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Electrokinetic Flow in Micro- and Nano-Fluidic Components

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Electrokinetic Flow in Micro- and Nano-Fluidic Components ELECTROKINETIC FLOW IN MICRO- AND NANO-FLUIDIC COMPONENTS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Zhi Zheng, M.S. ***** The Ohio State University 2003 Dissertation Committee: Approved by Professor A. Terry Conlisk, Adviser Professor Derek J. Hansford __________________________ Adviser Professor L, James Lee Biomedical Engineering Center ABSTRACT In this work, electrokinetic flow through nano- and micro-channels is investigated. The governing equations for the flow in three dimensional channels are derived from Poisson-Nernst-Planck theory. The boundary conditions for the governing equations are obtained from the electrochemical equilibrium requirements. The results are compared with three sets of experimental data, provided by iMEDD inc., Oak Ridge National Laboratory, and Georgia Institute of Technology. The results of comparison are extremely good. A finite difference method is used to solve the governing equations numerically. For asymptotic cases, the governing equations are solved analytically using singular perturbation method. The results show that multivalent counterions decrease the electroosmotic flow extraordinarily. Scaling laws for the governing equations are introduced which clarify that several dimensionless parameters determine the potential and velocity profiles and the distribution patterns of ion species. The relationship between the channel surface charge density and the ζ potential is explored. The diffusive fluxes, electric migrational fluxes and convective fluxes of different ion species in the electrokinetic flow are obtained from the governing equations. Results are also obtained for electroosmosis in 2D nanochannels. At the end of this work, the governing equations for unsteady flow are derived, the transport of macromolecules through micro- and nano- channels is discussed and the future work in these areas is suggested. ii Dedicated to my parents iii ACKNOWLEDGMENTS It is a big challenge for me to complete my PhD program at Ohio State. There are many people to whom I owe grateful thanks for helping me coming through the whole procedure. I would like to express my gratitude to my advisor, Dr. A. Terry Conlisk, for the tremendous amount of support he has given me throughout this work, for his encouragement and enthusiasm which boosted my research work, and for his patience in correcting my scientific and linguistic errors. I am also grateful to the other members of my dissertation advisory committee: Dr. Derek Hansford and Dr. Jim Lee for their help with this work. I also want to thank all the other members of our research group, especially Kelly Evers, Jennifer McFerran, and Dr. Somnath Bhattacharyya. This work is part of the project funded by DARPA. I am grateful to the contract monitors Dr. Anantha Krishnan (DARPA), Mr. Clare Thiem and Mr. Duane Gilmour (IFTC) for their support. I also thank Dr. Mike Ramsey, Steve Jacobson, and J. P. Alarie of ORNL; Rob Walczak and Tony Boiarski of iMEDD; Dr. Minami Yoda and Reza Sadr of Georgia Tech; Dr. Sherwin Singer and Wei Zhu of OSU and Dr. Jim Coe of OSU for many discussions and for the use of their experimental results. iv VITA February 29, 1976……………………Born – Jinan, China 1998…………………………………B.S. Physics, Tsinghua University, Beijing. June, 2003……………………………M.S. Biomedical Engineering, the Ohio State University. 1998 – present………………………Graduate Teaching and Research Associate, The Ohio State University PUBLICATIONS Research Publication 1. “Mass Transfer and Flow in Electrically Charged Micro- and Nanochannels”, A.T. Conlisk, Jennifer Mcferran, Zhi Zheng, Derek Hansford, Anal. Chem. 2002, 74, 2139-2150. 2. “Effects of Multivalent Ions on Electroosmotic Flow in Micro and Nanochannels”, Zhi Zheng, Derek J. Hansford, A. T. Conlisk, Electrophoresis, 2003, 24, 3006- 3017. 3. “Asymptotic Solutions for Electroosmotic Flow in Two-Dimensional Charged Micro- and Nano-channels”, S. Bhattacharyya, Zhi Zheng, A. T. Conlisk, 33rd AIAA Fluid Dynamics Conference, 2003. 4. “An Experimental and Modeling Study of Electroosmotic Bulk and Near-Wall Flows in Two-Dimensional Micro- and Nanochannels”, R. Sadr, Zhi Zheng, M. Yoda, A. T. Conlisk, IMECE, 2003-42917 FIELD OF STUDY Major Field: Biomedical Engineering v TABLE OF CONTENTS Page Dedication………………………………………………………………...…………iii Acknowledgements………………………………………………………………….iv Vita……………..…………………………………………………………………….v LIST OF TABLES...................................................................................................viii LIST OF FIGURES ................................................................................................... xi CHAPTER 1 INTRODUCTION ................................................................................ 