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A Study of Non-Newtonian Viscosity and Yield Stress of Blood in a Scanning Capillary-Tube Rheometer Sangho Kim Professors Young I

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A Study of Non-Newtonian Viscosity and Yield Stress of Blood in a Scanning Capillary-Tube Rheometer Sangho Kim Professors Young I A Study of Non-Newtonian Viscosity and Yield Stress of Blood in a Scanning Capillary-Tube Rheometer A Thesis Submitted to the Faculty of Drexel University by Sangho Kim in partial fulfillment of the requirements for the degree of Doctor of Philosophy December 2002 ii Acknowledgments I wish to express my sincere gratitude to Dr. Young I. Cho, for his guidance and inspiration during my entire tenure in graduate school. His experience and idea have proven to be invaluable. I also wish to thank Dr. David M. Wootton for serving as my co-advisor, and for his valuable suggestions and guidance on Biofluid Dynamics. I wish to express my appreciation to the members of my dissertation committee, including: Dr. Ken Choi and Dr. Alan Lau from the MEM Department, and Dr. Peter Lelkes from the School of Biomedical Engineering. I am deeply indebted to Dr. Kenneth Kensey, Mr. William Hogenauer, and Dr. Larry Goldstein from Rheologics, Inc. for providing valuable comments on the test methods and data reduction procedure. A sincere appreciation is extended to several colleagues whose friendship I have cherished during my graduate studies, including: Dr.Wontae Kim, Dr. Sunghyuk Lee, Chagbeom Kim, Giyoung Tak, Dohyung Lim, and Jinyong Wee. Last but not least, I wish to thank my parents for their unbounded support throughout my life. Their reliable provision of emotional, spiritual, and financial support has allowed me to accomplish tasks that would have otherwise been impossible. iii Table of Contents LIST OF TABLES.....................................................................................................viii LIST OF FIGURES ................................................................................................... x ABSTRACT...............................................................................................................xiv CHAPTER 1 INTRODUCTION .............................................................................. 1 1.1 Clinical Significance of Blood Viscosity.................................................... 1 1.2 Motivation of the Present Study ................................................................. 3 1.3 Objectives of the Present Study .................................................................. 3 1.4 Outline of the Dissertation .......................................................................... 4 CHAPTER 2 CONSTITUTIVE MODELS.............................................................. 5 2.1 Newtonian Fluid.......................................................................................... 5 2.2 Non-Newtonian Fluid ................................................................................. 10 2.2.1 General Non-Newtonian Fluid........................................................... 10 2.2.1.1 Power-law Model...................................................................... 11 2.2.1.2 Cross Model.............................................................................. 12 2.2.2 Viscoplastic Fluid .............................................................................. 13 2.2.2.1 Bingham Plastic Model............................................................. 13 2.2.2.2 Casson Model............................................................................ 14 2.2.2.3 Herschel-Bulkley Model........................................................... 15 2.3 Rheology of Blood...................................................................................... 19 2.3.1 Determination of Blood Viscosity ..................................................... 19 iv 2.3.1.1 Plasma Viscosity....................................................................... 20 2.3.1.2 Hematocrit................................................................................. 20 2.3.1.3 RBC Deformability................................................................... 21 2.3.1.4 RBC Aggregation - Major Factor of Shear-Thinning Characteristics........................................................................... 21 2.3.1.5 Temperature .............................................................................. 22 2.3.2 Yield Stress and Thixopropy ............................................................. 23 2.3.2.1 Yield Stress ............................................................................... 23 2.3.2.2 Thixotropy - Time Dependence................................................ 24 CHAPTER 3 CONVENTIONAL RHEOMETRY: STATE-OF-THE-ART ........... 30 3.1 Introduction................................................................................................. 30 3.2 Rotational Viscometer ................................................................................ 34 3.2.1 Rotational Coaxial-Cylinder (Couette Type)..................................... 34 3.2.2 Cone-and-Plate................................................................................... 35 3.3 Capillary-Tube Viscometer......................................................................... 38 3.4 Yield Stress Measurement .......................................................................... 41 3.4.1 Indirect Method.................................................................................. 42 3.4.1.1 Direct Data Extrapolation ......................................................... 42 3.4.1.2 Extrapolation Using Constitutive Models................................. 43 3.4.2 Direct Method .................................................................................... 44 3.5 Problems with Conventional Viscometers for Clinical Applications......... 46 3.5.1 Problems with Rotational Viscometers.............................................. 46 3.5.2 Problems with Capillary-Tube Viscometers...................................... 48 v CHAPTER 4 THEORY OF SCANNING CAPILLARY-TUBE RHEOMETER.... 49 4.1 Scanning Capillary-Tube Rheometer (SCTR)............................................ 49 4.1.1 U-Shaped Tube Set ............................................................................ 50 4.1.2 Energy Balance .................................................................................. 51 4.2 Mathematical Procedure for Data Reduction.............................................. 60 4.2.1 Power-law Model............................................................................... 60 4.2.2 Casson Model..................................................................................... 66 4.2.3 Herschel-Bulkley (H-B) Model ......................................................... 72 CHAPTER 5 CONSIDERATIONS FOR EXPERIMENTAL STUDY................... 81 5.1 Unsteady Effect ........................................................................................... 82 5.2 End Effect.................................................................................................... 87 5.3 Wall Effect (Fahraeus-Lindqvist Effect)..................................................... 90 5.4 Other Effects................................................................................................ 95 5.4.1 Pressure Drop at Riser Tube .............................................................. 95 5.4.2 Effect of Density Variation................................................................ 96 5.4.3 Aggregation Rate of RBCs - Thixotropy........................................... 97 5.5 Temperature Considerations for Viscosity Measurement of Human Blood..........................................................................................101 5.6 Effect of Dye Concentration on Viscosity of Water ...................................104 5.6.1 Introduction........................................................................................104 5.6.2 Experimental Method.........................................................................106 5.6.3 Results and Discussion ......................................................................107 CHAPTER 6 EXPERIMENTAL STUDY WITH SCTR.........................................112 6.1 Experiments with SCTR (with Precision Glass Riser Tubes) ....................112 vi 6.1.1 Description of Instrument ..................................................................113 6.1.2 Testing Procedure ..............................................................................114 6.1.3 Data Reduction with Power-law Model.............................................116 6.1.4 Results and Discussion ......................................................................117 6.2 Experiments with SCTR (with Plastic Riser Tubes)...................................130 6.2.1 Description of Instrument ..................................................................131 6.2.2 Testing Procedure ..............................................................................132 6.2.3 Data Reduction with Casson Mocel...................................................133 6.2.3.1 Curve Fitting .............................................................................134 6.2.3.2 Results and Discussion .............................................................135 6.2.4 Data Reduction with Herschel-Bulkley (H-B) Model .......................139 6.3 Comparison of Non-Newtonian Constitutive Models ................................158 6.3.1 Comparison of Viscosity Results.......................................................159 6.3.2 Comparison of Yield Stress Results ..................................................162 6.3.3 Effects of Yield Stress on Flow Patterns ...........................................164 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS
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