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One-Dimensional Differential Newtonian Analysis for Applications in Saliva Rheology

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One-Dimensional Differential Newtonian Analysis for Applications in Saliva Rheology One-dimensional Differential Newtonian Analysis for Applications in Saliva Rheology by Louise Lu McCarroll A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mechanical Engineering) in The University of Michigan 2017 Doctoral Committee: Professor William W Schultz, Co-Chair Professor Michael J Solomon, Co-Chair Professor Joseph Bull Dr. Joseph T Murray, Veterans Affairs Hospital Professor Alan S Wineman Louise Lu McCarroll [email protected] ORCID iD: 0000-0003-1471-0655 © Louise Lu McCarroll 2017 For my parents, Yin and Lin Lin ii ACKNOWLEDGEMENTS I think the best phrase that describes this experience for me is \it takes a village" or in my case it should be \it takes a whole metropolitan area and then some." But I'll stick with the \village" analogy for now. The chief villagers I'd like to thank are my advisors, Professor William Schultz and Professor Michael Solomon, for their seemingly unlimited supply of patience with me, especially when I was feeling like the village idiot. Thank you for your guidance these past few years, for teaching me to be resourceful, to a construct logical argument and perform novel analyses, for propping me up when my spirits were low, and last but not least, for being so approachable. I have really enjoyed working on this project with you both. Bill - I am still trying to learn how to \embrace chaos." Mike - I appreciate all the structure you have imposed on this process. I'd also like to extend my gratitude to my committee members, Professor Alan Wineman, Professor Joseph Bull, and Dr. Joseph Murray, for helping me put bounds on this project. It is likely that without the advice of my committee I would have continued to run simulations and agonize over my data instead of writing. I am also grateful for all the time and guidance you have given me and even lab space when it was needed. I'd also like to thank Professor David Dowling for always being an extra mentor and a cheerleader for me. I have really appreciated all the academic and professional advice he has given me. Of course I can't forget my wonderful co-hort in the Autolab, at the NCRC, in iii the Biotransport Lab, and now scattered all over the world. I wish I could list all the individual names but truth be told, I'd probably just start crying. The friendships I have made during this process have made the last few years of grad school so enjoyable. I looked forward to making the trek to school everyday because of these friendships. Last but certainly not least, I must thank my family. I am grateful to my parents, Yin and Lin Lin, for encouraging me to study engineering. My parents, especially my dad, taught me what it means to persevere - an indispensible quality that I needed for this work. I also must thank my wonderfully supportive husband, Kellen. I'm not sure how he has managed the seemingly Herculean effort of starting a new job in Pittsburgh, driving back and forth to Ann Arbor to pack and move us out of our house, and looking for a new place for us to live all by himself. But I am grateful that he has taken over all the household duties to let me burrow into a hole and concentrate on writing. I am looking forward to starting in a new place with him and our son (dog), Boston. iv TABLE OF CONTENTS DEDICATION :::::::::::::::::::::::::::::::::: ii ACKNOWLEDGEMENTS :::::::::::::::::::::::::: iii LIST OF FIGURES ::::::::::::::::::::::::::::::: vii LIST OF APPENDICES :::::::::::::::::::::::::::: xi ABSTRACT ::::::::::::::::::::::::::::::::::: xii CHAPTER I. Introduction ..............................1 1.1 Introduction and Motivation . .1 1.2 Extensional Flow Kinematics . .4 1.3 Extensional Rheometry for Low-Viscosity Fluids . .5 1.3.1 Extensional flow oscillatory rheometer . .5 1.3.2 Capillary break-up rheometry . .6 1.4 Scope of this work . 11 II. One-dimensional Differential Newtonian Analysis ....... 13 2.1 Introduction . 13 2.2 Differential Analysis . 15 2.3 Experimental Methods . 17 2.4 Image and Data Analysis . 19 2.5 Numerical Model . 22 2.6 Results and Discussion . 24 2.7 Conclusions . 32 III. One-dimensional non-Newtonian Analyses without Stretching 35 3.1 Introduction . 35 v 3.2 Surfactants . 36 3.3 Viscoelastic Models . 39 3.3.1 Maxwell, Oldroyd-B and FENE-P models . 39 3.3.2 Current 1D viscoelastic CBR analysis . 43 3.3.3 1D viscoelastic model and simulation . 46 3.3.4 Characterizing the early viscous regime { high-viscosity (large Oh)....................... 54 3.3.5 Characterizing the early viscous regime { low-viscosity (small Oh)....................... 64 3.3.6 Discussion . 71 3.4 Conclusions . 