TRANSITION TO TURBULENCE IN NON-NEWTONIAN FLUIDS: AN IN-VITRO STUDY USING PULSED DOPPLER ULTRASOUND FOR BIOLOGICAL FLOWS Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Dipankar Biswas December, 2014 TRANSITION TO TURBULENCE IN NON-NEWTONIAN FLUIDS: AN IN-VITRO STUDY USING PULSED DOPPLER ULTRASOUND FOR BIOLOGICAL FLOWS Dipankar Biswas Dissertation Approved: Accepted: __________________________ __________________________ Advisor Department Chair Dr. Francis Loth Dr. Sergio D. Felicelli __________________________ __________________________ Committee Member Dean of the College Dr. Yang H. Yun Dr. George K. Haritos __________________________ __________________________ Committee Member Vice Provost Dr. Abhilash Chandy Dr. Rex D. Ramsier __________________________ __________________________ Committee Member Date: Dr. Alex Povitsky __________________________ Committee Member Dr. Peter H. Niewiarowski ii ABSTRACT Blood is a complex fluid and has been established to behave as a shear thinning non-Newtonian fluid when exposed to low shear rates (<200s-1). Many hemodynamic investigations use a Newtonian fluid to represent blood when the flow field of study has relatively high shear rates. Shear thinning fluids have been shown to exhibit differences in transition to turbulence compared to that of Newtonian fluids. Incorrect assumption of the transition point in a simulation could result in erroneous prediction of hemodynamic forces. The goal of the present study was to compare velocity profiles near transition to turbulence of whole blood and standard blood analogs in a straight rigid pipe and an S-shaped pipe under a range of steady flow conditions. Reynolds number for blood was defined based on the viscosity at a shear rate of 400s-1. The rheometer was calibrated at shear rates of interest using Newtonian viscosity standards. Doppler ultrasound was used to measure velocity profiles of whole porcine blood and a Newtonian fluid in an in vitro experiment at 18 different Reynolds numbers ranging from 750 to 3500 (straight pipe) and 21 different Reynolds numbers ranging from 500 to 2800 (S- shaped pipe). Three samples of each fluid were examined and fluid rheology was measured before and after each experiment. Straight pipe results show parabolic iii velocity profiles for both whole blood and the Newtonian fluid at Reynolds numbers less than 2100 (based on high shear rate viscosity). The Newtonian fluid had blunt velocity profiles with large velocity fluctuations (root mean square as high as 18%) starting at Reynolds numbers ~2100-2300 which indicated transition to turbulence. In contrast, whole blood did not transition to turbulence until a Reynolds number of ~2500-2700. This delay was consistent for all three samples. For Reynolds numbers larger than 2100, the delay in transition resulted in differences in velocity profiles between the two fluids as high as 20%. A Newtonian assumption for blood at flow conditions near transition can lead to large errors in velocity prediction for steady flow in a straight pipe. For the S-shaped pipe geometry, the RMS velocity results show that the minimum Re where transition initiated for whole blood (~1000-1200) is slightly larger (>10%) than that observed for a Newtonian fluid (~900-1000) under steady flow conditions. Repeated measurements show these results to be consistent for three different samples. These results show large differences in the magnitude of mean and fluctuation velocity between whole blood and a Newtonian fluid for Re>1000. Further research is necessary to understand this relation in more complex geometries and under pulsatile flow conditions. iv DEDICATION This dissertation is dedicated to my dad: Dilip Kumar Biswas And to my mom: Malati Biswas You have made this possible with your everlasting love, support, sacrifice and encouragement. v ACKNOWLEDGEMENTS This work would not have been completed without the support, assistance, guidance and advice of a lot of people; all of who have in someway shaped my thoughts towards research, science and life in general. First, I must thank my advisor and mentor Dr. Francis Loth who has supported, guided and motivated me at every stage of my research career and gave me the opportunity to get started with research in the field of biofluids. I would like to also acknowledge Drs. David Smith and Sang-Wook Lee for their research findings that motivated this research, David M. Casey, Narender Ambati and Ian Key for their contribution in building the experimental setup, Kenneth W. Smith Jr. avd Kevin Razavet for their help in running the experiments, Drs. Stanley Rittgers and Stephen Jones for their invaluable suggestions on the experimental procedure and processing, Richard Nemer for his support in acquiring some instrumentation, Dale Ertley for his help in the design and construction of the experiment system and, Walid Qaqish and Douglas C. Crowder for their help with blood analysis. Finally, I thank Dr. Paul Fischer for his invaluable discussion over many years, which helped craft the overall design of this experiment. vi TABLE OF CONTENTS Page LIST OF TABLES ................................................................................................. x LIST OF FIGURES ...............................................................................................xi CHAPTER I. INTRODUCTION AND BACKGROUND ............................................................ 1 II. LITERATURE REVIEW .................................................................................... 7 2.1 Hemodynamics and morphogenesis ........................................................... 7 2.2 Ultrasound and velocity measurement ........................................................ 9 2.3 Recr in non-Newtonian fluids ....................................................................... 9 2.4 Recr and velocity profile in blood ............................................................... 10 2.5 Recr in S-shaped pipe ................................................................................ 13 2.6 Rheology of blood ..................................................................................... 14 2.7 Temperature dependence of viscosity of Newtonian fluids ....................... 16 III. PROPOSED STUDIES .................................................................................. 17 IV. METHODS .................................................................................................... 20 4.1 Design of In Vitro Hemodynamics System (Straight Pipe) ........................ 20 4.2 Design of In Vitro Hemodynamics System (S-Shaped Pipe) ..................... 25 4.3 Viscosity Measurement ............................................................................. 26 4.4 Data acquisition and processing................................................................ 29 4.5 Importance of Quadrature Signal .............................................................. 37 vii 4.6 Voltage and Temperature Gradient Calibration ......................................... 38 4.7 Ultrasound Probe Range and Rotational Orientation ................................ 40 4.8 Temperature Control ................................................................................. 42 4.9 Red Blood Cell Evaluation ......................................................................... 44 4.10 Statistics .................................................................................................. 44 V. RESULTS (STRAIGHT PIPE) ........................................................................ 46 5.1 Results Overview ...................................................................................... 46 5.2 Microscopy ................................................................................................ 46 5.3 Rheology ................................................................................................... 48 5.4 Transition to Turbulence ............................................................................ 49 VI. RESULTS (S-SHAPED PIPE) ....................................................................... 70 6.1 Results Overview ...................................................................................... 70 6.2 Rheology ................................................................................................... 71 6.3 Transition to Turbulence ............................................................................ 72 VII. DISCUSSION ............................................................................................... 85 7.1 Overview ................................................................................................... 85 7.2 Straight Pipe .............................................................................................. 85 7.3 S-Shaped Pipe .......................................................................................... 90 7.4 Overall Discussion ..................................................................................... 93 VIII. LIMITATIONS .............................................................................................. 95 8.1 Straight Pipe .............................................................................................. 96 8.2 S-Shaped Pipe .......................................................................................... 98 IX. CONCLUSION ...........................................................................................