ot her predictive models for this type of structure. Additionally, their concise theoretical development of the heat transfer model further elucidates the potential physical mechanisms governing the underlying heat transfer enhancement produced by this partic ular type of surface structure. Using anisotropic etching and wafer bonding techniques Goyal et al.  created reentrant cavities in a silicon substra te in order to investigate their pool boiling performance. The cavities had a pyramidal internal structure with cavity openings ranging from 12 to 20 m. Two refrigerants and one dielectric fluid were used to characterize the surface s boiling performance. Additionally experiments were conducted with a smooth silicon substrate; the reentrant cavities showed markedly better incipience superheats compared to the smooth surface. Partial film boiling was also observed near critical heat flux. Messina et al.  used a photographic etching method to create precise arrays of pits on copper surfaces. Pit density is observed to have a profound effect on the location of the nucleate boiling curve. Increase d pit density increased heat transfer but Shallow and malformed pits showed anomalously efficient heat transfer. Comparisons with surfaces roughened using two grades of sandpaper as well as a mirror finished surface were also reported. boiling and CHF. Miller et al.  conducted pool boiling experiments on an array of hexagonal dimples 9 um in diameter and 3.3 um deep. The investigation was aimed at
46 understanding the effect of non boiling im mersion time on bubble incipience. Immersion time varied from 5 hours to 16 days. Surface degassing through pre boiling was not used as the e xperiments were used to observe the vapor trapping capability of the features depending on immersion time. The shor t duration immersion showed a slightly lower incipience superheat ; however for larger immersion times no significant variation could be a function of the size of the feature and its geometry. Mitrovic et al.  developed a novel microstructure for boiling heat transfer enhancement. The new str u cture resembles rod like features with spherical tips. Using the new features boiling studies were conducted on tubular surfaces. A comparison of the modified t ube with the unmodified tube shows that the novel structure has a profound effect on heat transfer and incipience. Ramaswamy et al.  used an enhanced structure composed of a stacked network of interconnecting channels to investigate the effects of varying the geometric parameters on boiling heat transfer. The three salient parameters for investigation were the pore size, pitch and height. Their three dimensional enhanced st ructure mimics that of a porous structure. Heat transfer enhancement was observed to occur in the 0 30 K range. Additionally, increasing the number of layers was observed to produce a proportional increase in heat dissipation in this temperature range. The overall enhancement is proposed to be from the combined effects of altered boiling phenomena and fin effects in the sub surface layers. 1.4 Thermodynamics of Metastable Liquids Much of the pioneering work on metastable liquids was conducted in the early 19 60 s Since then further developments as to the detailed understanding of the
47 complex physical processes that occur within metastable fluids have been sparse. A thorough and concise explanation of metastable liquids can be found in the monograph by Skripov  A late r book coauthored by Skripov et al.  contains a compendium of theoretical developments and experimental data on the thermophysical properties of metastable li quids. All phases can exist in a metastable state, no matter whether they possess isotropy or anisotropy. Multi component mixtures can also exist in metastable states. Despite this, the foregoing explanation will solely pertain to homogeneous substances. H owever it should be noted that the concepts presented regarding pure substances can easily be extended to heterogeneous substances (i.e. multi component mixtures). The equilibrium lines on a typical pressure temperature diagram divide the thermodynamic spa ce into regions that correspond to the three distinct phases of matter. Heating or cooling a substance to its equilibrium point is generally not sufficient enough to induce phase change. Generally one must either heat or cool a substance above or below its equilibrium state in order to induce phase transition. Therefore it can be said that the equilibrium lines on a typical pressure temperature diagram are bounded by regions of the thermodynamic space which are accessible to both phases of the corresponding region. A substance is said to be in a metastable state if it passes through an equilibrium line without changing phase. There are many ways to bring a fluid into a metastable state such as isothermal or adiabatic expansion as well as increasing its tempe rature at constant pressure. The method we are most familiar with is of course heating at constant pressure (boiling); we encounter this on a day to day basis. Of utmost importance when considering metastable states is the metastability or the depth
48 of pe netration into the metastable region. As will be explained later, the metastability of the substance can have significant effects on the rate of phase change. Extensive studies have confirmed the potential for metastable states in boiling, condensation, so lidification and melting. Possessing a fundamental understanding of such phenomena can aid in the understanding of more complex physical processes. Before proceeding further, as a point of clarity, it may be suitable to further define what it is to be in a metastable state. Metastability is prevalent in all facets of physics such as Quantum Mechanics, Chemistry, Biochemistry and Condensed Matter Physics. Electronic circuits can even exhibit metastability. Conceptually, any dynamic system can exist in a meta stable state. The propensity for metastable states to exist in any system can be directly attributed to the presence of complex non linear dynamical interactions. A metastable state is essentially a state of local equilibrium that is stable for small pertu rbations of the state variables but can rapidly change state in the presence of large perturbations. Any substance (i.e. solid, liquid, gas) can further be regarded as a complex dynamic system owing to the many body intermolecular interactions which contro l its physical nature The capacity for metastability in any of the phases of matter is as a result of the difficulties in disrupting the intermolecular forces which bind these substances in their initial state. In the absence of external perturbations ph ase transition in a pure metastable system arises solely by thermal fluctuations and given the delicate equilibrium of the metastable state these fluctuations are enough to disrupt the intermolecular interactions. Figure 1 3 show s a conceptual depiction of an arbitrary thermodynamic system in a metastable state. The solid curve represents the projection of the pseudo potential
49 Figure 1 3 Conceptual depiction of the potential ener gy surface of an arbitrary thermodynamic system. energy surface for the current state of the system. It can be seen that the metastable state is actually a local minimum and not the thermodynamically favorable global minimum. As mentioned previously in the absence of external perturbations the system can exist in the metastable state for an extended period of time. Additionally, the potential energy wells can locally be approximated as quadratic. Synonymous with a damped harmonic system it can be seen that small perturbations in the state variables will similarly relax towards the metastable state via energy dissipation by intermolecular collisions However large enough perturbations that are capable of exciting the system beyond the potential energy barrier will induce a change of state to the more thermodynamically favorable state. Imagining further that the system were moved to a state with increased metastability then the height of the energy barrier would be reduced, increasing the likelihood of state tr ansition for smaller perturbations.
50 The initiation of phase transition begins with the transitory formation of a localized region of the new phase. The general theory of nucleation from a metastable phase asserts that the embryonic new phase (i.e. small bu bble, droplet or crystallite) is very small, on the order of 10 2 to 10 3 molecules. Consequently, a suitable thermodynamic description of such a small quantity of molecules is difficult to ascertain both theoretically and experimentally. Therefore the more accessible methods for the description of nucleation phenomena are through the use of kinetic theories. However, a complete understanding of the kinetics of nucleation is not the sole complication to developing a complete physical description of metastable liquids. Inherent in any model of boiling heat transfer is the need to know the variation of the thermal and physical properties of the liquid in the metastable region. The area enclosed by the saturation line (binodal) shown in F igure 1 4 demarcates the region of liquid vapor coexistence. Thermodynamically the saturation line satisfies the condition equality of the chemical potentials. Typically the state of a two phase mixture can be determined by traversing the line a c. Although we regard the phase change process as an isobaric isothermal process in reality the true thermodynamic state can differ from that represented on a typical pressure volume diagram. Isotherms I 1 and I 2 in Figure 1 4 represent the shape of true isotherms that pass through the coexistence region. Noticeable features of the true isotherms are the minima and maxima present. Each denotes the intrinsic limit of stability for liquid and vapor, respectively. The locus of these minima and maxima form the spinodal curve. This locus of points satisfies the condition as expected. Additionally it can
51 be observed that the saturation line and the spinodal share a common vertex at the critical p oint (point CP). Figure 1 4 Generic pressure volume diagram with metastable regions and real isotherms. This feature of the two curves is not by coincidence but can be explained by the simple fact that at the critical point both phases are identical. Hence there is only a single representative point for both curves. From Figure 1 4 it can be seen that the spinodal curve further divides the coexistence region into those regions whi ch are thermodynamically stable and those that are unfavorable and therefore unstable. As mentioned previously, liquids in the metastable state can persist in that state provided that external disturbances are not present Any thermodynamic ensemble is sub ject to fluctuations in the thermodynamic state variables, such as density and energy; this can be attributed to the thermal motion of the molecules in the ensemble. On approach to
52 point (b) density and energy fluctuations increase in intensity. Upon reach ing point (b), the intrinsic limit of stability for the given pressure, small perturbations grow almost exponentially and spontaneous phase separation is observed. Intense nucleation at the spinodal is typically observed; owing to the purity of the substan ce nucleation at this degree of metastability is generally referred to as homogeneous nucleation. Nucleation events within the metastable region, away from the spinodal, are the result of heterogeneous nucleation or perturbations induced by external excita tion. Examples include nucleation in the presence of foreign particles and surfaces as well as phase transition induced by ion bombardment or radiation. The most frequently observed instances of heterogeneous nucleation typically occur as the result of act ive centers on bounding surfaces that are sources of heat. Active centers for nucleation reduce the potential barrier for new phase formation; whereas external excitations can superimpose fluctuations upon the already present internal fluctuations. Both re sult in premature phase transition as a result of surpassing the potential energy barrier. In addition, the heterogeneous nucleation rate strongly depends on the depth of penetration into the metastable region. This can be attributed to two factors, a redu ction in the work of formation of the critical embryo and a decrease in the size of the critical embryo, both of which decrease with increasing superheat. 1.5 Fundamentals of Nucleation Theory Heterogeneous bubble nucleation via bubble embryo formation is the precursor to boiling incipience. It was previously noted that the metastable nature has a direct impact on the nucleation kinetics for all types of phase transition (i.e. melting, freezing, boiling and condensation). To further elucidate the thermodynamics and kinetics involved in bubble nucleation the proceeding section will cover the various methods for ascertaining
53 the nucleation threshold for both homogeneous and heterogeneous nucleation. The classical methods for developing bubble nucleation theory gen erally begin with a series of simplifying assumptions with regards to the kinetics of embryo formation. More recent methods have adapted density functional theory (DFT) in order to capture non classical effects that occur for very small bubble embryos. Non classical effects observed from DFT calculations do show a significant difference when compared to classical nucleation rates [47; 48; 49; 50] However, experimental confirmation of the results obtained using DFT are still lacking. Similar efforts have been made to extend DFT to heterogeneous bubble nucleation  but experimental confirmation of the results is still necessary. A thorough understanding of bubble nucleation begins with an e xplan at ion of the physical mechanisms involved in homogeneous nucleation. The most important parameter in nucleation theory is the rate at which embryos of a critical size are generated (i.e. the nucleation rate). Numerous derivations can be foun d among the various text s and journal articles relevant to boiling heat transfer and phase change physics [3; 46; 52] The proceeding derivation is a summary of that given by Carey  and is presented here to highlight the fundamentals of nucleation theory Derivation of the homogeneous nucleation rate of bubbles in a superheated liquid begins with the idealized assumption that an equilibrium distribution of bubble embryos is already present. It can then further be postulated that the numb er distribution of embryos can be expressed as 1 1
54 is the number of embryos of size n per unit volume. is the number of liquid molecules per unit volume. In the exponential is the work of formation of the critical embryo, and are the Boltzmann constant and liquid temperature. The radius of the bubble embryo can related to the number of molecules in the bubble by 1 2 Furthermore, the size of the embryo bubble is dictated by the rates of evaporation and condensation of molecules at the interface. It is additionally assumed that each of these processes occurs by single molecule addition or removal. Alt hough this assumption may no t be completely accurate it will suffice for the current simplified derivation. The rates of evaporation and condensation of molecules from the surface per unit area per unit time can be represented as and respectively. At equilibrium the rate at which embryos of size n grow to n+1 and those of size n+1 shrink to n are equal. This may be expressed as 1 3 Although equation 1 3 is representative of the equilibrium state in actuality a superheated liquid is in a state of non equilibrium. Therefore the rates of bubble volume increase and decrease, due to evaporation and condensation, are not equal. This implies that there will be a net flux of embryos in size space ( n space). 1 4 In equation 1 4 represents the non equilibrium number distribution of embryos of size n per un it volume and represents the net flux of bubble embryos of size n that grow to n+1 Equation 1 4 can further be simplified using equation 1 3
55 1 5 Additionally, the rate of change of the embryos can be expressed in terms of as 1 6 To further simplify the derivation it will be assumed that n can be represented as a continuous variable. Then equations 1 5 and 1 6 can be rew ritten as 1 7 1 8 For a steady flow of embryos through size space it ca n be shown from equation 1 8 that Furthermore, it is postulated that for small bubble embryos any deviation from equilibrium will have a negligible effect on the number density of embryos and the refore as essentially the great number of very small embryos precludes any possible effect. Performing an integration of equation 1 7 and rearranging gives 1 9 Further approximations are necessary in order to proceed in deriving an analytical expression for the homogeneous bubble nucleation rate. From the kinetic theory of gas es the evaporation rate may be approximated as which represents the rate of molecules leaving a planar interface. At this point it may seem suspect to use such an approximation when in fact the embryo interface is not planar, however for a preliminary assessment of the nucleation kinetics this assumption is
56 sufficient to describe the events that transpire at the liquid vapor interface of the embryo. In equation 1 9 the limit s of integration may be taken as because the integrand rapidly goes to zero for It is also suitable to evaluate the integral in the small embryo limit since we are interested in the growth of said small embryos to the critical size. Equation 1 9 can now be written as 1 10 The integral over n may be converted to an integral over r usi ng equation 1 2 the ideal gas law and the Clausius Clayperon equation. The surface area in the integrand is that of a sphere. The resulting relation relating dn to dr is 1 11 The work of formation of the critical embryo in equation 1 1 can be expanded in a taylor series about the equilibrium embryo radius 1 12 Substitution of equation 1 11 and 1 12 after trunca ting the third order terms, into equation 1 10 using the expression for the equilibrium bubble radius, derived from the Clausius Clayperon equation gives the final expression fo r the homogeneous nucleation rate. 1 13 This expression represents the rate at which embryos gr ow from size n to n+1 Consequently, because was assumed to be independent of n then this also
57 represents the rate at which critical embryos are generated. It can further be seen from equation 1 13 that the nucle ation rate strongly depends on temperature. This can be inferred from the strong temperature dependency of the term in the exponent. Aside from the several approximations used in the process of deriving equation 1 13 its predictiv e capability is actually quite good for most liquids. Derivation of the nucleation rate for heterogeneous bubble nucleation on a solid surface proceeds in the same manner as that for the derivation for homogeneous nucleation. The sole difference between th e two expressions arises from the inclusion of the contact angle to account for the wettability of the substrate ( Figure 1 5 ). The observed macroscopic contact angle results in a reduced volume for the critical embryo. Subsequentl y there is a decrease in the work of formation, which is dependent on the wettability (contact angle). Figure 1 5 Classical heterogeneous bubble nucleation model. Accounting for the reduced volume and sur face area of the truncated sphere the expression for the rate of heterogeneous bubble nucleation is 
58 1 14 Equation 1 14 captures the general trend of the effect of contact angle on heterogeneous nucleation for moderate to poor wetting surfaces. For highly wetting fluids the contact angle is very close to zero. In the limit as contact angle goes to zero equation 1 14 becomes eq uation 1 13 if in addition is neglected in comparison with 2 in the pre exponential factor. Furthermore, it should be noted that the heterogeneous nucleation rate is per unit surface area of the heating surface as opposed to the homogeneous nucleation rate which is per unit volume. That is why the heterogeneous nucleation rate is presumed to be proportional to The equivalency of the heterogeneous and homogeneous nucleation rates for small contact angle is a consequence of the model used for the deriva tion of equation 1 14 ( Figure 1 5 ). Recent experimental studies [10; 14] have shown that low to moderate incipient superheats are attainable on smooth surfaces (p articularly metal surfaces) despite the theoretical prediction of heterogeneous bubble incipience occurring at the homogeneous superheat. Historically, vapor trapping has been regarded as the sole mechanism responsible for seeding bubble nucleation. Trapp ed vapor and non condensable gases in surface inclusions act as ready centers for nucleation; their presence is as a result of the dynamic wetting conditions present at the solid liquid interface. Surface wettability will inherently have a significant effe ct on the amount of vapor trapped on the surface. For highly wetting fluids cavities of all sizes become flooded due to the strong interaction at the solid liquid interface. The low superheats experimentally observed in comparison
59 with the superheat predic ted by conventional theory, with certainty, confirm that other mechanisms are present that can initiate boiling ot her than vapor trapping As mentioned previously DFT has also been employed to investigate the kinetics and mechanics of nucleation. Most comm only used for the analysis of homogeneous condensation and seldom for vaporization. Some investigators have further advanced the method so as to understand the heterogeneous interaction of a drop and a bubble on a solid substrate Talanquer et al.  and Berim et al.  investigated droplet nucleation on a solid substrate u sing density functional theory In both instances interaction strength between the solid and the liquid is observed to have significant effects on the droplet density profile and nucleation rate. Comparisons with the classical nucleation rate shows that no n classical effects can drastically alter the supersaturation dependence of the nucleation rate. In the study conducted by Berim et al.  the effects of nano scale roughness and chemical heterogeneity were also considered Both factors are observed to have marked effects on droplet wetting and density distribution. Intermolecular forces are an intrinsic par t of phase change and the thermodynamics that govern the processes that bring about phase change. Intermolecu lar forces can vary in strength and directionality  Common thermodynamic properties such as boiling temperature h ave been shown to strongly depend on intermolecular strength  Chandra  developed a theory to explain the effects of long range interactions on nucleation. The author finds that the presence of long range interactions induces cooperative nucleation and growth processes. The
60 however, once the stable nuclei is formed the subsequent cost of format ion of additional nuclei is reduced. Clearly a more indepth description of the molecular processes that are undergone in phase transitions is not available. One route to providing such a description is by simulating the behavior of the molecules. Molecular dynamics studies have also provided additional insight into the molecular interactions and behaviors that lead to void (bubble embryo) formation. Brian et al.  performed molecular dynamics simulations in order to study the effects of nanoscale defects on heterogeneous bubble nucleation. The y found that surface defects smaller than the critical nucleus had no effect on the nucleation rates when compared to atomically smooth surfaces. Large indentations, larger than the critical nucleus, increased the nucleation rates by two orders of magnitud e. Both constant temperature and constant heat flux test cases were simulated. Fluid solid interaction strength was also varied amongst the various simulations. Localized heating was observed in the large indentation for the constant heat flux case. Void f ormation probability in the vicinity of the indentation was strongly dependent on the strength of the fluid solid interaction strength. Weak interactions promoted void formation near the surface within the indentation. Strong interactions reduced the effec tive size of the indentation due to the presence of the adsorbed liquid layer; this reduced the void formation probability in the indentation. The authors note that for all the cases with the large indentation void formation was still favored within the in dentation. Wang et al.  performed a molecular dynamics study on homogeneous bubble nucleation. The ir work was particularly aimed at investigating nucleation driven by local hot spots. These local hot spots are essentially local temperature fluctuations that bring
61 about void formation. There results also show that the nucleation rate is greater than tha t estimated by the classical expression. Bubble embryos are noted as being compact, as opposed to large ramified structures. A direct correlation between local thermal fluctuations and void formation was observed. 1.6 Dissertation Outline Chapter 2 provides a description of the experimental facility design. Details of the data acquisition and methods for data measurement are outlined and relevant uncertainty quantifications are mentioned. Data post processing and Image analysis me thods are also explained in detail. Representative figures concerning the image processing method are also shown for clarity. Chapter 3 presents the results from the first set experiments aimed at elucidating the fundamental me chanisms involved in boiling heat transfer. A brief introduction to the current theory on boiling heat transfer of highly wetting fluids on smooth surfaces is presented in addition to a detailed explanation of the experimental design from the perspective o f fluid and surface selection. A discussion of the plausible mechanisms that bring about the observed trends is provided. Chapter 4 is the first of two chapters devoted to the experimental investigation of structured surfaces. This first chapter presents the results from pool boiling of FC 72 on cylindrical cavity arrays. Following a presentation of the results a discussion regarding the implications of the parametric investigation is provided. Chapt er 5 is the second chapter concerning pool boiling from structured surfaces. This chapter presents the pool boiling results from boiling on an array of novel surface structures. These novel surface structures, whose structural details will be further expl ained in the chapter, were designed to include the most influential characteristics of
62 other surface enhancement structures that have likewise proven to be effective. Plausible mechanisms for the observed trends in heat transfer are discussed. Chapter 6 provides a discussion on recommended areas of future research. Some analysis pending the discussion of future research is outlined in Appendix A.