1 1.1 Background........................................................................................... 1 1.2 The Basics of Electroosmosis ............................................................... 5 1.3 Properties of Channel Surfaces........................................................... 10 1.4 Previous Work on Modeling Electroosmotic Flow ............................ 13 1.5 Outline of Dissertation........................................................................ 16 CHAPTER 2 GOVERNING EQUATIONS............................................................. 19 2.1 Introduction......................................................................................... 19 2.2 Classical Electric Double Layer Theories........................................... 20 2.3 The Three Dimensional Governing Equations ................................... 33 2.4 The One Dimensional Governing Equations ...................................... 39 2.5 Singular Perturbation Equations ......................................................... 41 2.6 Debye-Hückel Approximaton for Nanochannels where ε = Ο (1) ..... 47 2.7 Electrochemical Potential ................................................................... 49 2.8 Electrochemical Consideration for a Channel-Reservoir System....... 51 CHAPTER 3 RESULTS FOR ONE DIMENSIONAL CHANNELS...................... 58 3.1 Introduction......................................................................................... 58 3.2 Finite Difference Method.................................................................... 59 3.3 Results for Monovalent Binary Electrolytes....................................... 64 3.4 Monovalent Binary Electrolytes In a Channel-Reservoir System ...... 73 3.5 Using Scaling Laws to Simplify Governing Equations ...................... 81 3.6 Results for Multivalent Binary Electrolyte and Multi-component Electrolytes. ........................................................................................ 90 vi CHAPTER 4 COMPARISON WITH EXPERIMENTS ........................................ 113 4.1 Introduction....................................................................................... 113 4.2 Comparison with the iMEDD Experiments...................................... 114 4.3 Comparison with the ORNL Experiments........................................ 125 4.4 Comparison with the Georgia Tech Experiments............................. 148 4.5 Issues of Surface Charge Density ..................................................... 154 CHAPTER 5 ELECTROPHORESIS AND ION FLUXES.................................... 156 5.1 Introduction....................................................................................... 156 5.2 Classical Theory of Capillary Electrophoresis ................................. 157 5.3 Governing Equations ........................................................................ 159 5.4 Numerical Method ............................................................................ 164 5.5 Results............................................................................................... 166 CHAPTER 6 EOF IN RECTANGULAR CHANNELS ........................................ 219 6.1 Introduction....................................................................................... 219 6.2 Governing Equations ........................................................................ 220 6.3 Numerical Method ............................................................................ 222 6.4 Results For Symmetrical Cases ........................................................ 223 6.5 Results for Asymmetrical cases........................................................ 238 CHAPTER 7 UNSTEADY FLOW ........................................................................ 248 CHAPTER 8 SUMMARY AND FUTURE WORK .............................................. 252 8.1 Introduction....................................................................................... 252 8.2 Transport of Macromolecules in Micro- and Nano- capillaries........ 253 APPENDICES…………………………………………………………………….257 BIBLIOGRAPHY................................................................................................... 261 vii LIST OF TABLES Page Table 2.1 Mean activity coefficients of aqueous salts at 25ºC. (http://www.psigate.ac.uk/newsite/reference/plambeck/chem2/p01193.htm, 07/18/03)................................................................................................................... 50 Table 2.2 Experimental activity coefficients of NaCl at 298K. [50]................................ 50 Table 3.1 Molarity of ions in the reservoir, units=M; the ionic strength is 0.33288M. ... 93 Table 3.2 Average molarity of ions
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