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Investigation of Fluid Wicking Behavior in Micro- Channels and Porous Media by Direct Numerical Simulation

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Investigation of Fluid Wicking Behavior in Micro- Channels and Porous Media by Direct Numerical Simulation Investigation of Fluid Wicking Behavior in Micro- Channels and Porous Media by Direct Numerical Simulation Ph.D. Dissertation By An Fu Master of Science, Mechanical Engineering, University of Cincinnati, 2016 April. 12th, 2019 Committee Chair: Dr. Milind Jog 1 A B S T R A C T Capillary transport phenomenon in porous media can be found in numerous natural processes and industrial applications such as inkjet printing, filtration, and enhanced oil recovery. In many of these applications, fluid penetration can be categorized into two orientations, viz., unidirectional (linear) and radial. In this thesis, the wicking process for both orientations has been investigated. Direct numerical simulation with Volume-of-Fluid (VOF) method has been implemented at pore scale (micro-scale simulation) to solve the transient governing equations, and global properties such as meniscus displacement and capillary pressure have been calculated to investigate macroscopic spontaneous imbibition (wicking) process. Linear fluid penetration kinetics within the viscous stage is first considered to investigate if the pore size and distribution are contributing factors which shift the overall kinetics, and how interface mobility is influenced by geometry layout. Various cases are simulated with increasing geometric complexity; from simple pore space connection with uniform pore size to complicated connection with random pore sizes. Average meniscus location, capillary pressure and other global variables are examined. The results indicate that within the viscous regime, the Lucas-Washburn behavior is valid in homogeneous porous media, even with random pore size and connection. However, in non-homogeneous structure, the wicking kinetic does depend on the distribution of pore spaces, and Lucas-Washburn equation fails to describe the linear macroscopic capillarity. Next, capillary action in radial porous media is examined which is relevant in applications such as oil liquid drop absorption on tissues, ink penetrating thin paper, and blood spreading on band-aid, etc. The wicking dynamic in radial geometry with different pore complexity (variation i of pore size and connection) has been studied. To investigate the effect of pore size and connection on macroscopic wicking, meniscus location and capillary pressure have been analyzed. It is found that the slower kinetics underlying radial capillarity is due to an increasing meniscus surface area while the penetration takes place. Also, fluid wicking dynamic in homogeneous structure under viscous regime can be fitted into one curve, which means that the variations in pore size and connections do not shift the macroscopic wicking rate. The last part of this research focuses on non-Newtonian fluid dynamics within porous media. Different micro-geometries are considered to understand shear-thinning fluid wicking. To overcome the limitations of the power-law model, which over-estimates viscosity at low shear rate region, truncated power-law model is implemented. The result reveals that the interface has different mobility in each geometric configuration compared to Newtonian fluids. With changing pore size the shear rate experienced by the fluid varies and that alters its effective viscosity. As a result, the local pore geometry has substantial impact on the wicking kinetic of shear thinning fluids. ii Special dedication to my parents, family and friends iii Acknowledgements I would like to express my genuine appreciation to Dr. Milind Jog. It has been more than five years since Dr. Jog accepted me as his student on Jan, 2014 and Dr. Jog helps me to overcome every research obstacle. Dr. Jog made it possible for me to pursue my research interest in Fluid Mechanics. Here, many thanks! I also would like to thank Dr. Ken Comer and Dr. Nikhil Palakurthi for their valuable thought and input regarding to every aspect of my research. More importantly, I really enjoy our collaboration and every meeting because I learn a lot from it. Special thanks to Dr. Manglik, my committee member for both of my M.S and Ph.D. My research work becomes fresher under your advisory. I also very appreciate my committee member Dr. Je-Heyong Bahk and Dr. Lilit Yeghiazarian for every generous help and insight regarding to my research work. You make my Ph.D. journey more special and memorable. Thanks. I owe a special debt of gratitude to UC Simulation Center and The Procter and Gamble Company. My research is purely built from these platforms. UCSC and P&G not only financially support me along my Ph.D. career, they also generously offer me computational resources to perform my simulation work. Thank you Fred, our site leader, for your support! Thank you Bernie and Melissa, for being our great directors at Sim Center. Thanks to all my friend and fellows, in UCSC and TFTPL. iv Table of Contents Chapter 1 INTRODUCTION .......................................................................................................... 1 1.1 Porous Medium: Applications ............................................................................................................ 1 1.2 Aims and Scope of This Study ............................................................................................................ 2 1.3 Thesis Layout ...................................................................................................................................... 4 Chapter 2 BACKGROUND-CAPILLARY TRANSPORT............................................................ 5 2.1 Fundamentals of Capillary Action ...................................................................................................... 5 2.2 Capillary Tube .................................................................................................................................... 6 2.2.1 Overview ...................................................................................................................................... 6 2.2.2 Governing Equation for Flow in a Capillary................................................................................ 7 2.3 Porous Media ...................................................................................................................................... 9 2.3.1 Linear Capillarity ......................................................................................................................... 9 2.3.2 Radial Capillarity ....................................................................................................................... 11 2.3.3 Numerical Simulation Approach................................................................................................ 13 2.4 Non-Newtonian Fluid Wicking ......................................................................................................... 13 Chapter 3 TOOL VALIDATION ................................................................................................. 15 3.1 Numerical Simulation Approach ...................................................................................................... 15 3.2 Flow Calculation and VOF Method .................................................................................................. 16 3.2.1 Governing Equations.................................................................................................................. 16 3.2.2 Volume of Fluid (VOF) Method ................................................................................................ 17 v 3.2.3 Initial and Boundary Condition .................................................................................................. 19 3.2.4 Computational Procedure ........................................................................................................... 20 3.3 Geometry........................................................................................................................................... 20 3.4 Computational Grid Generation ........................................................................................................ 22 3.5 Validation Result .............................................................................................................................. 26 3.6 Conclusion ........................................................................................................................................ 31 Chapter 4 LINEAR CAPILLARITY ............................................................................................ 33 4.1 Background ....................................................................................................................................... 33 4.2 Methodology ..................................................................................................................................... 36 4.2.1 3-D Porous Media ...................................................................................................................... 37 4.2.2 Simulation & Boundary Conditions ........................................................................................... 38 4.2.3 Computational Grid & Grid Convergence ................................................................................. 39 4.3 Results and Discussion ..................................................................................................................... 43 4.3.1 Parallel Plate .............................................................................................................................. 43 4.3.2 Converging & Diverging Tube .................................................................................................
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