63 CHAPTER 2 EXPERIMENTAL FACILIT Y 2.1 Substrate Heater The heater, shown in Figure 2 1 is comprised of a metal block with a 1 cm 2 cross section. For the experiments done with smooth surfaces t he heating block material i s brass. The experiments do ne with structured surfaces use a copper heating block. This change in material w as to improve thermocouple response to transient events and decrease the uncertainty associated with the measured heat flux by using a material with an exactly known thermal conductivity. Brass thermal conductivity is typically reported to fall within the range 90 120 W/m K at room temperature and this translates into a greater uncertainty than that of the values report for copper which are in the range 385 400 W/m K. Figure 2 1 Substrate heating block as sembly. (1. Thermocouple slots, 2. PEEK flange, 3. DURALCO 4700 epoxy, 4. Substrate, 5. S BOND 220 solder, 6. DURALCO 4460 epoxy, 7. Cartridge heater slot, 8. Set screw hole.)
64 Four type E thermocouples are embedded 4 mm into the side of the heater at 2.5mm 7.5mm, 12.5mm and 17.5mm from the top surface. A high temperature solder, S BOND 400 with a melting temperature of 400 C, is used to assure good thermal contact between the thermocouples and the heating block. All of the thermocouples in the brass heate r were calibrated using a constant temperature water bath up to 90 C, after being soldered into the heating block. They were a ll found to agree with the NIST curve data within the error associated with type E thermocouples. Thermocouples in the copper he ating block were soldered into the block using the same solder. However calibration was done in a silicone bath using a hot plate with a magnetic stirrer. The silicone bath fluid (Clearco HT 110 High Temp Silicone Bath Fluid) is able to reach temperatures as high as 288 C. For the purpo ses of the experiments calibration up to 200 C i s sufficient as shown in Figure 2 2 and Figure 2 3 Comparison of the calibration data with the NIST data for type E thermoc ouples shows marginal deviation for the higher temperatures. Direct calibration of the thermocouples by curve fitting over the calibrated temperature range i s the most suitable means of assuring reliable temperature measurements. Fitting coefficients are s hown in Table 2 1 the mean and standard deviation of the coefficients obtained for the respective heaters shows good agreement at steady state.
65 Figure 2 2 Calibration of heater 1. Figure 2 3 Calibration of heater 2.
66 Table 2 1 Fitting coefficients for the calibration curves generated for heaters 1 and 2. Statistical parameters are included to verify accuracy. TC 1 TC 2 TC 3 TC 4 Mean Standard Deviation Heater 1 0.1121 0.1122 0.1118 0.1125 0.1122 0.00028 16.2010 16.199 16.1890 16.1950 16.1960 0.0053 2.8912 2.9586 3.0518 3.0718 2.9931 0.08 Heater 2 0.1026 0.1093 0.1113 0.1149 0.1095 0.0052 16.0100 16.1280 16.1640 16.2250 16.1318 0.0905 4.2645 3.9192 3.7987 3.6237 3.9015 0.27 Heat is supplied using a 100 W cartridge heater inserted from below and held in place using a brass bushing and set screw. A low therma l conductivity epoxy, Duralco 4700 from Cotronics (k = 1.87 W/m K), is used to bond a PEEK (Polyether ether ketone) flange to the brass heating block near the uppermost thermocouple. PEEK is a high temperature, low thermal conductivity (k =0.25 W/m K) the rmopl astic with excellent mechanical and chemical resistance properties. Test surfaces were soldered to the top surface using another high temperature solder, S BOND 220 with a melting temperature of 220C. Again this assures that there is excellent therma l contact between the heating block and the heating surface. After soldering the substrate onto the heating block the lateral portions of the heating block and substrate were encapsulated using a high temperature, low viscosity and low thermal conductivity epoxy Duralco 4460 from Cotronics (k = 0.57 W/m K). The low viscosity of the epoxy assures that all vacancies are filled during the curing process, providing adequate surface coverage for the lateral portions of the substrate. Extraneous bubbles that for med on the Teflon mold used for the encapsulation required a second coat of epoxy to be applied to prevent nucleation from cavities present in the outer portions of the epoxy. Inspection of the smooth surfaces after the soldering and encapsulation processe s using an SEM and optical profilometer
67 shows an increase in the maximum roughness among the substrates to 50nm. The observed increased roughness can be attributed to oxide layer formation due to the elevated temperatures required for the soldering and enc apsulation processes. Additionally, the i ncrease in roughness observed i s also inversely related to the substrate hardness. The lower portion of the heating block was then wrapped in fiberglass insulation during the experiments. Due to low heat loss, less than 5%, one dimensional heat flow in the heating block can be ass umed. The surface temperature i s extrapolated using a least squares fit of the measured thermocouple temperatures with respect to location within the heating block. A small correcti on to the surface temperature i s used to account for the thermal resistance across the solder and substra te; however this i s less than 2 C with the most extreme heat flux ap plied. The thermal resistance i s determined through calibration and found to agree with the calculated thermal resistance based on the known thermal properties of the intervening materials The measured voltage and current supplied to the cartridge heater from the variable transformer is used to determine the applied heat flux. Comparison of the applied heat flux with the measured heat flux shows that he at losses are less than 5%. 2.2 Pool Boiling Chamber The pool boiling chamber shown in Figure 2 4 consists of two machined stainless steel plates used to compr ess a Pyrex glass cylinder with viton o rings to form a tight seal. A helical bulk fluid heater is inserted through an opening in the lower plate. This specific heater shape allows the fluid to reach saturation faster as well as minimize the strength of co nvection currents in the test chamber. The condensing coil is located in the chamber to maintain the desired pressure and maintain a constant liquid level
68 height. A needle valve located on the outlet of the condensing coil allows for fine increments of the condenser flow rate. Additionally, the bulk heater power is controlled with a variable transformer so that the minimum required power can be set to assure that background convective turbulence is minimized. Pressure in the chamber is measured with a press ure tran sducer that i s calibrated for the desired pressure range in the chamber. Bulk fluid temperature is measured using a thermocouple located near the chamber floor; this assures that the measured bulk temperature i s that near the heating surface. The b ulk fluid thermocouple is also calibrated using a constant temperature bath. Figure 2 4 Pool boiling facility (1. Heater assembly, 2. Stainless steel bottom plate, 3. Viton O ring, 4. Bulk fluid heater, 5. Pyrex glass cylinder, 6. Filling valve, 7. Condenser inlet, 8. Condenser outlet, 9. To pressure transducer, 10. Stainless steel top plate, 11. Bulk thermocouple.)
69 2.3 Data Acquisition A national instruments data acquisition board, NI 6218, is used to c olle ct the thermocouple and pressure voltage s A Labview virtual instrument is used to observe and collect the experimental data. A reference junction circuit is used to accurately measure the junction temperature to determine the true measured thermocouple te mper atures. Data are sampled at 1000 Hz to assure accurate representation of any transient events. The voltage and current applied to the cartridge heaters is recorded at steady state for each point on the boiling curve. To assure quasi steady conditions p receding transient events, like incipience and critical heat flux (CHF), voltage increments are kept to one volt until such ev ents occur. All recorded data a re then post processed using MATLAB to produce the boiling curves. 2.4 Image Acquisition Two methods o f image acquisition a re utilized to observe and document the dynamics and phenomena of pool boiling heat transfer on smooth and structured surfaces. For the preliminary experiments concerning pool boiling on smooth surfaces a NAC Hi Dcam 2 high speed camer a operating from 500 to 3000 frames per second wa s used with a Sigma 52mm macro lens to record the incipience events. Lower frame rates a re used to record boiling dynamics during intermediate heat fluxes. The higher frame rates a re used to record incipienc e events. Incipient events a re more dynamic and spontaneous. S urface activation can occur within 12ms of t he first vapor nuclei appearing; therefore frame rates in excess of 1000 frame s per second a re required to capture bubble incipience in vivid detail. For structure d surfaces the number of active sites is of utmost importance in ascertaining their boiling performance characteristics. Therefore, for bubble counting, a
70 N ikon D5000 digital SLR camera i s used in conjunction with a Sigma 105mm macro lens. A T iffen 58mm circular polarizer i s also used to enhance bubble contrast with the surface. The camera i s set to long exposure times and small aperture. These settings aid in distinguishing bubbles on the surface with those that have departed. The advantage t o using long exposure times to capture objects in periodic motion is that objects in motion will result in blurs or streaks in the image. Whereas stationary objects, or objects whose motion is slower than the camera frame rate, will be distinguishable in t he image. Therefore when capturing images at low heat flux, the time spent on the surface by the bubble is greater than the characteristic time of motion due to buoyancy. Using the camera set to long exposure times all bubbles residing on surface show up as distinct bright white points on the surface and departing bubbles show up as streaks due to their rapid upward motion. The only limitation of the method is that for moderate to low heat fluxes the higher departure frequency of bubbles means that departi ng bubbles in the foreground obscure bubbles on the surface in the background. 2.5 Experimental Procedure After filling the chamber with the desired test fluid the bulk heater is adjusted to a level sufficient to produce vigorous boiling. The condense r valve remains closed so as not to condense any excess water vapor from the air initially contained in the chamber. The chamber pressure increases and non condensable gases are purged by opening the fill valve. The procedure continues until visual inspection conf irms that only vapor from the test fluid is present. The condenser valve is then gradually opened until the chamber pressure reaches one atmosphere. Upon reaching saturated conditions, the surface heater is set to a heat flux 80 90% of the expected CHF for the test fluid. The
71 high applied heat flux assures that almost all potential sites on the surface are active so that any adsorbed foreign particles or gases are carried away by the vigorous boiling at the surface. The surface is degassed at this heat flux for approximately one hour, after which the surface is cooled to below the saturation temperature to assure that any remnant vapor condenses. For a given test fluid, the initial applied voltage to the heater is set by requiring the observed temperature di fferences between the thermocouples to be greater than the known error in the thermocouples. This is only a concern at low heat fluxes, where temperature gradients in the brass heater are observed to be small. The applied voltage is then increased in one v olt increments until incipience. This gradual increase in applied voltage assures quasi steady conditions during step increases in heat flux. This assures minimal error when using a steady state assumption in extrapolating surface temperatures preceding hi ghly transient events like incipience and CHF. After incipience, the magnitude of voltage increments is increased depending on the test fluid. Upon a pproaching CHF, voltage increments are then decreased to one volt increments, again assuring quasi steady c onditions during step changes. Repeatability studies have confirmed that heat transfer performance from test to test does not change even for studies conducted more than twenty four hours apart. Experiments were conducted to assess the repeatability of the soldering process; it was observed that the wall superheat for a given applied heat flux varied less than 10% for different soldering applications. 2.6 Data Post Processing A MATLAB code is utilized to post process the data. Only steady state portions of the transient temperature histories are used for boiling curve calculations. For transient
72 events such as incipience and critical heat flux the steady state data preceding the event is used to generate a point on the boiling curve. The use of steady state data does not require an inclusion of sensor dynamics as dynamic data is never processed for heat transfer analysis. Figure 2 5 shows the recorded time histories of apparent heat flux and wall superheat temperature that are typically observed during incipience events. The sharp decreas e in wall superheat can be seen; this occurs as a result of the latent heat removal from rapid bubble nucleation. The spike in apparent heat flux is a phenomena generated from the method of measurement. T he slope of the temperature distribution inside the heater is used to provide a real time estimate of the steady state heat flux D uring highly transient events the true temperature distribution deviates from linearity. The least squares method adopted for determining the real time heat flux then over estimates the heat flux as the thermal disturbance propagates through the heating block. True applied heat flux measurements are determined from the power supplied and real time measurements are used to assess heat losses. A simple mathematical analysis can reveal the sensitivity of the given method of measurement to transient thermal propagation. For the transient events of concern in pool boiling, incipience and CHF, the duration of the actual event is short relative to the duration with which the heater takes to reach steady state. To facilitate the analysis assume that for small times after the event that that material can be assumed to be semi infinite. The appropriate governing equation and its associated boundary and initial conditions becomes 2 1
73 2 2 2 3 Figure 2 5 Apparent heat flux and wall superheat time histories during an incipience event for the pool boiling of hexane on single crystal Al<100>. For any given event the solid will initially be at some steady state temperat ure distribution for the given heat flux. As a result of this condition the intial temperature distribution will be linear. It can therefore be concluded that: 2 4 2 5 Using conditions 2 4 and 2 5 the following change of vari ables can be implemented to simplify the foregoing analysis. 2 6
74 And therefore 2 7 2 8 2 9 The governing equation and boundary and initial conditions can be expressed as: 2 10 2 11 2 12 For further simplification it will be assum ed that the transient event can be modeled as an instantaneous step change in surface temperature. Therefore 2 13 The solution to the present problem can be readily achieved w ith the use of the laplace transform method. Foregoing the tedious derivation, the solution to equation 2 10 subject to conditions 2 11 and 2 12 with the assumption 2 13 can be expressed as: 2 14 Based on the given conditions and assumptions the initial temperature distribution takes the form: 2 15 Further simplification of equation 2 14 using equation 2 15 results in:
75 2 16 Equation 2 16 can now be used to determine the apparent transient heat flux error associated with the current measurement method. A least squares regression fit is used to determine the slope of the temperature distributi on in the solid at steady state. The general expression for the slope given arbitrary data can be expressed as: 2 17 The denominator of equation 2 17 is a constant that is so lely dependent on the number of thermocouples and their respective distances from the top of the heater. Substitution of the known distances into the expression for the denominator yields Use of equation 2 16 in the numerator in equation 2 17 with some simplification, yields: 2 18
76 Figure 2 6 Time history of the apparent heat flux determined from equation 2 18 with k= 110 W/cm 2 K, = 33.9 10 6 T= 28 C, and q= 6 W/cm 2 The thermal properties given are that of Brass. Thermal conditions were chosen to mimic those observed during incipience. From equation 2 18 it can be seen that the slope of the least squares fit for the temperature distribution i s a function of time. It can also be observed that it is dependent on four parameters : the initial heat flux, thermal conductivity of the heating block, temperature change, and the thermal diffusivity. To further understand the dynamics of the apparent hea t flux error it is important to determine the relationship between the time at which the peak value of the apparent heat flux occurs and the thermal diffusivity of the material. In order to do so one must determine the time at which the peak in apparent he at flux occurs. Taking the derivative with respect to time of equation 2 18 and setting it equal to zero results in a transcendental equation
77 equation 2 19 Numerically solving for for a given over a range of different thermal diffusivities results in a very simple relationship, which can be observed in Figure 2 7 2 19 A least squares regression fit of the numerical output allows for the determination of the simple expression for the time at the peak in apparent heat flux. 2 20 Equations 2 18 and 2 20 now permit the estimation of the temperature drop at the surface with use of the measured apparent heat flux. Substitution of equation 2 20 into 2 18 and rearranging yields an expression for the temperature drop at the interface. Figure 2 7 Relationship between the time till the maximum in appare nt heat flux and thermal diffusivity. The discrete points are the result of numerically solving equation 2 19 and the solid line is a least squares fit to the numerical output.
78 2 21 In equation 2 21 is the maximum value of the measured apparent heat flux and is the initial applied hea t flux. The constants and were previously defined. It should be noted that this error analysis for dynamic events is only applicable to transient events that result in rapid changes in surface temperature over very short time periods, such as incipience. Although CHF is also a transient event, the time period over which the transition occurs is much longer than that of incipience. Therefore, a different approximation for the boundary condition would be required to determine the dynamics of the measurement method for such an event. For CHF the most appropriate boundary condition for small times proceeding the event would be instantaneous insulation of the heating surface. This slight modification in the boundary condition does not change the gov erning equations or initial condition. The resulting boundary condition, using the change of variables previously used, becomes: 2 22 Using the same solution procedure as before y ields the following for the temperature distribution. 2 23
79 It can be observed that at the wall the surface temperatu re variation with time will exhibit a behavior. This can be observed in the latter portion of the temperature history shown in Figure 2 8 For further simplification let 2 24 Such that equation 2 23 can now be written as 2 25 Now proceeding wit h a similar analysis as before, the variation of the apparent heat flux with time can be determined from the slope of the least squares fit using the exact solution The expression for the slope is now expressed as: 2 26 Figure 2 8 shows the apparent heat flux and wall superheat time histories during CHF. Two notable features are the sharp drop in apparent heat flux and t he drastic increase in wall temperature. Again, some of the transient heat flux phenomena recorded for incipience and CHF are as a result of the measurement method. Although none of the physics are altered C areful inspection of the data is required to rea ch the proper conclusion about what portion s of the data record are valid. At CHF the formation of the vapor film adds a thermal resistance at the interface due to the low thermal conductivity of the vapor film. The thermocouple nearest the surface begins to increase in temperature first before the thermal perturbation reaches the subsequent thermocouples. The thermal profile at this instant is no longer linear and the method employed incorrectly predicts the heat flux during the event. However as noted
80 pre viously, measurements in the boiling curves were used for steady state portions of the recorded histories. Using the measurement method analysis given previously the predicted behavior of the apparent heat flux, given in Figure 2 9 can be seen to agree well with that observed in Figure 2 8 Additionally, the predicted wall temperature change in Figure 2 10 can be seen to agree with the measured variation given in Figure 2 8 The preceding analysis for the measurement method employed in these experiments could be further utilized to extract values for salient parameters of the given transient events. However, this was not presently employed in any post exp eriment analysis. Figure 2 8 Apparent heat flux and wall superheat time histories for CHF during pool boiling of hexane on single crystal Al<100>.
81 Figure 2 9 Variation of apparent heat flux following CHF. This solid curve is the predicted behavior of the measurement method based on the preceding analysis. Figure 2 10 Wall temperature change following CHF Predicted behavior based on preceding analysis.
82 2.7 Image Analysis for Determining Nucleation Site Density on Structured Surfaces Images are taken at low heat flux to allow the number of active sites to be counted. A MATLAB code was written to facilitate the bubble counting process. Image processing begins by initially using a mask image Figure 2 11 to remove extraneous background features from the boiling image Figure 2 12 This initial step enhances the contrast between the bubbles on the surface and the surface itself Figure 2 13 The target image is then converted from RGB to gray scale, Figure 2 14 This then allows in cont rast limited adaptive histogram equalization function. This function further enhances the contrast of the gray scale image, Figure 2 15 The post processed image is then used to manually determine the number of bubbles on the surf ace. A MATLAB code was written to facilitate the counting process by allowing the user to mark counted bubbles in the image, this also assured that bubbles are not double counted Figure 2 11 Mask image taken of surface before boiling.
83 Figure 2 12 Image taken at steady state for a given heat flux. Figure 2 13 Subtraction of mask image from target image. Figure 2 14 Conversion of target image from RGB to gray scale.
84 Figure 2 15 Application of built in MATLAB function for contrast limited adaptive histog ram equalization.
85 CHAPTER 3 POOL BOILING ON SMOO TH SURFACES 3.1 Nucleation and Heat Transfer on Smooth Surfaces The conventional theory of heterogeneous nucleation asserts that the propensity for bubble nucleation is dependent on the cavity size distribution, cavity geometry and surface wettability. Many conventional surface fluid combinations result in moderate w etting conditions which promote boiling at low wall superheats due to surface trapped non condensable gases. In contrast highly wetting surface conditions result in flooded cavities and conventional theory breaks down. For heterogeneous bubble nucleation on a smooth surface with no vapor trapping cavities, conventional theory predicts that the nucleation rate will have a strong dependence on the wetting pro perties of the fluid as was shown in section 1.5 However for decreasing contact angle (i.e. increasing wettability) conventional theory predicts that the incipient wall superheat will approach the homogeneous superheat due to the almost spherical shape of the bubble embryo  Relative to the homogeneous superheat, p revious investigators have observed both low and high incipient superheats on metallic surfaces [10; 14; 15; 29; 38; 5 9] The disparity among reported incipient superheats hinders the development of a complete understanding of the effects of the solid liquid interaction of highly wetting fluids on bubble incipience and nucleate boiling heat transfer. An accurate descript ion of nucleate boiling heat transfer inherently relies upon the heating surface characteristics and fluid properties  Surface geom etry, thermophysical properties, orientation and microstructure are just some of the characteristic parameters that have a significant influence on the boiling curve. In
86 addition to the brief review of current literature in section 1.3 a plethora of data are available on all facets of surface enhancement for nucleate boiling. At least one prior experimental investigation has considered the effects of crystal plane orientation and wetting on the boiling process. Harrison et al.  investigated the effects of wetting on the boiling heat transfer characteristics of stearic acid on copper by using si ngle crystal copper of two different orientations. They observed a significant difference in the measured heat transfer rate among the crystal planes tested, with no difference in the measured contact angle. They concluded that use of only the measured con tact angle is not sufficient to characterize boiling heat transfer characteristics of highly wetting fluids on smooth surfaces. Torii et al.  used molecular dynamics simulations to investigate the effects of molecular interaction parameters and crystal plane orientation on energy transfer at the solid liquid interface. The ir resu lts showed that molecular scale surface corrugation and number density, two parameters associated with crystal plane orientation had a noticeable effect on energy transfer at the solid liquid interface. Their study also revealed the complex nature of inte rfacial heat transfer between different crystal planes and the fluid. Surfaces with greater corrugation resulted in significant increases in in plane thermal transport. Conversely, smoother surfaces showed reduced in plane heat transfer and nominal thermal transport perpendicular to the surface. Other investigators have also employed molecular dynamics simulations in an effort to resolve the fundamental phenomena governing molecular scale interfacial heat transfer. However, most simulations resort to using simple monatomic fluids for the simulation fluid. Although this is sufficient to study the basic interaction it does not comprehensively
87 include all possible phenomena that occur for polyatomic molecules. Hence a n ab initio understanding of the salient mo lecular influences at the solid liquid interface and the resultant effects on bubble nucleation and nucleate boiling heat transfer remains elusive. For the current investigation, two series of experiments have been conducted. The first series of experiment s investigated pool boiling heat transfer on both single crystal and polycrystalline smooth metal substrates Whereas the second series of experiments was conducted to further expound on the trends concerning planar density and heat transfer performance, o bserved in the first series of experiments. For the first series, s ingle crystal Silicon substrates of three different crystal plane orientations were used. In addition, two crystal plane orientations of single crystal Copper and Aluminum were used. In the second series of experiments five different crystal planes of single crystal Silicon along with three different crystal planes of Copper were used. The addition of more crystal planes to the second series of experiments seeks to further understand the eff ects of crystal structure on boiling heat transfer. All the substrates we re obtained from the MTI Corporation with one side optically polished to sub nanometer roughness. All surfaces tested were 1cm 2 in size. The single crystal substrates provide a heatin g surface devoid of nucleation promoting cavities. Therefore, the essential macroscopic parameters become the thermophysical properties, surface size and wettability. Table 3 1 displays the relevant thermophysical parameters for th e substrates used.
