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Numerical Simulations of High Knudsen Number Gas Flows and Microchannel Electrokinetic Liquid Flows Fang Yan Bakhtier Farouk, Ph

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Numerical Simulations of High Knudsen Number Gas Flows and Microchannel Electrokinetic Liquid Flows Fang Yan Bakhtier Farouk, Ph Numerical Simulations of High Knudsen Number Gas Flows and Microchannel Electrokinetic Liquid Flows A Thesis Submitted to the Faculty of Drexel University by Fang Yan in partial fulfillment of the requirements for the degree of Doctor of Philosophy May 2003 ii ACKNOWLEDGMENTS I express my gratitude to my advisor, Prof. B. Farouk at Drexel University for his valuable guidance, support, encouragement and patience during my studies at Drexel University. I am also grateful to Prof. N. Cernansky, Prof. Y. Gogotsi, Prof. M. Vallieres, Prof. D. Wootton and Prof. K. Choi from Drexel University for their Valuable advice on this thesis as committee members. I acknowledge the financial support from Department of Mechanical Engineering and Mechanics, Drexel University that provide me the opportunity to pursue my doctoral study. I appreciate the help from the fellow laboratory members Dr. K. Bera, Dr. J. Yi, and Mr. M. Aktas. I wish to express my special gratitude to my parents and wife for their understanding and encouragement during my stay in the U. S. A. iii TABLE OF CONTENTS LIST OF TABLES......................................................................................................................... v LIST OF FIGURES...................................................................................................................... vi ABSTRACT .................................................................................................................................. x 1. INTRODUCTION ................................................................................................................ 1 1.1. Motivation .................................................................................................................... 1 1.2. Objectives.................................................................................................................... 6 1.3. Outline of the thesis..................................................................................................... 7 2. BACKGROUND AND LITERATURE SURVEY ................................................................ 10 2.1. High Kn number gas flows......................................................................................... 10 2.2. Liquid flows in microchannels.................................................................................... 13 3. NUMERICAL AND MATHEMATICAL MODELS............................................................... 16 3.1. Overview of research work ........................................................................................ 16 3.2. Direct simulation Monte Carlo model for high Knudsen number gas flows ................................................................................ 19 3.3. Mathematical model of microchannel liquid flows...................................................... 27 4. LOW PRESSURE GAS FLOW AND HEAT TRANSFER IN DUCTS ............................... 38 4.1. Introduction................................................................................................................ 38 4.2. Problem description................................................................................................... 39 4.3. Model description ...................................................................................................... 40 4.4. Results and discussion.............................................................................................. 42 5. MIXING GAS FLOWS IN A MICROCHANNEL ................................................................ 60 5.1. Introduction................................................................................................................ 60 5.2. Problem description................................................................................................... 62 5.3. Model description ...................................................................................................... 62 5.4. Results and discussion.............................................................................................. 63 iv 6. THREE DIMENSIONAL LOW PRESSURE COUETTE FLOWS...................................... 77 6.1. Introduction................................................................................................................ 77 6.2. Problem description................................................................................................... 79 6.3. Parallelization of DSMC............................................................................................. 79 6.4. Results and discussion.............................................................................................. 82 7. NUMERICAL SIMULATION OF CAPILLARY ELECTROKINETIC SEPARATION FLOWS IN MICROCHANNEL .......................................................................................... 93 7.1. Introduction................................................................................................................ 93 7.2. Problem geometry ..................................................................................................... 95 7.3. Mathematical modeling.............................................................................................. 96 7.4 Results and discussion............................................................................................... 99 8. SUMMARY AND CONCLUSIONS ................................................................................. 118 8.1. Summary ................................................................................................................. 118 8.2. Recommendations for future work........................................................................... 120 LIST OF REFERENCES .......................................................................................................... 123 VITA ......................................................................................................................................... 134 v LIST OF TABLES 4.1. Values of Nu vs Re, Kn and Pr for Pin = 6.7 Pa and Pout = 5.3 Pa ................................... 49 4.2. Values of Nu vs Re, Kn and Pr for Pin = 0.67 Pa and Pout = 0.53 Pa ................................ 49 4.3. Values of Nu vs Re, Kn and Pr for Pin = 0.067 Pa and Pout = 0.053 Pa.............................................................................. 50 5.1a. Inlet and solid wall conditions for equal inlet pressure cases ........................................... 69 5.1b. Inlet and solid wall conditions for cases with variable inlet pressure of the H2 stream................................................................................................. 69 5.1c. Inlet and solid wall conditions for cases with variable accommodation coefficients ............................................................................................. 69 6.1. Inlet and solid wall conditions for cases studied for 3D Couette flows.................................................................................................................... 85 6.2. Inlet and solid wall conditions for cases studied for ‘ultimate pressure’ calculations.................................................................................... 85 7.1. Electric field distribution of cases considered for simulation........................................... 106 vi LIST OF FIGURES 1.1. The Knudsen number limits on the mathematical models (Bird, 1994) ........................... 3 3.1. Flow chart of DSMC procedure ..................................................................................... 34 3.2. Schematic of single component gas flow in microchannel ............................................ 35 3.3. Comparison of axial pressure distribution for channel flow (with slip-walls) .............................................................................................................. 35 3.4. Comparison of numerical results with experiment data of pressure distribution along the channel...............................................................................................36 3.5. Cross-channel device for electrophoresis separation..........................................................37 3.6. Description of electric double layer (a) formation of electric double layer (b) potential ψ distribution within the electric double layer (c) velocity distribution within the electric double layer ......................................... 37 4.1. Schematic of the problem geometry.............................................................................. 50 4.2a. The effect of cell size on temperature profile at x = 0 .0 m (50 particles / cell) ......................................................................................................... 51 4.2b. The effect of cell size on temperature profile at x = 0.4 m (50 particles / cell) ......................................................................................................... 51 4.3. The effect of particle number on temperature profile at x = 0 (350 × 80 cells) ................................................................................................. 52 4.4. Temperature contours for the base case....................................................................... 52 4.5. Velocity vectors for the base case................................................................................. 53 4.6. Pressure distribution along centerline for the base case..................................................53 4.7. Heat flux along the plate for the
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