73 IV. Expanding the CBR Method .................... 76 4.1 Introduction . 76 4.2 1D Model and Simulation . 78 4.3 Approximate Axial Step-strain . 85 4.4 Oscillatory Boundary Motion . 88 4.5 Discussion . 93 4.6 Conclusions & Future Work . 96 V. Conclusions & Future Work ..................... 99 5.1 Summary and Key Findings . 99 5.2 Future Work . 104 5.2.1 Experiments . 104 5.2.2 1D modeling . 105 5.2.3 Characterizing the Oh − De − S space . 106 5.2.4 Oscillatory boundary motion . 106 APPENDICES :::::::::::::::::::::::::::::::::: 107 BIBLIOGRAPHY :::::::::::::::::::::::::::::::: 122 vi LIST OF FIGURES Figure 1.1 Shear rheometry of water, saliva, and commercial products for dys- phagia patients performed in a cone-and-plate rheometer . .4 1.2 An elongated saliva filament after an imposed axial step-strain in a CBR experiment forms beads-on-a-string . .5 1.3 Schematic of the extensional flow oscillatory rheometer (EFOR) . .6 1.4 Schematic of capillary break-up rheometr (CBR) . .8 2.1 Demonstration of CBR experiments, image-postprocessing, and data reduction to determine surface tension to viscosity ratio α by the 1D differential analysis (2.7) . 21 2.2 Performances of the differential method (2.7) and the standard inte- gral method (2.4) evaluated by experimental and numerical 1D model data . 25 2.3 Experimental results for dimensionless surface tension to viscosity ratios α∗(t) determined by (2.7) plotted against two dimensionless time-dependent parameters . 29 2.4 Experimental results for time-averaged dimensionless surface tension to viscosity ratios hα∗i determined by the differential method (2.7) versus viscosity µ ............................ 30 2.5 Experimental results for dimensionless surface tension to viscosity ratios α∗(t) determined by (2.7) versus asymmetry Ω(t) (2.9) for Bo(t) < 0:3 ............................... 31 vii 3.1 Dimensionless (a) filament midpoint evolution R=Rp for Oh = 3:16; De = 94:9 and S = 0:25 plotted with dimensionless time t=tc; (b) free sur- face profiles R(z); and (c) magnitude of even Chebyshev coefficients jr^nj .................................... 55 3.2 Dimensionless (a) filament midpoint evolution R=Rp for Oh = 3:16; De = 94:9 and S = 0 plotted with dimensionless time t=tc; (b) free surface profiles R(z); and (c) magnitude of even Chebyshev coefficients jr^nj 56 3.3 Dimensionless filament midpoint evolution R=Rp for Oh = 3:16;S = 0:25 and 0 ≤ De ≤ 100 . 58 3.4 Dimensionless surface tension to viscosity ratios α∗ determined by the differential method (3.16) for Oh = 3:16;S = 0:25 and 0 ≤ De ≤ 100 plotted with dimensionless time t=tc throughout the initial viscous regime . 59 3.5 Evolutions of dimensionless capillary, viscous solvent, and elastic terms in the midfilament force balance (3.8) as functions of dimen- sionless time t=tc for Oh = 3:16;S = 0:25 and De = 0; 1; 10 and 100. 61 3.6 Dimensionless filament free surface profiles R(z) at several times for Oh = 3:16;S = 0:25 and (a) De = 0 (a Newtonian limit with µ = µ0); (b) De =100 .............................. 62 3.7 Dimensionless (a) midfilament evolution R=Rp; and (b) differential ∗ method results for α (3.16) as a function of dimensionless time, t=tc for Oh = 3:16; De = 94:9 and 0 ≤ S ≤ 1 throughout the initial viscous phase . 65 3.8 Evolutions of dimensionless capillary, viscous solvent, and elastic terms in the midfilament force balance (3.8) as functions of dimen- sionless time t=tc for Oh = 3:16; De = 100 and S = 0; 0:25; 0:75; 0:95 and 1. 66 3.9 Dimensionless (a) midfilament evolution R=Rp; and (b) differential ∗ method results for α (3.16) as functions of dimensionless time t=tc for Oh = 0:002;S = 0:98 and De = 0; 1; 10; and 100 . 67 3.10 Evolutions of dimensionless capillary, viscous solvent, and elastic terms in the midfilament force balance (3.8) as functions of dimen- sionless time t=tc for Oh = 0:002;S = 0:98 and De = 0; 1; 10; and 100. 68 viii 3.11 Dimensionless filament free surface profiles R(z) for Oh = 0:002;S = 0:98; and 0 ≤ De ≤ 100 . 69 3.12 Dimensionless (a) midfilament evolution R=Rp; and (b) differential ∗ method results for α (3.16) as functions of dimensionless time t=tc for Oh = 0:002; De = 100 and 0 ≤ S ≤ 1 ............... 70 3.13 Evolutions of dimensionless capillary, viscous solvent, and elastic terms in the midfilament force balance (3.8) as functions of dimen- sionless time t=tc for Oh = 0:002; De = 100 and S = 0; 0:25; 0:75; 0:98 and 1. 72 4.1 Dimensionless filament midpoint evolutions R=Rp for saliva filaments after imposed strains of Lf =L0 = 2:33 and Lf =L0 = 2:66 (inset) plotted with dimensional time t..................... 78 4.2 (a) Dimensionless velocity Vp (4.2) applied at the boundaries to model an approximate step-strain; (b) the corresponding dimensionless spa- tial domain length L (4.3) .
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