88 Table 3 1 Thermophysical properties of the different heating surfaces used. Material K (W/m K) (kg/m 3 ) C P (J/kg K) 5 (m 2 /s) C P x 10 6 (J/m 3 K) Cu 401 8940 384.6 11.66 3.44 Al 237 2700 896.9 9.79 2.42 Si 149 2329 704.6 9.08 1.64 Ni 90.9 8908 444.2 2.30 3.96 Ti 21.9 4506 523.5 0.93 2.36 An additional feature that must be accounted for with the single crystal substrates is the crystal plane orientation. Some crystals can exhi bit anisotropic properties depending on the inherent structure of the crystal. However the crystals used in this study possess no anisotropy with respect to thermal properties. Table 3 2 shows the crystal structure for copper a n FCC crystal Both top views and side views are given of the specified planes. For all images shown the top most layer of atoms are colored black. All other layers below the plane specified are colored orange. Only for Cu(111) is the second layer colored gr ey so that the hexagonal arrangement of lower layers can be distinguished. Table 3 3 shows the top and side views for the five crystal planes of silicon used in the second series of boiling experiments. The images shown in Tables 3 2 and 3 3 were made using CrystalMaker, which is commercial software used for constructing and analyzing crystal structures. It is important to note that despite the misleading simplicity of a monatomi c crystal. Varying the crystal plane orientation can lead to vastly different in plane and perpendicular structures. This inherently makes it difficult to determine the most influential features of the structure as they relate to interfacial thermal transp ort and internal thermal transport.
89 One hydrocarbon and fluorocarbon fluid, n hexane and perfluoro n hexane (FC 72) respectively, were chosen as the test fluids due to their highly wetting properties. The only structural similarity among normal hydrocarbon s and fluorocarbons is the carbon chain backbone. Both types of molecules are non polar, meaning that dispersion forces are the sole component of their intermolecular interactions. Hydrocarbons, as the name implies, form a homologous series of hydrogen con taining compounds. Similarly fluorocarbons are part of a homologous series of fluorine containing compounds. This subtle difference in the two homologous series results in significantly different thermophysical properties. The difference in thermophysical properties becomes more apparent when viewing a direct comparison, as in Table 3 4 Table 3 2 Planar structure and planar density for an FCC crystal. The crystal planes shown are t hose that were tested. Crystal Plane Top View Side View 100 110 111
90 Table 3 3 Crystal structure of five different crystal planes of Silicon. Atoms colored black are those that are at the topmost layer of the crystal. Crystal Plane Top View Side View 100 110 111 210 211
91 Table 3 4 Thermophysical property comparison of hexane and perfluo rohexane. Property Units Hex ane Perfluorohexane Molecular Mass g/mol 86 388 Density kg/m 3 613 1680 Heat Capacity kJ/kg K 2.45 1.1 Thermal Conductivity W/m K 0.112 0.057 Viscosity cP 0.196 0.64 Surface Tension N/m 0.013 0.01 Enthalpy of Vaporization kJ/kg 335.6 87.9 Boiling Te mperature C 69 56 Molecular Polarizability 3 11.8 12.6 Ionization Energy eV 10.2 19.7 The difference between two molecules of equal chain length taken from each series arises from a difference in the intermolecular interaction energy. Due to the sma ll size of the H atom the H H, C H and C C interactions of adjacent hydrocarbon molecules are all of importance; this implies that intermolecular forces among hydrocarbons is strong due to the increased number of interaction centers  Due to the markedly larger size of the fluorine atom as compared to the H atom, F F and to some extent C F interactions of adjacent molecules are the primary contributors to the intermolecular forces among fluorocarbons. The reduced number of interaction centers results in a reduction of the intermolecular interaction strength. The reduction of intermolecular interaction strength results in a reduced latent heat of vaporization, surface tension, density, liquid viscosity, and speed of sound. The increased distance between nea rest neighbor molecules in fluorocarbons results in increased liquid compressibility and gas solubility. Fluorocarbons are both thermally and chemically
92 stable due to the strength of the C F bonds  They also have high dielectric strengths which make them suitable for use in electronics cooling  A preliminary step to understanding the possible molecular influences on boiling heat transfer has been undertaken by the current set of experiments. Smooth metallic and non metallic heati ng surfaces a re used in conjunction with highly wetting fluids to study nucleate boiling heat transfer and bubble incipience. Aside from their differing thermophysical properties due to molecular differences, the highly wetting nature of the fluids used as sures that there is a strong interaction at the solid liquid interface. Additionally the use of single crystal surfaces will elucidate any phenomena that are influenced by crystal structure 3.2 Pool Boiling Results for Smooth Surfaces 3.2.1 Experiment Series 1 Figure 3 1 and Figure 3 2 respectively show the boiling curves for perfluorohexane and hexane on the two polycrystalline surfaces, Nickel and Titanium, as well as for the Copp er, Aluminum and Silicon single crystal surfaces of the <111> crystal plane orientation. The <111> plane is chosen for comparison because it has the highest packing density and is therefore the smoothest on a molecular scale. Differentiating between the si ngle crystal and polycrystalline surfaces, it can be observed that the heat flux for a given superheat increases with increasing thermal conductivity for both groups of surfaces. This trend among the two mentioned groups occurs for pool boiling of both per fluorohexane and hexane. The trend along the entire boiling curve is more readily apparent with hexane than for perfluorohexane.
93 Figure 3 1 Boiling curves for perfluorohexane on all the polycrystalline an d single crystal <111> orientation surfaces. Figure 3 2 B oiling curves for hexane on all the polycrystalline and single crystal <111> orientation surfaces
94 Large incipient superheats can be observed for b oth the metals and silicon. Curves that show no temperature hysteresis are due to edge bubble nucleation which can be attributed to poor bonding between the encapsulating epoxy and the substrate. The incipient superheats for perfluorohexane vary greatly am ong the surfaces shown as compared with hexane in which the superheats are more closely spaced. However, no obvious trend with either thermal conductivity or crystal plane orientation can be discerned from the measured incipience data. Critical heat flux i s seen to increase slightly with increasing surface thermal conductivity. In Figure s 3 3 through 3 6 the boiling curves for perfluorohexane and hexane on different crystal plane orientations of Aluminum a nd Copper are shown. For both the aluminum and copper surfaces, there is essentially no effect of crystal plane orientation on nucleate boiling heat transfer of perfluorohexane. However, there is a slight increase in heat transfer of the <100> surface orie ntation over the <111> orientation for hexane with a greater increase occurring on the aluminum surface. This occurrence suggests that for the single crystal metal surfaces, the heat transfer is weakly inversely proportional to the planar density. Incipien t superheats are seen to be between 30 35 K for perfluorohexane and 40 60 K for hexane on both surfaces. The homogeneous superheats for perfluorohexane and hexane are 80 C and 121 C, respectively  There is no discernable trend betwee n the magnitude of incipient superheat and the crystal plane orientation for the metal surfaces. Figure s 3 7 and 3 8 show the boiling curves for three crystal plane orientations of silicon. For both perfl uorohexane and hexane it can be seen that heat transfer increases with increasing planar density. Incipient superheats range from 30 50 K and 50 80 K for
95 perfluorohexane and hexane, respectively. Higher Incipient superheats are observed for hexane, with so me instances resulting in a direct transition from natural convection to film boiling. This phenomenon, typically termed film boiling incipience (FBI)  is only sustainable fo r hexane. The temperature excursion beyond 80C observed in Figure 3 8 is for film boiling after FBI. For perfluorohexane instances of film boiling at incipience are short lived, only lasting until the surface temperature drops lo w enough to transition back to nucleate boiling. Additional runs for the above two orientations of silicon with hexane as the test fluid result in similarly high superheats; although not all incipient events result in a direct film boiling transition. Film boiling incipience events are also observed for nickel and aluminum; however the vapor film is short lived. No discernable trend can be observed from the data relating incipient superheat to crystal plane orientation. Figure 3 3 Boiling curves for perfluo rohexane on two different crystal plane orientations of Aluminum.
96 Figure 3 4 Boiling curves for hexane on two different crystal plane orientations of A luminum. Figure 3 5 Boiling curves for perfluo rohexane on two different crystal plane orientations of copper.
97 Figure 3 6 Boiling curves for hexane on tw o different crystal plane orientations of copper. Figure 3 7 Boiling curves for perfluo rohexane on three different crystal plane orientations of Silicon.
98 Figure 3 8 Boiling curves for hexane on three different crystal plane orientations of Silicon. However it must also be noted that although surface roughness remains very low, less than 50 nm, other factors such as surface oxide structure and composition, may also contribute to the observed reduction in incipient superheats. Despite the presence of the native oxide layer there is a clear distinction between the different crystal planes and their effect on nucleate boiling heat transfer. Surely the underlyi ng crystal structure has a significant influence on the interfacial thermal transport. 3.2.2 Visual Observations for Series 1 Typical incipience events result in rapid cooling of the surface due to latent heat removal. However for large enough superheats, where the heat flux is also higher than normal incipience events, sustained film boiling can be initiated without ever having achieved nucleate boiling. Figure 3 9 shows the film boiling transition at incipience for pool boiling of hexa ne on Si <110>. It can be seen that upon first sight of the initial
99 bubble that full surface coverage occurs only one millisecond later, indicating a high nucleation rate. The high wall superheat results in a very high nucleation rate and subsequently the elevated heat flux at incipience assures that the thermal energy is enough to balance the initial latent heat removed during incipience of the vapor film. Sustained film boiling at incipience is only observed for perfluorohexane on Si<110> and hexane on Si <110> and Si<100>. Instances of film boiling at incipience are observed for perfluorohexane on Si<111> and hexane on Al<100>. Careful inspection of the data show that there is a higher probability of film boiling at incipience when the heat flux is at leas t one third of the expected critical heat flux and the wall superheat is at least 30% of the homogeneous superheat. Figure s 3 10 and 3 11 show a similar set of time series for perfluorohexane on Si<110> and hexane on Al<100>. High nucleation rates are also observed, resulting in vapor film formation. Comparison of the film boiling incipience images with those taken at CHF confirms that the difference in heat flux and superheat at the two different events does not alter the two phase flow structure upon formation of the vapor film. A particular characteristic of the two phase flow structure for film boiling on a square surface are the four bubbles generated from the corners of the surface, which is observed for both FBI and CHF. The four departing bubbles are a consequence of the smaller critical wavelength of perfluorohexane and presence of boundary layer merging zones. Visual observations of hexane film boiling confirm that the critical wavelength governs the number of departing bubbles during film boiling. For hexane, the wavelength is approximately twice that of perfluorohexane. The larger wavelength is proportional to surface size and therefore only permits a single bubble to depart.
100 0.0 ms 0.5 ms 1.0 ms 1.5 ms 2.0 ms 2.5 ms 3.0 ms 13 ms 23 ms 33 ms 43 ms 53 ms 63 ms 83 ms Figure 3 9 Time series of film boiling transition at incipience for hexane w,i =78 C, q=10 W/cm 2 ) 0.0 ms 1.0 ms 2.0 ms 3.0 ms 4.0 ms 5.0 ms 25 ms 45 ms 65 ms 85 ms 105 ms 145 ms Figure 3 10 Time series of film boiling transition for perfluo rohexane on Si<110> su rface. ( T w,i =40 C, q=5 W/cm 2 )
101 0 ms 2 ms 4 ms 6 ms 8 ms 10 ms 12 ms 14 ms 16 ms 36 ms 56 ms 76 ms Figure 3 11 Time series of transient film boiling at incipience for hexane on Al<100> sur face. ( T w,i =60 C, q=10 W/cm 2 ) 0.0 ms 0.33 ms 0.66 ms 1.0 ms 1.33 ms 1.66 ms 2.0 ms 2.33 ms 2.66 ms 12.66 ms 22.66 ms 32.66 ms 42.66 ms 62.66 ms Figure 3 12 Time series of inc ipience for hexane on Al<111> surface. ( T w,i =44 C, q=5 W/cm 2 )
102 Incipient events that do not result in film boiling are also observed, and the nucleation rate strongly depends on the degree of superheat. For instance in Figure 3 12 pool boiling of hexane on Al<100>, the initial bubble takes about 12 ms to grow before it significantly perturbs the boundary layer enough to initiate rapid vaporization. The resulting vapor front propagates across the heating surface within 10 ms of t he critical perturbation. Incipience observed on other surfaces shows similar behavior with time for full surface coverage, and the propagation time varies with the initial superheat. However no conclusive trend is observed for the various heating surfaces It should also be noted that the residual bubbles seen in the foreground and background of the time series are not produced from the surface prior to incipience. These peripheral bubbles form in cavities located on the outer portions of the epoxy used t o encapsulate the heater. Their buoyancy is sufficient to overcome entrainment from t he natural convection currents induced by the heating surface prior to boiling incipience 3.2.3 Experiment Series 2 Following the results of experimental series 1 for the singl e crystal surfaces it was determined that planar structure had an influence on pool boiling heat transfer. The second series of experiments with single crystal surfaces was conducted in order to further understand the influences of planar structure by inc luding more crystal planes for the respective test surfaces. Two additional crystal planes of Silicon were obtained to add to the three previously tested. This resulted in a total of five different crystal planes of Silicon. For copper, only one additional crystal plane was obtainable. Therefore a total of three different crystal planes of copper were used. The heating block material was changed to copper, which resulted in an overall change in the shape of the boiling
103 curve. The change in the heater materi al can have a significant effect on the bubble growth and departure cycle [66; 67] The alteration of bubble growth dynamics can suppress or promote interfacial effects. Figure 3 13 shows the boiling curves for the five different crystal planes of Silicon tested with FC 72. It can be seen that Si(111) again shows the best heat transfer performance. However, Si(100) and Si(110) show different performances with respect to the first series of experiments. The previo us results conclusively identified planar density as a major parameter in assessing boiling performance for a particular planar structure Along this line of reasoning Si(110) should have performed better because it possesses a slightly higher planar densi ty than Si(100). But it is important to note that this variation is small (a difference of approximately 0.8). Therefore, planar density may not play as strong a role as previously believed. This is most noticeable when comparing Figure s 3 13 and 3 14 with Figure s 3 7 and 3 8 respectively. The two new planes of Silicon tested in series 2 sho w lower heat transfer performance than Si(111), Si(110), and Si(100). This is as expected because their planar densities are much lower than the three previously tested surface orientations. Although planar density is not the sole indicator of heat transfe r performance it does provide some insight as to the expected performance. This can further be observed in Figures 3 15 and 3 16 which show the pool boiling curves obtained for three different crystal pl anes of copper. A comparison with the previous results obtained on single crystal copper surfaces confirms a reduced planar density effect. From the current results it is plausible that the subsurface crystal structure can also be of importance in determin ing the heat transfer performance of single crystal surfaces. The effectiveness of molecular transport within
104 the solid is one mechanism that controls the interfacial thermal transport. But the physics that govern such transport mechanisms are quite comple x. For any given solid the dominant energy carrier will depend on the nature of the solid. This makes it difficult to determine the most important parameter to characterize the effectiveness of the crystal structure normal to the crystal plane Looking at Figure s 3 13 and 3 14 it can be observed that for FC 72 and hexane the boiling curves begin to diverge past a heat flux equivalent to roughly 60% of the measured CHF. This is most certainly attributable to the increased nucleation site density that is associated with boiling heat transfer in between the isolated bubble regime and regime of slugs and columns. The most likely means for heat transfer augmentation of the ebulli tion cycle from a smooth crystalline heating surface is via the microlayer region underneath the bubble. A major contribution to the overall heat transfer that occurs in the vicinity of the bubble can be associated with the heat flux produced in the microl ayer. Evaporative heat flux as a result of thin film evaporation is strongly affected by the molecular interaction at the solid liquid interface. Additionally, the strength of the intermolecular interaction will change the local liquid film profile. This w ill also significantly alter heat transfer near the base of the bubble. This effect is postulated to be most influential near the initial stages of bubble growth, during the formation of the microlayer.
105 Figure 3 13 Boiling curves for pool boiling heat transfer of FC 72 on five different crystal planes of single crystal Silicon. Figure 3 14 Boiling curves for pool boiling heat transfer of hexane on five di fferent crystal planes of single crystal Silicon.
106 Figure 3 15 Boiling curves for pool boiling heat transfer of FC 72 on three different crystal planes of single crystal Copper. Figure 3 16 Boiling curves for pool boiling heat transfer of hexane on three different crystal planes of single crystal Copper.
