AN EVANESCENT-WAVE BASED PARTICLE IMAGE VELOCIMETRY TECHNIQUE A Thesis Presented to The Academic Faculty by Haifeng Li In Partial Ful¯llment of the Requirements for the Degree Doctor of Philosophy in the George W. Woodru® School of Mechanical Engineering Georgia Institute of Technology December 2008 AN EVANESCENT-WAVE BASED PARTICLE IMAGE VELOCIMETRY TECHNIQUE Approved by: Professor Minami Yoda, Professor Cheng Zhu Committee Chair Wallace H. Coulter Department of George W. Woodruff School of Biomedical Engineering Mechanical Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Cyrus Aidun Professor Victor Breedveld George W. Woodruff School of School of Chemical and Biomolecular Mechanical Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Andrei Fedorov Date Approved: November 7 2008 George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology ACKNOWLEDGEMENTS The research involved in this thesis would not have been possible without the help and support of many people. Foremost, I would like to express my sincere gratitude to my advisor Professor Minami Yoda for her constant encouragement, trust and invaluable suggestions over all of these years. I am grateful to my reading committee members: Professor Cyrus Aidun, Professor Victor Breedveld, Professor Andrei Fedorov and Professor Cheng Zhu for their effort in reviewing this work and their advices and clarifying remarks. I would also like to extend my appreciation to Dr. Jean Pierre Alarie and Professor J. Michael Ramsey at the University of North Carolina for helping me fabricating the microchannels used in this thesis work; to Ms. Gwenaelle Philibert and Professor Susan V. Olesik at the Ohio State University and Dr. Yonghao Xiu and Professor C. P. Wong at the Georgia Institute of Technology for their help in surface modification and characterization; to Dr. Christel Hohenegger and Professor Peter J. Mucha at the University of North Carolina for their many insightful discussions on Brownian dynamic simulations; to Dr. Subhra Datta and Professor A. Terrence Conlisk for their help in the electroosmotic flow experiments; to Mr. Zhengchun Peng and Professor Peter Hesketh for helping me with the photo mask and PDMS fabrications; to Mr. Jack Wei Chen for his helpful suggestions on using micropipettes in the calibration experiments. The discussions and cooperations with all of my laboratory colleagues have also contributed substantially to this work. I would like to specially thank Dr. Reza Sadr for helping me get started with the experimental work and for always being iii there and providing great advices. Thanks also to my other colleagues, Keith Suda- Cederquist for constructing the hydrostatic flow-driving system; Domenico Lippolis for his help on the diffusion measurements; Myeongsub Kim for sharing his setup with me, Charlotte Kotas and Tim Koehler for their many helpful suggestions on the experimental setup. Finally, my deepest gratitude goes to my family and my wife for their continuous and unconditional support and persistent confidence in me. Without the love, none of this would have been possible. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS ............................ iii LISTOFTABLES ................................. ix LISTOFFIGURES ................................ xi SUMMARY.....................................xxviii I INTRODUCTION .............................. 1 1.1 Motivation ............................... 1 1.2 Tracer-Based Near-Wall Velocimetry Techniques . ..... 4 1.2.1 Fluorescence Correlation Spectroscopy (FCS) . .. 4 1.2.2 Molecular Tagging Velocimetry (MTV) . 5 1.2.3 Laser-Doppler Velocimetry (LDV) . 7 1.2.4 Micro-Particle Image Velocimetry (µPIV) .......... 8 1.2.5 Nano-Particle Image Velocimetry (nPIV) . 12 1.3 Objectives................................ 14 1.4 Outline ................................. 16 II LITERATUREREVIEW .......................... 17 2.1 Three Dimensional Particle Image Velocimetry Techniques..... 17 2.1.1 Single-Camera Based 2D-3C PIV Techniques . 18 2.1.2 Stereoscopic and Holographic PIV . 20 2.2 Evanescent Waves and Their Application in Tracer-based Velocime- tryTechniques ............................. 24 2.2.1 TotalInternalReflection. 24 2.2.2 EvanescentWave........................ 26 2.2.3 Evanescent Wave-Illumination in Tracer-Based Velocimetry Techniques ........................... 27 2.3 Hindered Brownian Diffusion: Theory and Modeling . .. 29 2.4 Liquid Slippage at the Submicron Scale . 34 v 2.4.1 Experimental Measurements of Slip Length . 36 2.4.2 WhatAffectsSlip? ....................... 41 III EVALUATING MNPIV USING SYNTHETIC IMAGES . 49 3.1 Generation of Synthetic MnPIV Images . 49 3.1.1 CreatingaSingleParticleImage . 49 3.1.2 GeneratinganImagePair . 