107 3.3 Discussion of Heat Transfer Results 3.3.1 Experiment Series 1 T he heat transfer data presented in series 1 suggest that surface effects are more pronounced with hexane than with perfluorohexane. Th is can plausibly be associated with the strength of the molecular interactions between the surface and the fluid The strength of the interaction between two differen t molecules can be approximated by the geometric mean of the strength of the intermolecular interaction s of the two separate molecules  As a general comparative analysis it can be shown that the surface hydrocarbon interac tion w ill be greater than that of the surface fluorocarbon interaction The hexane intermolecular interaction strength within the fluid is greate r than that of the fluorocarbon; this is most apparent from the difference in boiling temperatures. So it can t herefore be stated that : 3 1 In equation 3 1 E HC and E FC represent the strength of intermolecular interaction within the respective fluids. Intermolecular in teractions can be simply described by a Lennard Jones type of interaction; which includes an attractive and repulsive potential. However, this type interaction potential is most suitable for the description of molecules with spherical symmetry. For a simpl e comparative analysis this approximation will suffice. The depth of the energy well for the potential interaction can provide a means of characterizing the strength of the interactions. A more in depth quantification of the strength of interaction between molecules can be found in the monograph by Israelachvili  A n approximation for the strength of the surface hydrocarbon interaction can be expressed as:
108 3 2 A similar argument can be made for the surface fluorocarbon interaction. Using equation s 3 1 and 3 2 the ratio of the two different surface flu id interactions can be assessed, 3 3 So the strength of the surface fluid intermolecular interaction for perfluorohexane is weaker than that of hexane This is consistent with the reduced effect of crystal plane orientation observed for perfluorohexane in the first series The opposing trends of heat transfer with respect to planar density between the metal and non metal surfaces suggest that a distinct c haracteristic of the metal surfaces must drive the molecular enhancement of heat transfer. Presumably the direct improvement of heat transfer with increasing planar density for silicon is a result of the increased number of collision partners. S imary means of thermal transport within the solid is by phonon transport, it could reasonably be assumed that the higher density of collision partners improves energy transfer at the interface for a material whose dominant mode of energy exchange is by col lisions. Interfacial interactions on metal surfaces are more difficult to describe because multiple modes of energy exchange are available due to the presence of free electrons. Energy exchange can result due to phonon interactions, electron transport or a coupling of phonon and electron interactions. This can be even more difficult to describe when interaction at a solid liquid interface is concerned. T he observed improvement in heat transfer with decreasing planar density for metal surfaces could presumab ly be attributed to a change in the energy transfer
109 efficiency via phonon electron coupling at the interface. Reduced packing density increases the available space for free electrons near the interface which allows for the increased energy exchange betwee n molecule electron and molecule phonon interactions. Specifically the reduced packing density at the interface implies that the planar density of positive ion cores is reduced. T he force from the positive ion cores that normally occurs from all directions within the crystal is now reduced because of the decreased number of nearest neighbors at the surface. A ccounting for various atomic arrangements due to differing crystal planes it can be physically understood that e lectrons in the near surface region can now migrate further from the metal surface, as a result of the reduced attractive force. The extent to which the resultant charge distribution extends beyond the interface now depends on the local atomic arrangement of atoms at the interface. Different at om arrangements resulting from different crystal plane orientations changes the spatial variation of the electron charge distribution [68; 69; 70; 71; 72; 73] The observed enhancement in heat transfer is only obse rved in the nucleate boiling regime. Therefore it can be concluded that the crystal structure effects of metallic surfaces are most effective in the presence of two phase flow to the extent of enhancing heat transfer during the ebullition process. The mo st plausible link between atomic structure and nucleate boiling heat transfer is via the interaction with the microlayer. Beneath a growing bubble there is a microlayer of fluid that accounts for a portion of the heat transfer from the surface. The microla interactions and macroscale behavior. The microlayer consists of three distinct regions as can be seen in Figure 3 17 In the adsorbed film region an atom ically thin layer of
110 fluid molecules are attached to the surface. Molecules in the adsorbed film region are at a pressure in excess of the system pressure because of molecular interactions. This precludes any evaporative heat transfer from this region beca use the saturation temperature in the adsorbed film is greater than the surrounding bulk fluid. This results in a considerable thermal resistance in the adsorbed film region. In general, the adsorbed film thickness is a function of the wall temperature and surface fluid interaction strength [74; 75] In the bulk liquid region only macroscopic influences are of importance. This is the region where the typical contact angle for the bubble is measur ed. The transition r egion is where the microlayer transitions from atomic scale influences to macroscopic influences. A considerable portion of the heat transfer that occurs at the base of a bubble comes from the evaporative flux of the transition region. The transition from the adsorbed film to the thin film results in a large change in curvature which brings about a significant increase in evaporative flux at the interface. B ecause the thin film portion of the microlayer is adjacent to the adsorbed layer this region is als o under the influence of molecular forces. Subsequently, because the thin film portion of the microlayer provides a considerable contribution to heat transfer and is also significantly influenced by molecular forces, it can be inferred that any alteration of the molecular interaction will bring about significant changes in the thermal flux at the interface. It is generally very difficult to conduct measurements under a growing bubble, especially measurements concerning the microlayer. Fortunately the micr olayer is fundamentally analogous to an extended meniscus. An extended meniscus is the result
111 Figure 3 17 Different regions of the microlayer under a bubble. of wetting a surface with a fluid in which the re is a strong surface fluid interaction. A thin adsorbed film, thin film and bulk meniscus are all present. Many detailed analyses of extended wetting menisci have been reported in the literature. Studies have confirmed that the heat transfer in an exten ded meniscus can be changed by either surface morphology or external body forces Ojha et al.  conducted a set of experiments to explore the effects of surface structure on evaporative phase change from an extended meniscus. They used interferometry to measure the film thickness profile under both isothermal and evaporative heat transfer conditions. The adsorbed film was observed to decrease in thickness when under evaporative conditions. T he measured thickness was observed to be less than that measured under isothermal conditions. Surface roughness, however, still significantly increases the adsorbed film thickness. A sharp change in film curvature was observed in the transition region upon heating ; this was attributed to the high evaporative flux that
112 o ccurs with increased interface curvature Additionally the corner meniscus was observed to recede upon heating. This in turn increases the local capillary pressure and increases the local flow to the evaporative zone. Ojha et al.  further explain that t here are essentially two driving pressures controlling the evaporative region. The disjoin in g pressure, which results from molecular interactions, pulls fluid towards the adsorbed film region. Simultaneously, capillary pressure resulting from the change in film curvature also drives fluid towards the adsorbed film. They also note that increased wettability of the surface results in an elongation of the transition region and therefore increases heat transfer in that region. Their results further reveal that roughness on the order of the adsorbed film thickness can also significantly enhance heat transfer in the thin film region E lectrohydrodynamic forces have been shown to significantly alter boiling heat transfer [7 7; 78; 79; 80] Visual observations reported in the literature have also elucidated the strong effect of applied electric fields on the two phase flow structure. Gorla et al.  developed an analytical model to assess the eff ects of an applied electric field on the heat transfer in an extended meniscus. Their model showed that an applied electric field can significantly enhance heat transfer in an extended meniscus. The applicability of their model to boiling analysis stems fr om the similarity between t he microlayer region beneath a bubble and an extended meniscus wetting a surface Zhao et al.  investigated the effects of wall superheat and temperature dependent fluid prope rties on the heat transfer in the thin film region of an extended wetting meniscus. As expected, their model predicts wall superheat to have a significant effect on the film profile and subsequently evaporative heat transfer. Interestingly,
113 accounting for temperature dependent fluid properties shows that the adsorbed film thickness reaches a minimum at a superheat that is dependent on the physical properties of the fluid. Exceeding this temperature, the adsorbed film thickness increases. Their model suggest s that not accounting for the temperature dependency of the fluid properties can lead to erroneous film profiles and heat flux calculations. It is further interesting to note that for constant properties the total heat transfer rate almost linearly increas e with wall superheat. Whereas for the temperature dependent fluid properties there is a power law dependency on the wall superheat, with the exponent being less than unity. Conclusively, the heat transfer and fluid flow in the thin film region is sensitiv e to even minute changes in surface roughness  The application of external forces, via electric fields, can also produce significant changes in local convective heat transfer  Accounting for temperature dependency of th e fluid properties can also produce noticeable changes in heat transfer  For the two different types of surfaces tested, non metals and metals, there are plausible microscale mechanisms that explain the observed trends in nucleate boiling heat transfer for both types of surfaces For Silicon, as mentioned previously, the primary means of thermal transport is via phonons. Molecular dynamics studies have revealed that thermal boundary resistance can vary w ith planar density  Specifically, increased planar density results in a de crease in thermal boundary resistance. The model of Zhao et al.  showed that the evaporative heat transfer rate was particularly sensitive to the wall superheat. The effect of interfacial boundary resist ance on evaporative heat transfer can be inferred from the previous discussion. An increased thermal boundary resistance results in a reduced
114 wall temperature, as observed from the fluid. The reduced temperature subsequently reduces the evaporative heat tr ansfer rate and lowers the overall heat transfer. Conversely, the opposite can be said of a decrease in thermal boundary resistance. Lower boundary thermal resistance results in a higher wall interface temperature and an increased evaporative flux resultin g in an increased overall heat transfer rate. It can therefore be concluded, for non metals that increased planar density results in a lower boundary resistance and increased heat transfer in the thin film region of the microlayer. But emphasis must be pla ced on the fact that such a simple approximation to the vastly complex intermolecular interaction between a polyatomic molecule and the surface of a bulk crystalline solid will not fully capture the intrinsic characteristics that control interfacial energy transport. Thermal transport within metallic solids proceeds via more complex mechanisms. Near room temperature the primary means of thermal transport is by electrons. Yet at the interface between a metal and non metal the thermal transport mechanism beco me s difficult to define because of the vast number of molecular parameters needed to describe the interaction. It can most certainly be said that there is a strong coupling of electrons from the metal with phonons from the other interacting non metallic me dium. Phonon phonon coupling is also another mechanism of thermal transport to consider. As previously mentioned, atomic structure at the interface of a metal crystal can have marked effects on electron behavior. Reduced planar density allows for greater m igration from the interface and also alters the electron work function. The predominant electronic nature of metallic solids can most certainly imply that convective heat transfer in the thin film region is augmented by the presence of free electrons at th e interface.
115 The evanescent electric field produced by the electrons at the interface produce s electrohydrodynamic forces in the near wall region of the fluid in the thin film region. These electrohydrodynamic forces act to increase local fluid flow into t he thin film and also enhance interfacial transport at the liquid vapor interface. It can therefore be said that if electr on interaction is increased the magnitude of the electrohydrodynamic forces will also increase, resulting in increased heat transfer. Previous researchers [69; 70; 71; 72; 73] have shown that planar density will alter the evanescent electric field structure near the interface of a metallic crystal. Data reported from both experiments and numerica l models suggests that the extent of electron migration increases with decreasing planar density. Increased electron migration would result in a potential increase in electron interaction with the participating medium. Data collected for this series of exp eriments and the next confirms the hypothesis that decreasing planar density with metallic crystals increases nucleate boiling heat transfer. 3.3.2 Experiment Series 2 For t he second series of experiments a n expanded selection of test surfaces for Silicon was chosen so that it could be fully understood whether planar density was the controlling parameter in determining a crystalline surfaces contribution to interfacial heat transfer. The first series of experiments looked at the (100), (110) and (111) planes of silicon. For the second series of experiments the three original surfaces were retested along with two new planes, the (210) and (211) planes. An additional crystal plane orientation of Copper was also tested to provide further understanding of the effect s of electronic contributions to interfacial heat transfer.
116 Most important to note is the effect of the change in heating block material. The first series of experiments were conducted using a brass heating block. Whereas the second set of experiments use d a copper heating block. This re sults in a change in the heater thermal diffusivity and thermal conductivity by a factor of approximately 3.3 and 3.6, respectively. Mei et al. [66; 67] provide a detailed numerical investigation of the effects of heater thickness and thermophysical properties on bubble growth and thermal fields. The change in thermophysical properties of the heater from experiment series 1 to series 2 could have resulted in significant changes in bubble growth dynamics. This would p otent ially alter the thin film total contribution to heat transfer and thereby change the dependence on planar density. To further illustrate the effects of heating block material on the bubble growth dynamics Figure 3 18 shows a plot of the predicted bubble radius as a function of time for different heater material and fluid combinations. For a given fluid it can be seen that a brass heating block will produce larger bubbles in a longer period of time. This implies a lower bubble depar ture frequency and therefore lower heat transfer. When comparing the crystal plane influence on boiling heat transfer for series 1 and 2, a noticeable change in the dependency on crystal plane can be observed. The brass heating block produces larger bubble s with a lower departure frequency. This implies that the bubble will have an increased duration of interaction with the surface and a larger thin film region. These two factors enhance the effects of crystal plane orientation on bubble growth. Whereas for the copper heating block the reduced bubble size and increased departure frequency result in a reduced interaction period and smaller thin film region. Hence the effects of crystal plane are delayed to
117 higher heat fluxes when the nucleation site density i s great enough to be influenced by crystal plane orientation. Figure 3 18 Bubble radius time history for different fluid and heater combinations using the model of Chen et al.  Th e effect of heating block material becomes very clear when directly comparing the boiling curves measured on the two respective heating blo cks for differ ing substrates. In Figures 3 19 through 3 24 the boiling curves for Si(111), Si(100) and Si(110) are shown for both series 1, brass heating block, and series 2, copper heating block, for poo l boiling of FC 72 and hexane For single crystal silicon it can consistently be seen that the copper heating block results in an overall increase in boiling heat transfer for both fluids. This is in agreement with the previously discussed effects of heate r thermal properties on bubble growth. Figures 3 25 and 3 26 show the boiling curves for pool boiling with a Cu(100) substrate for both FC 72 and hexane respectively. The copper heating block is observed to increase boiling heat transfer in the low heat
118 flux region. Nearing CHF, however, a noticeable decrease in heat transfer is observed. This phenomenon is associated with the increased frequency of local dry out that occurs on highly conductive surfaces. Figure 3 19 Comparison of the effects heating block material on pool boiling of FC 72 on Si(111). Figure 3 20 Comparison of the effects heating block ma terial on pool boiling of hexane on Si(111).
119 Figure 3 21 Comparison of the effects heating block material on pool boiling of FC 72 on Si(100). Figure 3 22 Comparison of the effects heating block material on pool boiling of hexane on Si(100).
120 Figure 3 23 Comparison of the effects heating block material on pool boiling of FC 72 on Si(110). Figure 3 24 Comparison of the effects heating block material on pool boiling of hexane on Si(110).
121 Figure 3 25 Comparison of the effects heating block material on pool boiling of FC 72 on Cu(100). Figure 3 26 Comparison of the effects heating block material on pool boiling of hexane on Cu(100).
122 Nevertheless, t he results shown in section 3.2. 3 provide some further conclusive evidence that crystal plane orientation of smooth surfaces can have an effect on boiling heat transfer. From the data collected in both series of experiments It is difficult to discern whether planar density alone is a s uitable descriptive parameter for assessing the heat transfer potential of a given crystal pl ane. C omparing the first and second series of experiments with the s ilicon heating surfaces it can be seen that t he (100) and (110) planes switch places, with resp ect to boiling heat transfer performance. The (111) plane retains its position as the surface providing the greatest heat transfer performance. Whereas the two new planes, (210) and (211), both perform poorly with respect to the other planes tested. This w as initially hypothesized to be because of their low planar densities. Yet, it is still unknown whether the faceted structure associated with the (210) and (211) planes or low planar den sities are responsible for the poor performance. It was previously not ed that the almost similar planar densities of the (110) and (100) p lanes could have resulted in difficulty in discerning their difference in performance from both series of experiments along with the change in heating material For the single crystal copp er surfaces in experiment series 2 it can be seen for both FC 72 and hexane that the (100) plane performs better than the (110) plane. This is also consistent with the trends observed in experiment series 1. However it should also be noted that the trends observed in series 1 show less of an effect than those observed in series 2. This disparity in the observed effect of planar density is most likely attributed to the change in heater thermal properties. For t he new plane tested, the (111) plane, heat trans fer performance with respect to the planes tested varies with the
123 fluid tested. For FC 72 it performs worse than the other two planes, which is consistent with the proposed effect of the electric double layer and planar structure. However for hexane the ( 111) plane performs better than the (100) and (110) planes. This is consistent with a phonon interaction mechanism which is contradictory to the current hypothesis But it cannot be ruled out that other mechanisms could possibly be in effect, like chemica l mechanisms. It is difficult to determine the salient thermal interaction mechanisms at the interface because of the large number of variables that have effects on the measured boiling heat transfer rates at such small scales 3.4 Conclu ding Remarks on Boili ng Heat Transfer of Smooth Surfaces Two series of experiments were conducted to investigate the effects of crystal structure on pool boiling heat transfer from smooth metallic and non metallic surfaces. The goal of said experiments was to further develop a fundamental understanding of the multi scale mechanism s responsible for interfacial heat transfer at the solid liquid interface during boiling heat transfer. These experiments have conclusively revealed that even a subtle variation in atomic structure ca n result in noticeable differences in boiling heat transfer. Planar density was observed to have the greatest effect on boiling heat transfer for both the metal and non metal surfaces. However, a change in heating block material was observed to alter the m agnitude of the influence of planar density on boiling heat transfer. Nevertheless the results of this set of experiments have outlined the most plausible thermal interaction mechanisms at the solid liquid interface. For silicon, a non metal surface, the c onsistent increase in heat transfer with planar density for both series of experiments confirms that phonon interactions at the interface are the dominant means of energy transfer. The greater number of collision
124 partners that results from increased planar density subsequently reduces the thermal boundary resistance. This inherently increases energy transfer at the interface. For Aluminum and Copper, an increase in boiling heat transfer was observed for a decrease in planar density. The interfacial energy t ransport mechanisms in metallic solids are strongly influenced by their inherent electronic characteristics. Specifically, electron behavior at the interface of a metal has been reported to vary with crystal plane orientation. Lower planar densities result in enhanced electron interactions. These atomic scale electric fields are most influential in the thin film region underneath a growing bubble. In general for boiling heat transfer it has been shown that the presence of electric fields induces additional electrohydrodynamic body forces which, depending on the field orientation and homogeneity, can either aid or impede heat transfer and fluid flow. The strong dependence of the thin film profile on molecular interactions most certainly implies that the prese nce of an evanescent electric field will also provide additional enhancement in interfacial heat transfer. Molecular scale heat transfer mechanisms and their effects on boiling heat transfer have been revealed in these experiments. However a definitive mod el concerning the detailed effects of atomic scale interactions remains elusive. Further development of a complete multi scale understanding of interfacial heat transfer mechanisms in boiling systems requires a collaborative effort from various fields of s cience. Only with in depth microscale heat transfer models and validated molecular dynamics studies will we be able to unravel the intricate fundamental details governing boiling heat transfer.
125 CHAPTER 4 POOL BOILING ON CYLINDRICAL CAVITY A RRAYS 4.1 Introducti on to Cylindrical Cavity Arrays Understanding the effects of surface morphology is the key to developing a comprehensive model for boiling heat transfer. The overarching goal of any in depth fundamental pool boiling study that includes surface morphology is to b e able to predict the active nucleation site density and its effect on the measured heat transfer rate. Most industrial surfaces are inherently rough. Natural roughness, although beneficial for boiling heat transfer, hampers any rigorous understanding of t he underlying influences. This is because there is not one distinct size of surface cavities on the surface. Generally a more appropriate descriptor for surface morphology is the distribution of cavity sizes. Yet even this can prove to be difficult because most natural ly occurring cavities are nowhere near in similarity to the idealized conical cavities that the current theory utilizes. Instrumentation resolution and inherent surface ir regularity make it difficult to perform any fundamental analysis. Qi and Klausner  conducted gas nucleation experiments to investigate the effects of surface structure on nucleation site density. Surface topology measurements obtained via a scanning interferometer were used to determine the statistical distribution of cavities on t he surface. The cavity distribution was then used to generate a model to predict the nucleation site density. The statistical model achieved satisfactory agreement with water data obtained on a brass surface. However the model fails to accurately predict t he number of active sites with water on the stainless steel surface nor does it accurately predict nucleation site density with highly wetting fluids It can be concluded that in order to understand what characteristics of surface morphology are the most influential on nucleation phenomena
126 and boiling heat transfer manufactured idealized surface features should be very useful to gain a more fundamental understanding Conducting a parametric investigation of said artificial features would then permit a ful l understanding of what feature traits are the most important. The simplest structure that has been widely studied is the cylindrical cavity. The present capability of surface fabrication allows for cavities to be made on the micron scale. The set of exper iments presented in this chapter feature a small cylindrical cavity of 3 um in diameter as one of the test surfaces. Cavity depth, diameter and spacing are all perceived to be salient geometric parameters that can alter the boiling heat transfer performanc e of the surface. Other investigators have likewise studied the heat transfer from cylindrical cavities at various length scales. Sato et al.  studied the effect of spacing between cylindrical cavities on pool boiling heat transfer. The y used cylindrical cavities 10 um in diameter and 40 um deep arranged along a straight line with the center to center cavity spacing varying from 1 to 4 mm. Using laser heating and a high resolution radiation thermometer they were able to investigate nucle ation site interaction, bubble coalescence and heat transfer. Site interaction is seen to be greatest for the more closely spaced cavities Horizontal coalescence is observed to decrease while v erti cal coalescence increase s They also observed that for clo sely spaced cavities convective heat transfer plays the dominant role. Heled et al.  investigated pool boiling from large arrays of artificial nucleation sites using a variety of organic liquids. Site densities ranged from 8 to 16 sites per cm 2 with cavities 203 m in diameter and 990 m deep. The authors note that there is a
127 clear distinction between the two different boiling regimes from arrays of artificial is dominated by single phase convection and is dominated by the two phase flo w structure. The transition from one regime to the next constitutes a narrow portion of the boiling curve and it is readily apparent from their experimental data that these two regions indeed exist for their surfaces. Comparison of the boiling curves for s urfaces with different feature densities showed that at any applied heat flux the wall superheat is observed to be lower for a surface with a higher feature density than a surface with a low feature density. Chih Kuang et al.  conducted pool boiling experiments with FC 72 on cylindrical microcavity surfaces. They parametrically investigated cavity diameter and depth along with cavity density. Cavities were arranged in a rectangular array. Noticeabl e trends were observed showing a definite effect of cavity density and area enhancement on critical heat flux. Cavity density was noted to have a greater effect at high heat flux than low heat flux. Larger cavity diameters showed a degradation in heat tran sfer coefficient as well as increasing cavity depth. Qi and Klausner  investigated heterogeneous nucleation for pool boiling a nd gas nucleation in cylindrical cavities. Cylindrical cavities of different diameter as well as cavities with different geometric al cross sections were used to determine the incipience criterion for water and ethanol. Ethanol flooded cavities, due to its high wettability, where as water promoted vapor trapping. As a result of the differing wettabilities cavity activation was observ ed to occur at lower superheats for water than ethanol. Incipience
1 28 in the cavities with a non circular cross section showed similar behavior to cylindrical cavities whose diameter was equal to the width of the non circular cavity. Although cylindrical cavi ties have been previously investigated the procee ding set of experiments is conducted with the goal of further contributing to the available data and analysis of these types of surface features. This series of experiments was conducted in two phases. An in itial parametric study was conducted to determine the best cavity diameter, depth and spacing for improving boiling heat transfer performance with FC 72. The second phase then proceeded to further assess the effects of fluid properties on the optimum cylin drical cavity. The two part experimental investigation seeks to understand the physical mechanisms involved in boiling heat transfer from dense cylindrical cavity arrays. 4.2 Surface Fabrication Table 4 1 describes the facilities us ed for fabrication of both the cylindrical cavities and h oodoo surface features All test surfaces were f abricated from undoped single crystal Silicon wafers Fabrication of the cylindrical cavities proceeds by initially spin coating a 2 um layer of photo resist onto a silicon wafer. The photo resist is then soft baked at 105 C for 2 minutes. The mask pattern is then exposed to 436 nm G line for 21 seconds using the Karl Suss MA6 mask aligner. The wafer is then developed using 300MIF for 1 minute. The photo resist is then hard baked at 125 C for 3 minutes. The STS deep reactive ion etcher is then used to anisotropically etch down into the wafer. Etching proceeds by alternatiing between 7 seconds of SF 6 /O 2 and 5 seconds of C 4 F 8 for sidewall passivation. A tot al of 20 cycles are used for the desired depth. Any remaining passivation is removed with a 30 second O 2 etch. Any remaining photo resist
129 is removed by placing the wafer in a barrel asher using 600 watts and 600sccm O 2 for 10 minutes. Table 4 1 Facilities used for surface fabrication. Plasma Enhanced Chemical Vapor Deposition STS 310PC The PECVD STS deposition tool is used for depositing silicon nitride, silicon dioxide and amorphous silicon films. The system is equipped with 13.56 MHz and 187.5 kHz frequencies and is capable of mixed frequency recipes. The temperature of the system is normally kept at 300 C. Photo Lithography Karl Suss MA 6 The Karl Suss MA 6 Contact Aligner system can perform precision ma sk to wafer (sample) 1:1 contact printing in four modes; hard contact, soft contact, vacuum and proximity. It can accommodate exposure of irregularly shaped and IR capability Approxim ate Exposure Intensity: 8 mW/cm2@365 nm, 5 mW/cm2@405 nm Constant exposure intensity controller Two mask holder sizes are available, 4" and 5". Wafer size is 4" and pieces. Maximum wafer thickness 4.3mm Split field microscope for top side viewing/alignment resolution = down to .8um in vacuum contact mode @ 400nm Reactive Ion Etching Uniaxis SLR Unaxis Shuttlelock Reactive Ion Etcher with Inductively Coupled Plasma Module. Etch Capabilities: SiO2, Si3N4, photoresist, polyimide, Al, dielectrics and other c ommonly used materials. Image Reversal Oven YES The YES oven uses NH3 (ammonia) gas to reverse the tone of positive photoresist. This can be used to create an undercut profile in the photoresist for lift off processing. In the reversal process, the cham ber is purged of oxygen using vacuum and heat. It is then filled with NH3 (ammonia) vapor. The NH3 reacts with the acid in the exposed resist rendering it insoluble in developer. The proceeding flood exposure causes acid to form in the previously unexposed areas allowing them to be removed in development, leaving behind the negative image of the first exposure. Deep Reactive Ion Etching STS Deep reactive ion etcher capable of cycling between SF 6 gas for reactive etching and C 4 F 8 for coating the side walls The etching step rapidly removes the passivation on horizontal exposed surfaces allowing etching only tin the vertical direction. Sputter Deposition KJL CMS 18 Multi Source Combinatorial Materials Science thin film sputtering system 4 gas injected Magn etron sputter sources, DC, RF and Pulsed DC load lock module with rack and pinion transfer Substrate Platen: heating to 550 Deg C, rotation up nonmagnetic materials, reactive sputtering S canning Electron Microscope JEOL 5700 The JEOL CarryScope is a compact and portable SEM that utilizes a standard tungsten filament. The CarryScope is capable of imaging from 8X to 300,000X and up to 5nm resolution. Accelerating voltage can be varied from 5 kV to 20kV and the beam diameter can also be adjusted. It features manual XYZ stages with full 360 rotation and 10 to 90 tilt and can hold a
130 4.3 Cylindrical Cavity Array Boiling Heat Transfer Results Figure 4 1 sh ows the effect of cavity diameter on the boiling curve. It should be noted that all boiling curves shown unless otherwise stated are for pool boiling of FC 72. It can be seen that for cavi ty diameters of boiling. Increasing the cavity diameter is seen to degrade boiling heat transfer but the effect is marginal. In comparison with the smooth silicon surface it can be seen that the p resence of these shallow cavities is enough to significantly increase the heat transfer performance of the surface. Even for the shallow large diameter cavities there is a noticeable improvement in heat transfer. It can also be observed that incipience sup erheat decreases with the presence of the cylindrical cavities. However, no discernable trend can be observed relating cavity diameter to incipient superheat. Yet it can be observed from Figure 4 1 that the 9 the lowest incipient superheat. Interestingly the 3 a very high superheat almost comparable to that of the smooth silicon surface. Both the 27 have comparable incipient superheats. This suggest s that the 9 cavities are of optimum size for initiating boiling However because only one fluid i s used for testing FC 72, this particular cavity size may be important only for this one fluid. Presumably if the physical and thermodynamic properties of the fluid are key parameters in promoting incipience in cylindrical cavities then most likely the optimum cavity size for incipience depends on the fluid properties Another notable trend from Figure 4 1 is the decrease in cri tical heat flux with increasing cavity diameter. T his behavior is only observed with the shallow cavities when the diameter is varied
131 Upon examination of Figure 4 2 which shows the variation of heat transfer coefficient with cav ity diameter, it can be good at promoting incipience their heat transfer coefficient is not the highest. Although the difference in the observed heat transfer coefficients is marginal, within 15%, it can be previously, in comparison to the smooth silicon surface the shallow cylindrical cavities present a significant improvement in boiling heat transfer performance. It can be se en that heat transfer enhancement decreases with increasing heat flux. This suggest s that the cylindrical cavities assist in promoting boiling at lower superheats However at higher heat fluxes where the surface is hot enough to nucleate from the smooth p ortions of the surface, these structures have no significant effect on delaying the onset of film boiling. Figure 4 1 Effect of cavity diameter on the boiling heat transfer of FC 72.
132 Figure 4 2 Effect of cavity diameter on heat transfer coefficient of FC 72. Figure 4 3 also shows the effect of cavity diameter on pool boiling heat transfer. Figure 4 1 it can be seen that the effect of cavity depth with various cavity diameters for a fixed spacing ha s minimal impact o n heat transfer heat transfer performance than the smaller diameter cavities. However, it can be observed that the p resence of the cylindrical cavities, again, enhances nucleate boiling heat transfer. Incipience superheats observed for the deeper cavities showed similar anomalously low super This resulted from complete surface activation of the deep cavities, Figure 4 5 .A.
133 Figure 4 4 shows the effect of cavity diameter on heat transfer coef ficient for the diameter cavities compare d with the 27 cavities but in comparison with the smooth surface there is still a noticeable heat transfer at the lower heat fluxes due to the presence of nucleate boi ling. Figure 4 3 Effect of cavity diameter on the boiling heat transfer of FC 72.
134 Figure 4 4 Effect of cavity diameter on heat transfer coefficient of FC 72. spacing depth). Additionally images taken during the experiment sho have a significantly higher nucleation site density than any of the other surfaces tested. Looking at fig ure Figure 4 5 A for q=0.96 W/cm 2 it can be seen that all available cavities are activated even at this very low heat flux. Comparing to Figure 4 6 B and Figure 4 5 A it is seen t fluxes. Interestingly, although both depths show a high site density the deeper cavities promote more organization in the vapor structure on the surface. Presumably the shallow cavi ties are more susceptible to deactivation by convective surges along the surface.
135 A: 9 m diameter x 300 m spacing B: 27 m diameter x 75 m spacing C: 27 m diameter x 150 m spacing D: 27 m diameter x 300 m spacing E: 75 m diameter x 300 m spacing F: 75 m diameter x 600 m spacing Figure 4 5 Images taken at q=0.96 W/cm 2 for the various cylindrical cavity surfaces The measured nucleation site density for the respective cylindrical cavity surfaces are tabulated in Table 4 2 for the 6 m deep cavities and Table 4 3 for the 20 m deep cavities. Looking at Table 4 2 and Table 4 3 it can be seen that the nucleation site surfaces. Using the known number of cavities for a given cavity spacing, Table 4 4 .It can be seen that for all of the surfaces except the 9 cavities the measured nucleation site density at this low heat flux is less than 0.1% of the available number of
136 cavities. Only for the 9 cavities is it observed that the low heat flux NSD approaches 100% of the avail able number of cavities. Comparing the observed nucleation site densities with the measured heat transfer transfer coefficient along the entire boiling curve as compare d to the other surfaces, which show much lower nucleation site densities. Figure 4 7 shows the effect of center to As expected, decreasing the c avity spacing (i.e. increasing cavity density) improves the boiling performance of the heating surface. A higher incipient superheat is observed for the closest spaced cavities ; however because of the stochastic nature of incipience a greater number of exp eriments would have to be conducted in order to disc ern any influence of the feature density on incipience. The effect of cavity spacing on heat transfer coefficient can be seen in Figure 4 8 As was observed with the boiling curv es in Figure 4 7 the higher density of cavities promotes better heat transfer. In comparison to the smooth silicon surface the measured heat transfer coefficient of the test surfaces was enhanced by 30% to 1 00%, observed nucleation site densities for the three test surfaces does show that for moderately low heat fluxes that the nucleation site density is influenced by the cavity sp acing. Figure 4 9 depth cavities with different center to center distances. Similar to the shallow cavities it is observed that increasing cavity density improves boiling heat transfer performance.
137 Incipient superheats are observed to be slightly lower but again no discernable trends are observed. A: 3 m diameter x 300 m spacing B: 9 m diameter x 300 m spacing C: 27 m diameter x 75 m spacing D: 27 m diame ter x 150 m spacing E: 27 m diameter x 300 m spacing F: 75 m diameter x 300 m spacing Figure 4 6 Images taken at q=0.96 W/cm 2 for the various cylindrical cavity surfaces As expected a significant reduction in superheat is observed, compared to that of the smooth silicon surface. The effect of cavity spacing on the measured heat transfer coefficient for the deeper cavities, Figure 4 10 confirms the observed en hancement in
138 Tabl e 4 2 Measured nucleation site density for the shallow cylindrical cavities with varying cavity spacing and diameter at different heat fluxes. (Pool boiling of FC 72) Depth Diameter Spacing Heat Flux NSD m W/cm 2 Sites/cm 2 6 3 300 0.68 25 0.99 117 6 27 75 0.96 14 6 27 150 0.70 7 0.96 20 1.26 50 6 27 300 0.96 18 1.26 26 1.76 28 6 75 300 0.70 3 0.96 8 1.26 14 1.76 15 A comparison of the measured nucle ation site densities in Table 4 2 and Table 4 3 site densities at lower heat fluxes. The difference in nucleation si te density is more noticeable for the closer spaced cavities. Figures 4 6 C E and figures 4 5 B D confirm the trend that deeper cavities better sustain boiling even at low heat fluxes. Th e sustained high n ucleation site density for the deeper cavities can plausibly be attributed to vapor trapping via liquid inertia from the fluid entering the cavity upon wetting of the surface. This is supported by the conclusions of Qi and Klausner  Their experimental res ults also showed that if the arctangent of the cavity aspect ratio is less than the contact angle of the liquid then the cavity will trap vapor. The fluids However a more
139 plausible mechanism is through liquid inertia entrapment. Closer inspection of the criterion developed by Qi and Klausner  does show that for increasing cavity depth fluids with a greater wettability can trap vapor in the cylindrical cavity. Table 4 3 Measured nucleation site density for the deep cylindrical cavities with varying cavity spacing and diameter at different heat fluxes. (Pool Boiling of FC 72) Depth Diameter Spacing Heat Flux NSD m W/cm 2 Sites/cm 2 20 9 300 0.40 3 0.70 1061 0.96 1110 1.26 1283 20 27 75 0.40 42 0.70 93 0.96 154 1.26 179 20 27 150 0.40 2 0.70 24 0.96 35 1.26 35 20 27 300 0.77 22 0.96 21 1.17 24 1.26 41 20 75 300 0. 70 1 0.96 6 1.26 21 1.76 30 20 75 600 0.70 1 0.96 1 1.26 2 1.76 2 2.60 6
140 Table 4 4 The number of cylindrical cavities on a given surface as a function of cavity spa cing. Spacing ( m) Number of Cavities 75 20528 150 5132 300 1283 600 321 Figure 4 7 and FC 72 as the working fluid.
141 Figur e 4 8 depth with FC 72 as the working fluid Figure 4 9 Pool boiling curves with FC 72 as the working fluid
142 Figure 4 10 with FC 72 as the working fluid Similar test cavities to observe the effect of cavity spacing on heat transfer Figure 4 11 shows the boiling curves f it can be seen tha t for very large cavity spacings there is no effect on heat transfer. The incipient superheat is low and a slight decrease in critical heat flux is observed. Referring to Figure 4 6 F and Figure s 4 5 E F it is readily apparent that these larger diameter cavity features are inefficient at sustaining boiling at lower heat fluxes. It should be noted that the edge boiling occurring at the interface between the substrate and the epoxy does slightly alter the heat transfer occurring on the surface. However, solely looking at the inner portion of the surface it can be seen that the nucleation site density is very low. This edge boiling effect has a negligible effect on heat transfer at the higher heat fluxes.
143 Figure 4 12 cavities at two different spacings. The low incipient superheat produces better heat transfer at lower heat fluxes H owever comparing the two nucleate boiling regimes for the structure d an d non structure d surfaces, it can be seen that the enhancement in heat transfer is low. This can most likely be attributed to the shallow depth and large diameter of the cavities. Figure 4 11 Pool boilin with FC 72 as the working fluid
144 Figure 4 12 Figure 4 13 different spacings. Like the shallow cavities, the observed incipient superheat is much lower than that of the smooth silicon. A slight degradation of he at transfer is observed for higher heat fluxes near critical heat flux. Similarly, spacing is seen to have no effect on boiling heat transfer performance for the larger diameter cavities. However, comparing the observed nucleation site density for both sur faces, Figure 4 5 E and Figure 4 5 F, the spacing is seen to have an effect on the nucleation site density at low heat fluxes. Comparing Figure 4 12 and Fi gure 4 14 it is observed that the cavity depth has no effect on the heat transfer performance. This trend is similar to that observed with the cavities of varying diameter at fixed sp acing. Additionally, spacing has no effect on the heat transfer coeffici
145 Figure 4 13 Figure 4 14 Effect of cavity spacing
146 It is also of interest to understand what effect fluid properties have on the boiling heat transfer performance of these cavities. The boiling curves shown in Figure 4 1 5 are for diameter cylindrical cavities at three different spacings of 75, 150 and 300 m with FC 72 as the test fluid Heat transfer is observed to increase with decreasing feature spacing. CHF increase s with decreasing spacing as well The boiling curv e for cavities at 300 m spacing shows an almost linear variation with superheat. Whereas, it can be observed that for the 150 m spacing there is a slight change in curvature near a heat flux of 16 W/cm 2 The observed curvature of the boiling curve th en becomes a more prominent feature when the cavity spacing is further decreased to 75 m. The observed behavior can be attributed to the thermal and hydrodynamic interaction of adjacent nucleation sites. Thermal interactions occur through the solid substr ate, the periodic nature of the local temperature field beneath a growing bubble perturbs a finite region within the solid. The overall interaction volume due to this temperature variation will depend on the solids thermal properties. Yu Yan et al.  investigated the effects of surface thermal condu ctivity on nucleation site interaction. There results confirm that the interaction mechanisms are strongly dependent on surface thermal conductivity. Bubble growth and coalescence mechanisms are also reported to vary greatly with site spacing and surface t hermal conductivity. They also report that there critical site Hydrodynamic effects are as a result of the strong convective influence resulting from the growth and departure of a bubble. The convectiv e region of influence will also be proportionate to the instantaneous bubble radius A simple approximation using potential flow theory would suggest that for an expanding hemisphere in an unbounded
147 liquid a suitable region of influence is approximately 5 radii. This is due to the 1/r 2 dependence of the flow field. Therefore for cavity spacing that falls within either of the two zones a significant change in bubble growth dynamics and site activation are to be expected. Looking at F igure 4 16 which shows the variation of heat transfer coefficient with wall superheat, the observed change in curvature of the boiling curve is further confirmed by the decrease in heat transfer with increasing superheat It is of further interest to aga in comment on the effects of cavity diameter on pool boiling heat transfer. Examining Figure 4 17 it can be observed that the cavity diameter has a marginal effect on the boiling heat transfer performance. The natural convection p ortion for all six surfaces remains the same. The boiling curves for both the and the 2 diameter cavities at 30 spacing are the same. This is again observed for the 15 cavity spacing. However, it can be seen that the diameter cavities show better heat transfer performance at the lower heat fluxes than the 2 diameter cavities. For the cavities spaced at 7 the and 2 cavities show similar performance in the low heat flux region. Yet for higher heat fluxes it can be observed that the cavities perform better. Even CHF for the cavities at 7 spacing is greater than that measured with the 2 cavities. Comparing the three spacings for each of the two respective cavities it can be seen that the surface with the closest spacing shows greater nonlinearity in the high heat flux region. It is important to note that while CHF is observed to increase with decreasing spacing for the cavities the 2 cavities show a slightly different trend. The measured CHF is observed to increase up to 15 spacing. Thereafter it decreases for the 2 cavities at 7 spacing. Clearly, feature spacing is an important parameter in characterizing the boiling
148 performance of any structured surface. For t he closest spaced cavities cavity diameter becomes an additional important parameter because of the re duced solid material between cavities This would result in an increased interaction between adjacent cavities. Likewise the reduced distance between the peripheries of the adjacent cavities will result in greater hydrodynamic interactions. It is therefore important to observe what effects, if any, a change in thermophysical properties has on the trends observed. E xamin ation of Figure 4 18 which shows the boiling curves for diameter cylindrical cavities at 75 and 15 spacing with hexane as the test fluid further elucidates the important physical parameters The observable change in curvature near CHF is more pronounced than with FC 72. Examination of Figure 4 19 shows again that a de te rioration of the heat transfer coefficient occurs at elevated wall superheats where the number of active sites is approaching its zenith. Definitively, b ubble departure diameter is a controlling factor in boilin g heat transfer, especially in the high heat flux region. Since the feature arrangement and feature density control the number of available nucleation sites the remaining parameter that would influence the density of active sites would be the bubble depart ure diameter. The images used for measur ing the nucleation site density were also used to estimate the size of the bubbles on the surface. Using the known surface size in the image as a reference, the bubble departure diameter was estimated to be approxima tely 300 m for FC 72 Hutter et al.  investigated the bubble dynamics of FC 72 fro m a single 10 m diameter cylindrical cavity with a depth of 40, 80, and 100 m. Although their study is for a single feature and does not include the effect of neighboring nucleation sites, it does
149 provide plenty of detail concerning the bubble growth cyc le from a cylindrical cavity. Their data also confirms no effect of cavity depth on bubble departure frequency or diameter which is in agreement with the results observed in this study Further detail of the influence of fluid properties on bubble departur e diameter can be shown using bubble departure diameter  4 1 Figure 4 20 shows a plot of bubble departure diameter as a fun ction of wall superheat for FC 72 and hexane For convenience the resulting equations are listed in the figure. It can be seen that the slope of the curve for hexane is twice that of FC 72. This indicates that, within the accuracy of the given correlation, the bubble departure diameter at a given superheat for hexane will be twice that of FC 72. A more robust model for the determination of bubble departure diameters and growth rates can be found in the work of Chen et al.  Using the model of Chen et al.  the calculated bubble departure diameters still differed by a factor of two when comparing FC 72 to hexane. It is observed that for 75 m spacing the boiling curve for FC 72 exhibits a change in curvature nearing CHF. Based on the previous qualitative analysis concerning bubble departure diameter it can be inferred that a similar change in curvature will occur for hexane at the next large st spacing, 150 m, because of the increased bubble departure diameter. Examination of Figure 4 18 confirms this hypothesis. Unfortunately, data for pool boiling of hexane with cavities at 300 m spacing is not available. This ana lysis is based on bubble growth dynamics in the isolated bubble regime and therefore neglects the more complex physical mechanisms
150 present near CHF, namely slugs and columns. The increased amount of vapor volume produced relative to the heating surface are a would most certainly increase adjacent site interaction at lower heat fluxes. Any mechanisms that are controlled by site site interaction are therefore initiated earlier on in the boiling process. But most certainly it can be said that the variation in curvature for higher heat fluxes should be similar in behavior to the curve for FC 72 with cavities at 150 m spacing. The larger departure diameter of bubbles produced form boiling hexane can be directly associated with the observed change in heat transfe r nearing CHF. In the low heat flux region (i.e. isolated bubble regime) nucleation site interaction is minimal due to the smaller departure diameter of the bubbles therefore for any of the tested cavity spacings there is no observable nonlinearity in the boiling curve for this regime. At high enough heat fluxes, near CHF, the number of active sites has essentially reached its maximum. Bubble departure diameters are also at their maximums and it is therefore in this re gime where nucleation site spacing can introduce highly nonlinear effects. Zhang et al.  investigated the effects of nucleation site interaction on the pool boiling heat transfer of water. The surface consisted of only two cavities, each 10 m in diameter with 80 m depth and at spacings ranging from 1 to 8mm. They assert that there are three main nucleation site interaction mecha nisms: (1) Hydrodynamic, (2) Thermal, and (3) Coalescence interactions. From their experiments they determine d that there are distinct regimes of non dimensional cavity spacing the ratio of cavity spacing to average bubble departure diame ter, in which these three mechanisms are active. For their data confirms that all three interaction mechanisms are present. The current set of experiments all fall within this regime of site interaction.