51 3.2 ImageProcessing............................ 53 3.3 ResultsandDiscussion. 56 3.3.1 Results ............................. 56 3.3.2 Biases in the Measured Velocity Data . 59 3.4 Summary ................................ 60 IV A FURTHER LOOK INTO THE BIASES IN MNPIV . 62 4.1 The Effect of Non-uniform Illumination on the Accuracy of MnPIV 62 4.2 The Effect of Hindered Brownian Diffusion on the Accuracy of MnPIV 64 4.2.1 Effects of “In-Plane” Brownian Diffusion . 66 4.2.2 “Mismatched” Particles Due to “Out-of-Plane” Diffusion.. 66 4.2.3 Overestimation of Near-Wall Velocities . 71 4.3 Summary ................................ 81 V EXPERIMENTAL SETUP AND PROCEDURE FOR VALIDATING MN- PIV...................................... 84 5.1 CreatingPoiseuilleFlows . 84 5.1.1 Microchannels ......................... 84 5.1.2 SystemforDrivingtheFlow. 87 5.1.3 PreparationoftheWorkingFluids . 88 5.2 OpticalSetup.............................. 90 5.2.1 IlluminationSystem . 90 5.2.2 ImagingSystem ........................ 94 5.3 Calibration of the Experimental System . 102 vi 5.3.1 FlowSimulation . .. .. 102 5.3.2 Comparing Measured and Predicted Poiseuille Velocity Profiles106 5.3.3 Further Tests of the Flow Driving System . 108 5.4 ExperimentalProcedure . 110 VI TEST MNPIV WITH EXPERIMENTAL IMAGES . 113 6.1 Image Intensity of Particles Illuminated by Evanescent Waves . 113 6.1.1 Modeling the Fluorescence from a Colloidal Particle Illumi- nated by Evanescent Waves . 114 6.1.2 CalibrationExperiments . 117 6.2 ImageProcessing............................ 127 6.2.1 Particle Image Compensation and Detection . 127 6.2.2 Particle Distribution and Binning . 128 6.2.3 Expected Particle Velocity . 131 6.3 ResultsandDiscussion. 132 6.4 Summary ................................ 138 VII SLIPPAGE OF AQUEOUS SOLUTIONS OVER SOLID SURFACES WITH VARYINGWETTABILITY. 140 7.1 ExperimentalDescriptions. 140 7.2 ResultsandDiscussions . 144 7.3 Summary ................................ 152 VIII CONCLUSIONS AND RECOMMENDATIONS . 154 8.1 Conclusions............................... 155 8.1.1 Studies using Synthetic Images and Brownian Dynamics Sim- ulation ............................. 155 8.1.2 Experimental Measurements of Particle Distributions, Veloc- itiesandVelocityGradients . 156 8.1.3 Slip Lengths Measured with MnPIV . 157 8.2 Contributions.............................. 158 8.3 RecommendationsforFutureWork . 159 vii APPENDIX A SLIPPAGE OF AQUEOUS SOLUTIONS OVER SOLID SUR- FACES WITH VARYING WETTABILITY: MORE RESULTS . 161 APPENDIX B EVALUATION OF AN ALGORITHM FOR MEASURING “IN-PLANE” BROWNIAN DIFFUSION COEFFICIENT . 169 APPENDIX C UNCERTAINTY AND ERROR ANALYSIS . 181 APPENDIX D PARTICLE DETECTION . 189 APPENDIX E MAJOR AND MINOR LOSSES OF THE FLOW-DRIVING SYSTEM ................................... 195 APPENDIX F PARTICLE-WALL INTERACTION POTENTIAL DETER- MINED FROM MEASURED PARTICLE DISTRIBUTIONS . 198 REFERENCES................................... 203 viii LIST OF TABLES 1 Depth of correlation 2zcorr calculated using Equation 2. 12 2 Experimental parameters for the PDFs shown in Figure 30. .... 77 3 components of the illumination system. 91 4 Comparison between experimentally measured water viscosities at var- ious temperatures and a curve fitting of the data as shown in Equation 25.106 5 Comparison of zc and z for the three layers for C = 10 mM sodium h i tetraboratesolution. 132 6 Comparison of expected velocity gradients G (slope of the solid line in Figure 63), G3 from a curve-fit of the three MnPIV datapoints (slope of the dashed line in Figure 63) and G2 estimated from the MnPIV datapoints in layers II and III for three different shear rates. All the curve-fits assume no slip at the wall. 135 7 Comparison of velocity gradients G obtained from the predicted veloc- ity profile by Equation 24 using the measured pressure gradient and fluid viscosity (slope of the solid line in Figure 66), G3 from a curve-fit of the three MnPIV data points and origin (slope of the dashed line in Figure 66) and G2 estimated from the MnPIV data points in layers II and III and origin for three different shear rates. ... 137 8 Ionic strength and pH of the working fluids. 143 9 Comparison of expected velocity gradients G (slope of the solid line in Figure 71) and G3 from a curve-fit of the three MnPIV datapoints (slope of the dashed line in Figure 71) for the six different shear rates. The last column represents the slip lengths obtained for these cases. 148 10 Comparison of expected velocity gradients G (i.e., the slope of the solid line in Figure 73) and the velocity gradients obtained from linear curve- fits of the three MnPIV datapoints G3 (i.e., the slope of the dashed line in Figure 73) for the Poiseuille flow of 10 mM CH3COONH4 through the bare channel at six different