151 Hydrodynamic effects are induced by bubble growth and departure. A growing bubble at one nucleation site will generate convective currents in the surrounding region. Depending on the site to site spacing this additional convective flow may inhibit adjacent site activation until the bubbl e departs. T hermal effects are also of significance. Although the local fluid flow is coupled to the temperature field of the fluid, it is also of importance to understand the effects of the temperature field within the heating surface At the active site where a growing bubble is present the local temperature field is perturbed due to the latent heat remo val. Depending on the thermal properties of the heating surface the effective region of influence can be large or small relative to the size of the bubble If the region of thermal influence is on the order of the cavity spacing then the nearest neighbor cavities will not activate. The complex site interaction mechanisms make it difficult to discern the predominant factors that control boiling heat transfer performance on these dense feature arrays. Figure 4 15 The effect of cavity spacing, for diameter cylindrical cavities, on the boiling heat transfer performance of FC 72.
152 Figure 4 16 The effect of cavity spacing, for diameter cylindrical cavities, on the boiling heat transfer coefficient for FC 72. Figure 4 17 C omparison between and 2 diameter cavities and the effects of cavity spacing on pool boiling heat transfer. (D = diameter, S = spacing)
153 Figure 4 18 The effect of cavity spacing, for diameter cylindrical cavities, on the boi ling heat transfer performance of hexane Figure 4 19 The effect of cavity spacing, for diameter cylindrical cavities, on the boiling heat transfer coefficient for hexane
154 Figure 4 20 Variation of bubble departure diameter with wall superheat for FC 72 and hexane  4.4 Discussion and Conclu ding Remarks on Cylindrical Cavity Arrays The current set of experiments h as elucidated the effects of nucleation site interaction mechanisms on highly dense cavity arrays. In addition, it has also provided a parametric investigation of the various geometric parameters that effect pool boiling from cylindrical cavity arrays. Fun damental studies, like those of Hutter et al.  and Zhang et. al  to name a few, investigate a small number of cavities, usually one to three. Studies with a small number of cavities provide detailed insight into the complex interaction mechanisms prevalent in boiling heat transfer. But for practical engineering surfaces it is of interest to investigate highly dense arrays of surface features. Cavity spacing and bubb le departure diameter have a strong role in determining the most influential site interaction mechanisms. As mentioned previously hydrodynamic, thermal, and bubble coalescence mechanisms are all important for close ly spaced features.
155 For both FC 72 and he xane c avity spacing i s observed to have a significant effect on nucleate boiling heat transfer. Heat transfer is observed to increase with decreasing spacing. This r esult is in agreement with the results reported by Zhang et al.  For closely spaced cavities the enhanced site site interaction results in an increase in bubble departure frequen cy resulting in increased heat transfer The non dimensional cavity spacing for the current set of experiments fall in the regime in which all three mechanisms are in effect. This makes it difficult to determine which of the three mechanisms is the most in fluential for the current set of surfaces. Visual data is also of limited use because the high nucleation site density creates too many bubbles that cloud the view In addition to enhancing overall boiling heat transfer, critical heat flux is also observed to vary with cavity spacing. For FC 72 there is an increase in CHF with decreas ing cavity spacing hexane exhibits a decrease in CHF for cavity spacing below 150 m. Bubble departure diameter is definitively a controlling parameter in the observed CHF aug mentation. The bubble departure diameters of hexane and FC 72 In addition to cavity spacing, cavity diameter and depth w ere also investigated. For cavities with 2 0 depth and 30 spacing, it was observed that 27 m diameter cavities and below exhibit the same heat transfer performance. The 75 m diameter cavities showed a reduced boiling heat transfer performance. Two depths 6 m and 20 m were tested for all c avities mentioned. Cavity depth was observed to have an effect on boiling heat transfer in the low heat flux regime Increas ing the cavity spacing beyond 300 m for th e 75 m diameter cavity result ed in no increase in heat transfer. No significant changes in critical heat flux a re observed for change in cavity diameter
156 and depth. Only for the 9 m and 27 m cavities with 20 m depth and 75 m spacing is there an observed effect of cavity diameter on heat transfer and CHF. Active nucleation site density was also measured for the low heat flux regime. From the measured nucleation site densities it i s observed that the 9 m cavities with 20 m depth have the best cavity activation performance. Additionally, the measured incipient superheat on the 9 m diameter by 20 m depth surface i s very low. In general, deep smaller diameter cavities (below 27 m) showed increased nucleation site density. Decreasing cavity spacing result ed in increased nucleation site density, which is in further agreement with the observed increase in heat transfer. N ucleation site interaction mechanisms are an integral part of understanding boiling heat transfer. Development of a comprehensive boiling heat transfer model for structured surfaces requires a complete understanding of the eff ects of the different design parameters. There is a vast amount of data available concerning cylindrical cavities effects of fluid properties and surface thermal properties in one wor k. It would be most advantageous to conduct a study in which a small array of cavities is fabricated in three different materials of vastly different thermal properties. T he arrays should be made with and at least three different fluids should be used. Conducting such a study should provide conclusive evidence of the various nucleation site interaction mechanisms.
157 CHAPTER 5 POOL BOILING ON HOODOO STRUCTURE ARRAYS 5.1 Introduction to Hoodoos As was previously discussed in section 1.3.10 there are many types of surface features that have been employed for boiling heat transfer enhancement. Aside from improving the boiling heat transfer coefficient it is equally important to increase CHF. An increase in permit greater heat transfer rates at low superheats For industrial processes in which the state of the system is dynamically controlled there exist greater ranges of operation which can be desirable for processes that are more eff icient at high temperatures. Of the variety of features documented in the literature the most effective have been those that can introduce interconnectiv i ty between surface features and capillary flows. This is why porous surface coatings have proven to b e effective at enhancing heat transfer for all regimes of boiling. Micro scale extended surface features have also proven to be effective especially at high feature densities. This chapter presents an additional investigation as to the effects of micro sca le surface structures on boiling heat transfer. A novel surface feature originally devised by Tuteja et al.  has been employed in the present investigation. The primary goal f or the original design of the feature wa s to create a superoleophobic surface. Wetting studies conducted by Tuteja and his colleagues confirm the hig h ly non wetting nature of the surface features. Although this characteristic is important for surface science applications, it is particularly bad for boiling surfaces. Poorly wetting surfaces exhibit l ow incipient superheats which is a desirable property, but they reduce CHF. T he non wetting nature is due to a coating placed on the tops of the surface structures When the coating is eliminat ed which therefore makes the surface becomes
158 highly wetting. F ollowing a similar procedure to that of Tuteja et al.  arrays of similar surface features were fabricated on silicon wafers. Ahuja et al.  created a similar surface feature to that of Tuteja et al.  exhibits interesting wetting properties but what makes the feature most profound is the fact that the wettability of the surface can be tune d by an electric potential. The Tuteja structures were named Hoodoos because of their resemblance to the geological structure also called a Hoodoo. Figure 5 1 is an SEM image taken of a pit containing an array of hoodoo surface features. This image is not of the features used for the experiments but merely to show the general geometric configuration of the feature as well as the arrays used. Figure 5 1 Pit contai ning a small array of hoodoo surface structures. It can be seen that underneath the hoodoo tops is an interconnected network of tunnel like regions. At closer spacings the adjace nt hoodoo tops create thin gaps; additionally, in between every three adjacent hoodoos there is a larger opening. The openings present between adjacent hoodoo tops create a perforated upper structure
159 that permits liquid to reach the subsurface structure. Similar surfaces called pore and tunnel surfaces have been explored previously for boiling enhancement However, the dimensions of the features were typically on the millimeter scale. Das et al.  developed an analytical model to assess the effect of liquid intake on pore and tunnel structures as well as predict the heat transfer rate Conclusively, it was shown that liquid intake is an important characteristic of pore and tunnel structures that lead to increased heat transfer performance F rom close inspection of Figure 5 1 it can also be inferred that liquid intake should also be an important characteristic of the hoodoo surface feature. U nderstanding the extent of liquid intake may assist an in dep th understanding of the heat transfer performance of the hoodoo surface feature. Porous coatings have also been shown to be effective at enhancing boiling heat transfer [38; 45; 93; 94; 95; 96] Aside from the many nucleation sites available due to the high porosity the small dimension of the pores implies that capillary forces will also be prevalent. An analysis by Konev and Mitrovic  showed that boiling enhancement in capillary structures can be physically explained to occur as a result of the reduced superheat for bubble nucleation in capillary tubes. They further extend this observa tion to show that capillary structures, which would essentially be porous structures, can enhance incipience and heat transfer by reducing the required superheat for boiling initiation. In addition, it can further be understood that increasing liquid suppl y to the surface will delay the occurrence of CHF, which occurs as a result of surface dry out. Lastly, the table top feature of the hoodoo structure creates a region that is similar to that of a reentrant cavity. As is well known reentrant cavities are g ood for boiling heat transfer because vapor can remain in the cavity for high degrees of subcooling [41; 52]
160 The reentrant like feature of the hoodoo structure may also have similar nucleation site deactivation re sistance. It is expected that the hoodoo structure should provide excellent boiling heat transfer performance. Figure 5 2 Diagram depicting the relevant geometric parameters for calculating the characteris tic length scale of the hoodoo surface structure. (d = hoodoo size, g = gap spacing, Dp = hoodoo post diameter, u = undercut, D = hoodoo region size) There many physical characteristics of the hoodoo that can be varied. To completely understand all effects it is necessary to conduct a parametric investigation. Figure 5 2 gives a top view of the general hoodoo structure; some of the salient dimensions associated with the hoodoo structure are shown. Two of the most influential featur es of the hoodoo structure are certainly the size of the hoodoo and the spacing between adjacent features. Figure 5 3 shows SEM images taken of the 1 2 3 and 4 hoodoo surfaces. The two most important dimensions hoodoo size (d) and gap spacing (g) are given in Figure 5 3 It can be seen that hoodoo sizes are within 1um of the desired size and likewise gap spac ing shows a similar variation. The
161 edges of the hoodoo tops show up white under SEM due to electron reflection in the thinner silicon material. This phenomena conveniently allows for a visual evaluation of the amount of empty space beneath the hoodoo top s urface. This difference between the hoodoo post and hoodoo top is referred to as the undercut. For the current set of experiments the undercut for all the hoodoos tested is unless otherwise specified. Figure 5 3 Dimensions are measured via SEM and are given in m. (A: d = 8.65, g = 4.27; B: d = 18.52, g = 3.48; C: d = 27.65, g = 3.88; D: d = 37.08, g = 3.85) Similarly, Figure 5 4 shows SEM images for the 6 8 and 10 hoodoo surfaces. Again the most important dimensions are listed in Figure 5 4 The most noticeable difference with the larger hoodoos is the reduced amount of empty area
162 beneath the hoodoo tops. Hoodoo gap spacing is also an important parameter, Figure 5 5 shows the SEM images taken of the hoodoo surfaces with 2 hoodoos with and its general subsurface characteristics are also important because a majority of the two phase heat transfer initiates in this region. Figure 5 6 shows an angled view of the 1 hoodoo surface to reveal the subsurface structure. It is obvious from the SEM images taken of the hoodoo surfaces that the features are fabricated in a hexagonal array. The hexagonal close packed str ucture of the features assures that all adjacent hoodoos are at the same distance. The equidistant spacing between features further assures that there is no local directional dependence. Figure 5 4 SEM ima ges of the 6 8 and 10 hoodoo surfaces. Dimensions are measured via SEM and given in m. (A: d = 56.22, g = 3.78; B: d = 75.38, g = 3.69; C: d = 95.00, g = 3.33)
163 Figure 5 5 SEM images of the 2 hoodoo surface with different feature spacing. Feature spacing shown are 6um, 12um, 24um, and 48um. All dimensions are measured via SEM and given in m. (A: d = 18.73, g = 7.0; B: d = 18.9, g = 12.8; C: d = 18.8, g = 24.6; D: d = 19, g = 48.5) Figure 5 6 SEM image of the 1 hoodoo surface viewed at an angle to show the lower hoodoo structure.
164 5.2 Hoodoo Surface Fabrication Surface fabrication proceeds similar to that of the cylindrical surface feature fabricatio n. However, there are subtle important process variations that must be noted. Figure 5 7 diagrams the steps involved in the fabrication of the hoodoo surfaces. Figure 5 7 Diagram of the fabrication process used to create the hoodoo surfaces. Fabrication proceeds by first depositing a thin layer of SiO 2 on a silicon wafer using the STS 310PC PECVD. A 2 um layer of positive photo resist is spin coated onto the wafer followed by a s oft bake at 105 C for 2 minutes. The mask pattern is exposed to 436nm G line for 21 seconds using the Karl Suss MA6 mask aligner. The pattern is then reversed using the YES image reversal oven. The image reversal is c ompleted by a final flood exposure for 52.5 seconds. The wafer is then developed using 300MIF for 1 minute, followed by a hard bake of the photo resist at 125 C for 3 minutes. Using the
165 Uniaxis Shuttlecock reactive ion etcher, the SiO 2 layer is etched through. Gas flow is set to 25 sccm for CHF 3 and 3 sccm for O 2 the plasma power is 100W capacitively coupled and 600W inductively coupled. Pressure is set to 5 mtorr and the etching proceeds for 2 minutes. This is then followed by an anisotropic etch using the STS deep reactive ion etcher. As with the cylindrical cavities, 7 seconds of SF 6 /O 2 is followed by 5 seconds of C 4 F 8 for sidewall passivation. Any remaining passivation is removed using a 30 second O 2 etch. To create the characteristic table top feature isotropic etch ing under the SiO 2 caps is performed using 7 seconds of SF 6 followed by 14 seconds of no power to allow for product species to diffuse from that the etch rate remains isotropic during repeated etch ing cycles. Any remaining pho to resist is removed in the barrel asher under 600 watts of power and 600 sccm of O 2 for 10 minutes. 5.3 Hoodoo Array Pool Boiling Results Hoodoo size, spacing and physical attributes were all observed to have profound effects on incipience, boiling heat trans fer and critical heat flux. Two different sets of surfaces were tested. The first set of surfaces was used to determine the effects of hoodoo size and spacing on pool boiling heat transfer. The second set of surfaces, processed on a different wafer, were u sed to determine the effects of hoodoo physical attributes and fluid properties on boiling heat transfer performance. The fluid property comparison allows for a detailed understanding of how the structures interact with the two phase flow structure. 5.3.1 Hoodoo Size and Spacing The effect of hoodoo size on pool boiling heat transfer can be seen in Figure 5 8 For comparison the pool boiling curve for a smooth silicon surface is also presented.
166 Two notable features of the pool boiling cu rves are the low incipient superheats and increased critical heat fluxes. The incipient superheat is observed to be roughly half that of a smooth silicon surface for all of the hoodoo surfaces with fixed spacing. All hoodoo surfaces tested show an improvem ent in the critical heat flux. However of the four surfac es tested the optimum surface i be seen for some of the surfaces tested that there are multiple occurrences of temperature jumps at the lower heat fl uxes. These phenomena can be attributed to a poor ability to activate multiple site s at the onset of boiling. It i s observed that upon formation of the initial set of bubbles, usually no more than 6, the se bubbles persist on the surface until a suit able in crease in heat flux result s in further site activation The incipient front propagates in patches that gro w at each heat flux increment. Critical heat flux enhancement is presumably attributed to the interconnected reentrant structure created by the networ k of hoodoo surface features. The interconnected network aids in liquid replenishment of the macrolayer. Figure 5 9 shows the measured heat transfer coefficients from the boiling curves presented in Figure 5 8 for varying hoodoo size at constant spacing. As mentioned previously it can be s the optimum size compared to the others tested. But it should be noted that in the second set of experiments the 1 0 hoodoo surface is observed to be the better surface. This will be discussed in greater detail in section 5.3.3 when the effects of the subsurface structure are elucidated. It is apparent from Figure 5 9 enhance the critical heat flux ; erforms th e others In comparison with the cylindrical cavities it can be seen that for increasing heat flux in the
167 nucleate boiling regime the heat transfer coefficient for the cylindrical cavities reaches a maximum and then begins to decrease. Conversel y, for the hoodoo surfaces the heat transfer coefficient continues to increase up to critical heat flux. It is also observed that the heat transfer coefficient enhancement for the hoodoo surfaces continues to increase with increasing heat flux. The cylindr ical cavities show a degradation of heat transfer enhancement with increasing heat flux. The observed continued increase in heat enhance liquid entrainment. Figure 5 10 shows the effect of hoodoo size on CHF enhancement. For this set of surfaces the 5 m and 10 m perform worse than the 2 0 surface. This trend is contradictory to what is expected. Yet later examination of the second set of surfaces reveals that the surface preparation process can result in a degradation of the surfaces performance. There is some consistency with the 20, 30 and 4 hoodoos. CHF enhancement is observed to decrease up to 4 and then for hoodoos larger than 4 there is an increase in CHF. In general it can be said that hoodoos 2 and smaller promote CHF enhancement in excess of 25%. The effect of h oodoo spacing on pool boiling i s also investigated using the 2 hoodoo size. Figure 5 11 shows the effects of hoodoo spacing on pool boiling for the boiling performance. Relative to the smooth surface, incipient superheats are seen to be 50% lower Nucleation site activation stills remains difficult as can be seen by the stagger in the boiling curve proceeding incipience. Interestingly, critical heat flux enhancement remains constant for increasing spacing. Referring to Figure 5 12 it can further be confirmed that this surface structure improves boiling heat transfer in the high heat flux
168 regime of the nucleate boiling curve. Increasing the spacing between hoodoos reduces the density of surface features ; con tinui ng to increase the spacing inherently move s the boiling curve closer to the smooth surface boiling curve until the density of such features is too low to have any significant effect on pool boiling. Looking at Figure 5 12 it is seen the beginning of the nucleate boiling regime shows the same heat transfer as that of the smooth surface. Further increasing the heat flux it can be seen that the hoodoo boiling curve departs from the smooth surface boiling curve. Figure 5 13 shows the effect of hoodoo spacing on CHF enhancement. There is almost linear decrease in CHF enhancement with increasing hoodoo spacing. Hoodoo spacing 12um and below results in a significant in crease in CHF enhancement. It is interesting to note that even for 24 and 48um spacing there is still a 25% increase in CHF. Figure 5 8 Effect of hoodoo size on the pool boiling of FC 72
169 Figure 5 9 Effect of hoodoo size on the pool boiling heat transfer coefficient of FC 72 Figure 5 10 Effect of Hoodoo size on CHF enhancement for pool boiling of FC 7 2.
170 Figure 5 11 Effect of hoodoo spacing on the pool boiling of FC 72 It is apparent from Figure 5 9 and Figure 5 12 that the high heat flux enhancemen t in heat transfer is a result of the feature geometry itself. This is further confirmed by the fact that with varying spacing critical heat flux enhancement does not vary considerably, see Figure 5 13 However with varying hoodoo size cr itical heat flux enhancement does change. It can appears that the feature geometry aids in providing liquid flow to the surface during boiling and subsequently increasing the spacing between features reduces the capillary effect of the surface.
171 F igure 5 12 Effect of hoodoo spacing on the pool boiling heat transfer coefficient of FC 72 Figure 5 13 Effect of hoodoo spacing on CHF enhancement for po ol boiling of FC 72
172 5.3.2 Hoodoo Physical Attributes To further understand which physical attributes of the hoodoo surface feature s are most influential to boiling heat transfer enhancement, a series of experiments were conducted to vary the attributes that wer e hypothesized to have the greatest influence. Three physical attributes were varied ; the hoodoo height, top thickness and the amount of undercut. Figure 5 14 shows the resulting boiling curves for different attribute variations o f the hoodoo surface feature. All variations are observed to produce better heat transfer than the best single crystal silicon surface, Si(111). From c omparison of the variations tested it can be seen that the surface with the thicker tops provides a marg inal increase in heat transfer over the standard hoodoo. It should be noted here that all variations are of the 2 hoodoo with gap spacing. It can further be seen that the hoodoo height and the amount of undercut result in negligible changes in hea t transfer. Critical heat flux enhancement trends are also similar to those for heat transfer coefficient. Figure 5 15 shows the effects of physical attribute variation on CHF enhancement. Decreasing hoodoo height results in no ch ange in CHF enhancement. However, decreasing the amount of undercut does show a slight improvement in CHF enhancement. Surprisingly the thicker tops show a much greater increase in CHF enhancement compared to that of the standard hoodoo. F rom varying the physical attributes of the hoodoo surface feature it is clear that the top of the hoodoo i s the physical attribute that has the greatest effect on heat transfer and critical heat flux enhancement. As mentioned previously the hoodoo surface feature was init ially intended to be used in the development of oleophobic and hydrophobic surface s Droplet spreading studies on surfaces with features similar to those of the hoodoo have shown that fluid droplets will rest on the upper portion of the
173 structure leaving the lower portion dry The oleophobic nature of th e original hoodoo feature was a result of a non wetting coating placed on the tops of the hoodoos. The removal of such a coating makes the surface highly wetting The hoodoo wetting behavior is a result of the unique upper structure, which results in enhanced interfacial forces. It can therefore be hypothesized that similar interfacial forces may arise during bubble growth and departure all of which can be strongly influenced by the upper structure of the h oodoo. Internal surface flow, underneath the tops of the hoodoos, can also vastly enhance the ebullition cycle as well as delay critical heat flux. The 2 hoodoo with spacing was also coated with a layer of copper. This results in two effects, Incr eased thermal conductivity at the solid liquid interface and enhanced solid liquid interaction strength. Looking at Figure 5 16 it can be seen that the addition of the copper coating results in a significant increase in heat trans fer performance over the standard hoodoo surface. The magnitude of heat transfer enhancement can be more clearly observed in Figure 5 17 which shows a plot of heat transfer coefficient versus wall superheat. One notable feature o f the copper coated surface occurs near CHF. The standard hoodoo surface shows a n almost linear increase in wall superheat with heat flux up until CHF. Conversely, it can be seen that the copper coated surface exhibits a diminishing increase in heat flux w ith increase in wall superheat near CHF. Despite this behavior CHF remains unchanged, within the limits of uncertainty of the experiment. Nucleation site interactions are therefore the controlling phenomena in this regime of pool boiling. On approach to CH F it is hypothesized that there are local regions on the surface where the liquid layer near the surface has dried out. This local dry out phenomenon is not a
174 stable phenomenon but intermittent. Increasing the applied heat flux results in a greater dry out frequency and dry out area which, due to its dynamic nature, eventually results in a sudden transition to film boiling. It can further be hypothesized that a higher nucleation density will promote a more noticeable degradation in heat transfer near CHF. T his can most certainly explain the observed behavior of the copper coated hoodoo surface. Figure 5 14 Effect of physical attribute variations of the hoodoo surface feature on pool boiling heat transfer of FC 72. (d = 20 m, g = 3 m for all features)
175 Figure 5 15 Comparison of CHF enhancement for physical attribute variation. Figure 5 16 Effect of copper coating on pool boiling heat transfer of FC 72 on the hoodoo surface (d = 20 m, g = 3 m)
176 Figure 5 17 Effect of copper coating on pool boiling heat transfer coefficient of FC 72 on hoodoo surface (d = 20 m, g = 3 m ) 5.3.3 Fluid Property Effects on Hoodoo Boiling Heat Transfer The presentation of data to this point has shown the pool boiling heat transfer performance of the hoodoo surfaces with FC 72 as the working fluid. However, for both practicality and the development of fund amental knowledge it is of interest to understand the extent to which the surface enhances heat transfer for different working fluids. Figure 5 18 shows the boiling curves for hoodoo surfaces with 10 m 20 m, 40 m, and 80 m hoodoos with FC 72 as the working fluid and Figure 5 19 shows that with hexane The first most notable feature of all the hexane curves is the almost linear variation of heat f lux with wall superheat. Add itionally it can be seen that CHF increases with decreasing hoodoo size. However it can also be observed that for heat transfer in the lower heat flux regions of the curves that heat transfer improves with increasing hoodoo size. If it is hypothesized that every three hoodoos constitute a viable nucleation
177 site then it could be inferred that for small hoodoos the close proximity of neighboring sites coupled with the enhanced hydrodynamic interaction could in fact inhibit site activation. Whereas for larger hoodoo sizes the increased site spacing results in a diminished influence of neighboring sites, which facilitates activation. This effect is most noticeable in Figures 5 20 and 5 21 the measured heat tra nsfer coefficient for the 8 0 hoodoo surface is roughly 50% greater than the other surfaces for superheats below 30C. It can be seen that on approach to CHF the larger hoodoo surfaces quickly show degradation in heat transfer. Whereas the smaller hoodoo surfaces are capable of su pplying liquid to the surface at a rate comparable to the rate at which the liquid is vaporized from the macrolayer. Chen et. al.  investigated heat transfer and pressure drop in fractal microchannel networks. What they found was that increasing the fractal or der of the networks decreases the required pumping power and subsequently results in increased thermal efficiency of the heat sink. The subsurface structure of the hoodoo surface is also very similar to a microchannel network. The increased performance in the hoodoo surface for smaller features sizes is analogous to an increase in the fractal order of a microchannel network. It is further hypothesized that the onset of CHF occurs at the point when the vaporization momentum flux is greater than the liquid mo mentum flux due to capillary induced flow. The added liquid momentum flux due to capillary action results in an increased downward force on the macrolayer. The vaporization momentum flux required to remove the macrolayer is therefore increased.
178 Figure 5 18 The effect of hoodoo size on the pool boiling heat transfer performance of with FC 72 as the working fluid Hoodoo surfaces are from the second processed wafer. Figure 5 19 The effect of hoodoo size on pool boiling heat transfer performance with hexane as the working fluid. Hoodoo surfaces are from the second processed wafer.
179 Figure 5 20 The effect of h oodoo size on the pool boiling heat transfer coefficient of FC 72. Hoodoo surfaces are from the second processed wafer. Figure 5 21 The effect of hoodoo size on the pool boiling heat transfer coefficient with hexane as the working fluid. Hoodoo surfaces are from the second processed wafer.
180 A comparison of CHF enhancement percentage for FC 72 and hexane is presented in Figure 5 22 It is readily apparent that CHF enhancement is gre ater with hexane as the working fluid. It can be observed that for the 1 hoodoos there is approximately a 67% increase in the typical CHF measured on a smooth surface. For FC 72 there is a 48% improvement in CHF. Enhancement is observed to decrease wit h increasing hoodoo size until 4 Increasing the hoodoo size past 4 results in an increase in heat transfer and CHF. As mentioned previously this trend could be the result of two competing mechanisms. Namely, suppressed site activation due to subsu rface interconnectivity or liquid supply as the result of capillary action. It is interesting to note that the observed variation of CHF enhancement with hoodoo size is also the same trend observed with what is currently being called the characteristic len gth scale of the hoodoo surface, L*. The expression for L* is the result of dividing the liquid contained in one hoodoo region with the surface area of the hoodoo post. Since the region is axisymmetric the derivation of L* proceeds by a comparison the resp ective area and circumference. The region in question can be seen in Figure 5 2 The area contained in the dotted line is region occupied by the liquid. The volume of the hoodoo region is then the area of the dotted region minus t he post cross sectional area multiplied by the height of the hoodoo post (h). 5 1 The surface are of the hoodoo post can be expressed as 5 2 Dividing equation 5 1 by equation 5 2 results in the expression for L*.
181 5 3 A plot of equation 5 3 is shown in Figure 5 23 Markers are placed at the points that correspond to the hoodoo sizes tested. Interestingly, the dependency of L* on hoodoo size also shows a minimum near 4 which is the hoodoo surface that sho ws the poorest CHF enhancement. Additionally, it can be seen that decreasing hoodoo size results in a significant increase in L* which is similar to the increase in CHF enhancement observed in Figure 5 22 for both FC 72 and hexane A slower increase in L* occurs for sizes greater than 4 which is again similar to the measured CHF enhancement data for FC 72 and hexane. The liquid volume to hoodoo post surface area ratio can either represent hydrodynamic effects or thermal effects. It is less likely to be thermal effects because the flo or surface area must also contribute to heat transfer to the liquid within the dotted region. So only accounting for the hoodoo post surface area is not truly representative of conduction heat transfer effects. However, it is plausible that L* captures the hydrodynamic effects present in the subsurface structure. Since there is constant liquid and vapor flow passing through the subsurface region the hoodoo posts provide resistance to fluid flow. A minimum in L* physically corresponds to a small volume to ho odoo post surface area ratio. The larger surface area for the given volume of liquid can provide greater shearing resistance to liquid flow which would impede heat transfer. The smaller volume of liquid for the given area also means that it is easier to dr y out the region. Both of these mechanisms would result in a diminished CHF enhancement ability. Surface wetting is a complex multi scale dynamic phenomenon. There are equally as many variables involved in assessing a surface s wettability as there are in
182 determining its boiling performance. Realistically, surface wettability contains a subset of the variables needed to understand heterogeneous boiling heat transfer. For structured surfaces that are designed to promote wettability there can be multiple meta stable wetting states. A resting droplet on a surface can exhibit many different types of wetting behavior depending on the geometry of the surface features and on the intrinsic wettability of the surface material. A subtle change in surface structure can result in what is called super wetting or hemi wicking. Surface wicking studies were conducted with the hoodoo surfaces as well. Visual observation of a resting droplet revealed that for hoodoo sizes below 4 the surface promotes hemi wicking. For hoodo o sizes 4 and greater normal droplet spreading is observed. The hoodoo wicking studies will be discussed later during the evaluation of a potential CHF mechanism. At present, it is conceivable that the hemi wicking ability of the hoodoo surfaces at sma ll sizes results in improved liquid supply and heat transfer. Visual evidence of the hoodoo surfaces enhanced capillary interaction with the two phase flow field has been obtained during transition boiling of FC 72. In Figure 5 24 the circled regions show where holes in the vapor film have formed after the depart ure of a large mushroom bubble. Multiple images and visual observations revealed that the holes observed in the vapor film were stationary. There are essentially two likely mechanisms for the formation of the observed film boiling holes. The first probable mechanism can be explained as follows, upon departure of the mushroom bubble the enhanced wicking performance of the structure induces enough liquid flow towards the surfa ce to pin the film to the surface. This continues until vaporization of the incoming liquid results in the
183 release of excess vapor via mushroom bubble. The second probable mechanism results from vapor film pinning due to the complex upper structure of the hoodoo. Either way both mechanisms are as a result of the enhanced wetting ability of the hoodoo surface. Increased liquid supply to the vaporization front is believed to be induced by the vapor interface. Namely, the greater wicking ability of the surface structure is capable of replenishing the surface with liquid to the effect that surface dry out is mitigated or delayed. Recently, Guan et al.  developed a new mode l to predict the onset of CHF. The primary mechanism for CHF is postulated to be the lift off of the macrolayer due to vapor momentum flux. Their model incorporates a force balance on the liquid macrolayer to determine the necessary vapor velocity to overc ome surface tension forces arising from the curvature of the lower portion of the macrolayer. Figure 5 22 Comparison of the measured CHF enhancement for pool boiling of FC 72 and hexane on surfaces with d ifferent hoodoo sizes.
184 Figure 5 23 Variation of the characteristic length scale of the hoodoo surface structure with hoodoo size. (Gap spacing and undercut are both set to ). Figure 5 24 Images taken of holes present in the vapor film on a hoodoo surface.
185 The observed enhancement in CHF due to the hoodoo stru ctures can also be explained using the lift off model. The addition of a term to account for th e capillary induced liquid momentum flux towards the surface results in the following expression for the critical vapor velocity: 5 4 is the vapor density, is the liquid density, is the maximum curvature of the liquid vapor interface, is the s urface tension of the liquid, is the liquid velocity induced by capillary action. It can be seen that the capillary induced flow acts to increase the critical vapor velocity. In the lift off CHF model  the critical heat f lux is expressed as 5 5 Incorporation of the aforementioned capillary term in the lift off CHF model results in a quartic equation for determining CHF on an enhanced sur face. 5 6 In equation 5 6 is the critical heat flux for a surface with ca pillary action and is the critical heat flux for a plain horizontal surface, which from Guan et al.  is expressed as 5 7 Solving equation 5 6 results in the fo llowing expression for the enhancement in critical heat flux due to capillary action which has been non dimensionalized for general applicability
186 5 8 The non dimensional parameter is defined as 5 9 Using equation 5 7 can be exp ressed as 5 10 The modified lift off model, equation 5 8 is plotted in Figure 5 25 For small there is an almost quadratic variation in For larger it can be seen that linearly varies with Figure 5 26 shows a plot of for working fluids FC 72 and hexane It can be seen that for a given amount of desired CHF enhancement the required capillary velocity is greater for hexane than for FC 72. This difference in req uired capillary velocities is a result of the differenc e in densities. For two different fluids to supply same liquid momentum flux, due to capillary action, the ratio of capillary velocities will be equal to the square root of the density ratio. This can be seen in equation 5 11 For the two fluids in question the capillary velocity ratio is approximately 1.655. Close examination of Figure 5 26 confirms the analysis summarized in equation 5 11 5 11
187 Figure 5 25 Plo t of CHF enhancement versus non dimensional parameter Fi gure 5 26 Predicted CHF enhancement due to capillary action as predicted by the modified lift off model for working fluids FC 72 and hexane
188 To further confirm the validity of the postulated capillary enhan cement mechanism. The liquid front speed produced from a resting droplet was measured on two of the hoodoo surfaces. Particularly, front s peeds were measured on the 10 m and 30 m hoodoo surfaces. A high speed camera was used at 250 fps, to visually record the dynamic wetting of the subsurface structure. Matlab was then used to post process each frame of the recorded video. It should be noted that the front speeds meas ured on the 10 m surface are post experiment and pre experiment for the 30 m surface. Figure 5 27 shows one of the time series used in the measurement of the hoodoo surface wicking capability. A clear distinction between the edg e of the droplet and the edge of the subsurface liquid front can be observed in all the images. As was mentioned previously the smaller hoodoo sizes promote hemi wicking which results in rapid wetting of the structured surface. Two methods were employed to estimate the wicking effectiveness of the hoodoo surfaces. The r elative liquid front displacement was measured every frame from the initial frame shown in Figure 5 27 this results in a data point every 4ms. Not all the images pr ocessed are shown in Figure 5 27 as the front motion in 4ms is not easily discernable upon first examination of the image by eye. A plot of the relative front displacement is shown in Figure 5 28 It is c lear that hexane has a higher spreading velocity than FC 72. Both fluids have very similar surface tensions so this difference is most certainly attributed to the differences in density and viscosity. S preading on the hoodoo surface can be equated to sudde n flow in a capillary tube. It can be easily deduced that the two forces opposing the surface tension force would be both viscous and inertia forces. Since the surface tension force negligibly differs from hexane to FC 72 then it can be said that the drivi ng potential for flow in the capillary
189 network is reduced ; which results in lower spreading velocities. It can also be seen that the 30 m hoodoo surface shows much greater hemi wicking per formance for hexane than the 10 m sur face. Whereas, for FC 72 the 10 m hoodoo surface performs better. Figure 5 27 Time series showing the subsurfac e liquid front motion from a droplet of hexane on the 3 hoodoo surface at 25C (Area shown is 9.3mm x 9.3mm) It is difficult to discern whether this is the true behavior of the surface or an artifact of the state of the surface during testing. Compreh ensive wicking studies pre and post experiment would have to be conducted in order to assess whether boiling on the structured surface alters the wicking performance. For the purposes of understanding the fundamental enhancement mechanisms for structured s urfaces it is sufficient to
190 assess their wetting velocities semi quantitatively. Using the relative liquid front displacement measurement the estimated liquid front velocity is inevitably a function of time. For the sake of comparison the initial front vel ocities will be compared because this initial velocity would be what initiates liquid replenishment of the macrolayer. For hexane as the working fluid the estimated front velocities are on the order of 35 and 80 mm/s for the 10 m and 30 m hoodoo surfaces For FC 72 the initial velocities are on the order of 10 15 mm/s. For the 10 m hoodoo surface the measured CHF enhancement for FC 72 and hexane was 48% and 67% respectively. Using Figure 5 26 the p redicted liquid front speeds wo uld need to be 12.8 and 28 mm/s, respectively. This is excellent agreement with the measured front velocities for FC 72 Greater deviation is observed for hexane, however for such a simple approximation the results of the prediction are the correct order o f magnitude Figure 5 28 Measured relative liquid front motion fo r a hexane droplet on the 10 m and 30 m hoodoo surfaces at 25C.
191 A second method was employed to measure the liquid front velocities. In this second method position coordinates along the liquid front line near the location where the front displacement was initially measured using th e first method was obtained using MATLAB. The respective liquid front profiles were plotted and fit with quadratic functions. With the equation for the liquid front profile known the radius of curvature could be determined using the standard expression for radius of curvature given in equation 5 12 5 12 The profiles for a hexane droplet on the 10 m hoodoo surface are shown in Figure 5 29 The variation of the liquid front velocity with time is readily apparent from the decreasing spacing between subsequent liquid front profiles. It should be noted that each profile is comprised of 40 points. Figure 5 29 Capillary front profiles n ear the point of displacement measurement. Data is for hexane at 25C on the 1 hoodoo surface.
192 Figure 5 30 Measure d radius of curvature variation for the capillary liquid front. Data is for hexane at 25C on the 10 m hoodoo surface. Figure 5 31 Dependence of wetted fraction of subsurface structure on hoodoo size.
193 The respective radii of curvature for the profiles measured are plotted as a function of time in Figure 5 30 A curve fit is provided for two different time intervals. A single quadratic function was capable of fitting the data with a 0.99 coefficient of determination. However for larger time this fit predicts a linear decrease in velocity, which is not typically observed. For times less than 8 0ms a quadratic function is sufficiently capable of fitting the small time data with minimal discontinuity at the transition between fitted regions. For time greater than 80ms a power law fit returns the expected time variation of Using the equation fits from the curvature estimation method the initial wetting velocity is on the order of 79 mm/s. Which agrees with the data obtained previously using the relative front displacement. The amount of void space available for liquid flow in the subsurface s tructure is also important for understanding hoodoo feature heat transfer enhancement. As expected, it can be seen in Figure 5 31 that smaller hoodoo sizes posses a greater wetted fraction than larger hoodoo sizes. It is conceivab le that the greater volume of liquid in contact with the surface in the subsurface region will greatly enhance the thermal performance of the surface. But as previously observed, there is a critical hoodoo size at which heat transfer performance reaches a minimum. Therefore wetted fraction is not a controlling parameter. The great amount of variation in the measured velocities is resultant from the number of parameters which were not controlled. Most importantly, variations in liquid drop volumes will init ially affect the wetting velocity. As well as the vertical height from which the drop is released. As for the image analysis, all measurements were performed by manually selecting measurement points. An estimation of human error
194 can be approximated as abou t a 0.5mm uncertainty in measured quantities. All these factors combined assure that the measured velocities are at least good estimators of the true wetting performance of the surfaces. Figure 5 32 Compa rison of the measured CHF enhancement for pool boiling of FC 72 on different hoodoo surfaces for different batches of surfaces. A batch to batch comparison, Figure 5 32 shows some unwanted variability in the magnitude of CHF enha ncement. However it should be noted that this variability is a result of the pre experiment preparation. The high viscosity epoxy used to encapsulate the lateral portions of the substrate sometimes comes in contact with the fabricated portion of the surfac e. The strong wicking properties of the surface act to draw in epoxy into some regions of the surface. Optical microscopy and SEM were used to confirm the extent to which the epoxy invaded the hoodoo surface structure. Visual examination showed that region s that were believed to be contaminated with epoxy still possessed a tunnel structure. However the tunnel dimensions were reduced. This essentially
195 diminishes the surfaces ability to wick fluid. Therefore the drastic differences in CHF enhancement from the two different batches are as a result of variable amounts of epoxy contamination. Yet despite this unfortunate consequence of the heater preparation the surfaces are still capable of providing up to half of their maximum enhancement. 5.4 Discussion and Conc lu ding Remarks on Hoodoo Surface Structures A novel surface feature was designed to enhance boiling heat transfer and critical heat flux. All variations of the features structure were varied to fully understand the surface fluid interaction. Experimental a nd visual data confirm that the new structures primary enhancement mechanism is through capillary induced liquid flow and modified surface wetting dynamics. The surface feature is named the hoodoo due to its unique similarity to a geologic structure also n amed hoodoo. Aside from enhanced wetting performance the structures re entrant characteristic enhances vapor retention at reduced wall superheats. In addition, the high density of cavities, formed between every three adjacent features, also provides a grea ter number of potential nucleation sites. A series of parametric investigations were conducted to understand what physical attributes and geometric array parameters are the most important in enhancing boiling heat transfer with hoodoo surface features Na mely, the three most important parameters were feature size, spacing and physical a ttributes (i.e. height, undercut and top thickness). Experiments were conducted in two different sets. The first set of experiments looked at the effect of hoodoo size and s pacing. The effect of hoodoo size on pool boiling heat transfer of FC 72 was difficult to discern. No obvious trends were observed. However there were some sizes that resulted in notable improvements in
196 heat transfer and CHF. The 60 ease heat transfer in the low heat flux regime. The 20 m compared to pure Silicon. For the low heat flux regime the 5, 10 and 40 m performed poorer than smooth Silicon. Overall, all sizes showed at le ast a 20% increase in CHF with the 20 m Yet it should noted that epoxy contamination of some portions of the surface was observed. The strong wicking ability of the surface was even capable of wicking the high vis cosity epoxy used to encapsulate the upper portion of the heater assembly. Hoodoo spacing had a noticeable effect on pool boiling heat transfer but marginal effect on CHF. As expected increasing feature density resulted in an increase in heat transfer. Th e smallest gap spacing tested, 1.5 m resulted in the most significant improvement in heat transfer, compared to the other surfaces tested. Increasing the spacing from 1.5 m to 12 m a noticeable decrease in heat transfer was observed. Contrary to the hypothesis that further increase s in hoodoo spacing would result in decreased heat transfer. The 24 m and 48 m hoodoos showed an increase in heat transfer. Close inspection of the two surfaces revealed that a greater percentage of the hoodoo tops had broken off. The broken hoodoos act as mi cro fins, which increase heat transfer due to enhanced area effects. The 12, 24 and 48 m hoodoos performed either equivalent to or poorer than the smooth silicon surface in the low heat flux regime. For both variation in size or spacing no degradation in heat transfer coefficient was observed. This phenomenon is most certainly attributed to enhanced liquid entrainment, which is generated by the enhanced wicking abilit y of the hoodoos
197 The second set of experiments, processed on a new wafer, were conducted with the goal of understanding the effects of physical attributes and fluid properties on pool boiling heat transfer enhancement using hoodoo surface features. Attribute variations were observed to have a marginal effect on boiling heat transfer performanc e. Specifically, hoodoo height and undercut were observed to have virtually no effect on boiling heat transfer performance. Increasing top thickness resulted in a more significant improvement in heat transfer with respect to the other variations tested. Th e physical attribute variations have conclusively identified the hoodoo top to be one of the most important physical characteristic of the feature. This is as expected, because it is the top of the hoodoo which creates the sub surface tunnel network that e nhances liquid entrainment. Additionally, it is the hoodoo top that has been previously identified as the physical feature which brings about the most anomalous wetting behavior. It was of interest to explore the use of thermally conductive coatings with t he goal of further enhancing the heat transfer performance of the hoodoo. The addition of a copper coating resulted in a significant improvement in heat transfer. But, no improvement in CHF was observed. The copper coating improves heat transfer in the low to mid regime heat flux regime However, for heat fluxes approaching CHF little enhancement is observed. The addition of a thermally conductive layers acts to enhance heat transfer during the ebullition cycle and increase the maximum nucleation site densi ty achievable The resulting increase in bubble growth and higher nucleation site density aids in development of local dry out at lower heat fluxes than normally obse rved. The resulting increase of local dry out subsequently results in a gradual degradatio n in heat transfer.
198 Low incipient superheats a re observed (20 25C) in comparison with that of the smooth silicon surfaces. V isual observation of incipience shows that bubble nucleation on t he hoodoo surface features i s hindered This observed behavior is due to the interconnected structure of the surface. The nucleation of a single bubble anywhere on the heating surface will generate a suction effect from the bubble departure. On a normal flat surface this effect is convectively limited to the near field r egion in the bubble wake. However for the hoodoo surface the interconnected network below the features enhances the local liquid entrainment. Incipience is consequently observed to occur in stages Two fluids, FC 72 and hexane were used to assess the eff ects of fluid properties on the boiling heat transfer performance of the hoodoo surface feature for various hoodoo sizes. Both FC 72 and hexane show similar trends with both heat transfer enhancement and CHF enhancement. However CHF enhancement was observ ed to be greater with hexane than with FC 72. The 10 m hoodoo surface was also determined to be superior to any of the other hoodoo surfaces. A batch to batch comparison of the FC 72 pool boiling data confirmed the effect of epoxy contamination on the per formance of the hoodoo surface. CHF enhancement was observed to decrease with increasing hoodoo size until 40 m after 40 m CHF enhancement increases. A derived characteristic length scale for the hoodoo surface feature was observed to exhibit the same g eneral trend with hoodoo size as the measured CHF enhancement. Both the derived length scale and CHF enhancement exhibit a minimum near the 40 m hoodoo size. The observed similar variation asserts that hydrodynamic
199 forces and to a somewhat lesser extent t hermal effects are very important in the region below the hoodoo top. In addition a recently developed lift off CHF model was modified to account for the presence of capillary induced flow near the heating surface. The modified model was then validated wi th measured wicking velocities on the hoodoo surfaces for both FC 72 and hexane The simple modified lift off model predicts the required velocity very well for FC 72. There is larger deviation between the required wicking velocity and that measured with h exane; yet the prediction is the correct order of magnitude. Overall the hoodoo surface feature shows improved heat transfer performance throughout the entire boiling curve. The measured heat transfer coefficient was observed to increase up to CHF. This be havior is different tha n that observed with smooth surfaces and surfaces with cylindrical cavities. The unique structure of the hoodoo feature array promotes enhanced wicking, wetting dynamics and hydrodynamics. Improved thermal hydraulic performance coupl ed with simple fabrication make the hoodoo surface feature a viable surface structure for electronics cooling applications.
200 CHAPTER 6 RECOMMENDATIONS FOR FUTURE RESEARCH Our present understanding of boiling heat transfer remains limited by the vast fundamental gap between microscale phenomena and macroscale behavior. The development and application of molecular scale simulations to boiling heat transfer systems remains in its infancy. To fully reconcile the multi scale thermal transport mechanisms that prevail i n heterogeneous boiling a robust multi scale computational method o logy must be developed. This methodology would essentially bridg e the gap between molecular scale simulations and computational fluid dynamics. The currently available computational resource s still do not suffice to make such a development feasible with the typically expected simulation times. However some researchers have begun the arduous task of algorithm development and numerical implementation. With regards to the research that has been detailed throughout this document. There are some recommendations for future research that can prove fruitful to the fundamental development of boiling heat transfer physics 6.1 The Mitigation of Edge Boiling The current research has revealed that crystal s tructure of the heating surface can result in noticeable changes in nucleate boiling heat transfer. However the assessment of nucleation dynamics was hampered by the phenomenon typically referred to as edge boiling. It would be most advantageous to boil fr om a heating surface without the presence of edge boiling. The observed incipience temperatures would then be truly representative of the solid liquid interaction effect on bubble incipience. One researcher has devised such a surface; however the material of the heater is restricted to copper.
201 In the exploration of surface effects on boiling heat transfer it is most important to be able to vary the heating surface thermal and physical characteristics. In appendix A the design of a heating surface that miti gates the initiation of edge boiling is mathematically described in detail. All necessary design equations and plots have been given and are discussed. The main improvement over the previous researchers design is the account for differing thermal propertie s and sizes of the heating surface. This novel adaptation of a typical boiling heat transfer experiment must be coupled with inverse heat transfer methods in order to resolve non uniformities in the surface temperature that result from reducing the heating surfaces thermal conductivity. As mentioned previously further discussion can be found in appendix A. 6.2 Modified Heterogeneous Nucleation Theory The current theory of heterogeneous nucleation requires vapor trapping for incipience. In the absence of vapor trapping cavities homogeneous nucleation theory has been observed to overpredict the required wall superheat needed to initiate boiling on a highly wetting surface. The very simple modification of the classical homogeneous nucleation theory is most certain ly the cause for the discrepancy at low contact angles. Research in the area of crystal nucleation and diffusive nucleation has revealed that i n the presence of concentration gradients the work of formation for an embryo can be drastically reduced. In add ition, the initial embryo geometry is described as being ellipsoidal. The local concentration gradient restricts initial embryo growth which deforms its shape. The initial volume and surface area of the ellipsoidal embryo are then vastly skewed, depending the magnitude of the concentration gradient. Since all nucleation events are analogous in terms of kinetic mechanisms is can be said that the
202 initial formation of a bubble embryo near a heated surface would also be distorted. There is no concentration grad ient for a homogeneous fluid ; however there are both density and energy gradients in the near wall region. Both of these gradients could likely result in significant alterations in the initial nucleation kinetics that lead to the formation of the critical bubble embryo. Future research into the development of an improved heterogeneous nucleation model for highly wettin g fluids is of great importance and could serve to tie together many of the phenomena observed in this work. 6.3 Parametric Surface Structure St udies Surface structure at all length scales has been observed to have considerable effects on all aspects of boiling heat transfer. But our complete understanding of the effects of capillary structures is still limited by the variety of structures tested in the current literature. Each structure appears to have its own unique characteristics that affect boiling heat transfer in similar and sometimes vastly different ways. A unified understanding of the effect of capillary structures would provide additiona l insight as to the underlying wetting dynamics important during boiling heat transfer.
203 APPENDIX A HEATER DESIGN FOR TH E MITIGATION OF EDGE BOILING Throughout all of the experiments conducted the most notable uncontrollable phenomena was edge boiling. Ed ge boiling refers to the initiation of boiling at the edge of the heating surface. It is generally a very difficult phenomenon to prevent with the standard heater configuration. The only way to assure that edge boiling will not occur is by assuring that th e encapsulant used to insulate the lateral portio ns of the heating surface bonds well with the heater. This can most certainly be assured with the use of low viscosity thermally insulative encapsulants. However, thermal stresses can be particularly taxing on most standard epoxies. Repeated temperature cycling, especially for repeated boiling experiments, can expose the heater e poxy interface to very rapid changes in temperature in very short periods of time. This eventually weakens the bond and microscopic voids and cavities begin to form. This certainly does not exclude the cavities and voids already present from any random gaseous inclusions left after the curing process, that are subsequently near the interface. Depending on the heating surface conditions these cavities present at the edge of the surface could be more likely nucleation sites. Upon beginning the experiment the edge typically nucleates first and subsequent site activation propagat es along the surface In general the occurrence of edge boili ng prevents a full characterization of nucleation at low to moderate wall superheats However, other methods are available to guarantee that edge boiling will not occur. Kim et al.  designed a heating surface that prevents the occurrence of edge boiling. Their heater co nsists of a 20mm diameter cylinder of copper. At the top, where boiling would occur, they increased the heating surface size to 28mm creating a radial
204 fin that would be at a lower temperature than the rest of the heating surface. Having the heater made of copper assures that lateral heat loss from the fin will minimally distort the temperature field in the region of interest. Images shown in Kim et al.  of pool boiling on their surface confirms the ability to eliminate edge boiling. The design method they employed can be further adapted to use any heater material of any shape. But, reducing the thermal conductivity of the heater will result in increased non uniformity of the surface temperature distribution so several design constraints must be employed. What follows is a detailed analysis of the design of a circular and square heater that methodology The governing equations are solved exactly and further implemented in the development of design constraints. The experimental issue s concerni ng surface temperature non uniformity are addressed using the f ollowing mathematical analysis. Circular Heating Surface A 1 A 2
205 Let, A 3 The scale factor for the applied heat flux, is chosen to match the typicall y observed heat transfer coefficients preceding bubble incipience, therefore This approximation is appropriate before boiling occurs on the surface because natural convection heat transfer is observed to linearly vary with wall superh eat. For the rest of the analysis h will then be prescribed and T sat will be varied to change the applied heat flux. The governing equation and boundary conditions can now be expressed as: A 4 A 5 Using separation of variables the solution can be expressed as: A 6 The eigenvalues are determined as the roots of the following equation: A 7 and
206 A 8 The series constant is now expressed as: A 9 The surface superheat variation can be written as: A 10 A plot of wall superheat is given in figure A 1 for a heating zone radius equivalent to half of t he heater radius. Figures A 2 through A 4 give the radial surface wall superheat distributions for three different heating zone radii. For each figure the thermal conductivity ranges from 25 W/m K to 400 W/m K. Figure A 1. Wall superheat variation for a circular heating surface with a/ R = 0.5, h = 100 W/m 2 K H = 0.5 10 3 m k = 110 W/m K and T sat = 30 C
207 Figure A 2. Wall superheat variation for a circular heating surface with a/R=0.25, h=100 W/m 2 K H=0.5 10 3 m and T sat =30 C Figure A 3. Wall superheat variation for a circular heating surface with a/R=0.5, h=100 W/m 2 K H=0.5 10 3 m and T sat =30 C
208 Figure A 4. Wall superheat variation for a circular heating surface with a/R=0.75, h=100 W/m 2 K H=0.5 10 3 m and T sat =30 C Using the expression for the surface superheat variation the maximum center edge temperature difference ca n be written as: A 11 Figure A 5 shows the variation of T CE with wall superheat an d thermal conductivity. Parameter values of a/R=0.5 and h=100 W/m 2 K were specified.
209 Figure A 5. The dependence of the temperature difference between the center and the edge of the surface on applied wall superheat for different values of thermal conduc tivity. The bottom surface temperature. Which is of interest for experimental design can be written as: A 12 Thermocouple placement is dependent on the bottom surface temperature gradient and the standard error of the thermocouples used. A simple expression to determine the optimal location of the thermocouples can be expressed as: A 13 The surface radial temperature gradient can be expressed using the above solution as:
210 A 14 Square Heat ing Surface Analysis for the square heat ing surface proceeds much the same as that for the circul ar heater. A complete derivation of the equations and a discussion of the implications of the solutions is also presented. The design constraints remain unchanged. The governing equation and boundary conditions can be written as A 15 A 16 Let, A 17 The governing equation and boundary conditions can now be expressed as: A 18
211 A 19 Using separation of variables the solution can be expressed as: A 20 With the eigenvalues defined as: A 21 A nd A 22 W ith A 23 Admitting the following functions: A 24 A 25 The series constant can be compactly expressed as: A 26
212 The surface superheat variation can now be expressed as: A 27 A plot of the wall superheat distribution for a heating zone with length equal to half the heater length is given in figure A 6. Figures A 7 through A 9 are the plots of surface temperature distribution for different heater thermal conductivity and different heatin g zone areas. Design parameters for a suitable boiling experiment will surely depend on the working fluid. Figure A 6. Wall superheat variation for a square heating surface with a/L=0.5, h=100 W/m 2 K H=0.5 10 3 m k=110 W/m K and T sat =30 C
21 3 Figure A 7. Wall superheat variation for a square heating surface with a/L=0.25, h=100 W/m 2 K H=0.5 10 3 m and T sat =30 C Figure A 8. Wall superheat variation for a square heating surface with a/L=0.5, h=100 W/m 2 K H=0.5 10 3 m and T sat =30 C
214 Figure A 9. Wall superheat variation for a circular heating surface with a/L=0.75, h=100 W/m 2 K H=0.5 10 3 m and T sat =30 C The maximum temperature difference between the center and the edge can now be expressed as: A 28 The plot below shows the variation of with applied wall sup erheat and thermal conductivity. Parameter values of a/L=0.5 and h=100 W/m 2 K were specified.
215 Figure A 10. Variation of the center edge temperature difference with applied wall superheat for diff erent values of heating surface thermal conductivity. For experiment design the bottom surface temperature distribution is of importance. Using the solution for the present surface geometry yields: A 29 The gradient of the bottom surface temperature can then be used to determine the optimal thermocouple placement. The most important criterion for assuring that any inverse numerical techniques are successful would be to assure tha t the temperature gradient in the material is greater than the thermocouple error divided by their spacing.
216 Surface Temperature Non Uniformity Typical boiling experiments utilize the mean surface temperature as an estimation of the driving thermal poten uniformity of the surface temperature distribution that can make the proper assessment of the surface wall superheat difficult. However the effect of s urface temperature non uniformity should be reduced once boiling commences on the surface. The additional use of high speed video would facilitate the assessment of bubble nucleation even with surface temperature non uniformity.
217 APPENDIX B TABULATED POOL BOILING DATA This appendix contains all the boiling curve data presented in this dissertation in tabulated form. Particular data sets have been grouped according to their relevance and all are presented in sequence as they are presented in the dissertatio n. Table B 1. Pool boiling data for three crystal plane orientations of silicon with FC 72 as the working fluid.
218 Table B 2. Pool Boiling data for three crystal plane orientations of silicon with hexane as the working fluid.
219 Table B 3. Pool bo iling data for five different crystal planes of silicon with FC 72 as the working fluid.
220 Table B 4. Pool boiling data for five different crystal planes of silicon with hexane as the working fluid.
221 Table B 5. Pool boiling data for different crystal plane orientations of copper with FC 72 as the working fluid.
222 Table B 6. Pool boiling data for different crystal plane orientations of copper with hexane as the working fluid.
223 Table B 7. Pool boiling data for different crystal plane orientations of aluminum with FC 72 and hexane as the working fluids.
224 Table B 8. Pool boiling data for polycrystalline nickel and titanium with FC 72 and hexane as the working fluids.
225 Table B 9. Pool boiling data for shallow cylindrical cavity arrays with 3 m and 9 m diameter at 300 m spacing with FC 72 as the working fluid.
226 Table B 10. Pool boiling data for shallow cylindrical cavity arrays with 27 m diameter at 75, 150 and 300 m spacing with FC 72 as the working fluid.
227 Table B 11. Pool boi ling data for shallow cylindrical cavity arrays with 75 m diameter at 300 and 600 m spacing with FC 72 as the working fluid.
228 Table B 12. Pool boiling data for deep cylindrical cavity arrays with 3 m and 9 m diameter at 300 m spacing with FC 72 a s the working fluid.
229 Table B 13. Pool boiling data for deep cylindrical cavity arrays with 27 m diameter at 75, 150 and 300 m spacing with FC 72 as the working fluid.
230 Table B 14. Pool boiling data for deep cylindrical cavity arrays with 75 m diameter at 300 and 600 m spacing with FC 72 as the working fluid.
231 Table B 15. Pool boiling data for deep cylindrical cavity arrays with 9 m diameter at 75 and 150 m spacing with FC 72 and hexane as the working fluids.
232 Table B 16. Pool boiling data for different Hoodoo sizes with FC 72 as the working fluid (wafer 1).
233 Table B 17. Pool boiling data for different Hoodoo spacing with FC 72 as the working fluid.
234 Table B 18. Pool boiling data for hoodoo attribute variation with FC 72 as t he working fluid. (Standard, Short, Less Undercut)
235 Table B 19. Pool boiling data for hoodoo attribute variation with FC 72 as the working fluid. (No undercut, Thick top, Copper coating)
236 Table B 20. Pool boiling data for 10 and 20 m hoodoo with FC 72 as the working fluid. (wafer 2)
237 Table B 21. Pool boiling data for 40 and 80 m hoodoo with FC 72 as the working fluid. (wafer 2)
238 Table B 22. Pool boiling data for 10 and 20 m hoodoo with hexane as the working fluid. (wafer 2)
239 Table B 23. Pool boiling data for 40 and 80 m hoodoo with hexane as the working fluid. (wafer 2)
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249 BIOGRAPHICAL SKETCH Bradley obtained his Bachelor of Science and Master of Science degree in Mechanical Engineering from the University of Miami in 2007. Having interned at industry experience. Despite this he chose to continue on with his education by pursuing his Ph.D in mechanical engineering at the University of Florida. He was awarded two fellowships for his Ph.D. work the Alumni Fellowship as well as the GEM fellowship, offered by a national consortium for minority engineers. A natural interest in the thermal flui d sciences lead to him to further specialize in that field of engineering. Inclined to always investigate the most complex and challenging problems within his field he focused his studies on investigating the fundamental molecular and micro scale interacti ons prevalent during heterogeneous nucleate boiling heat transfer. Upon the culmination of his Ph.D. work he hopes to pursue work in research and development.