Scholars' Mine Masters Theses Student Theses and Dissertations Summer 2018 Numerical modeling of capillary-driven flow in open microchannels: An implication of optimized wicking fabric design Mehrad Gholizadeh Ansari Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Environmental Engineering Commons, Mathematics Commons, and the Mechanical Engineering Commons Department: Recommended Citation Ansari, Mehrad Gholizadeh, "Numerical modeling of capillary-driven flow in open microchannels: An implication of optimized wicking fabric design" (2018). Masters Theses. 7792. https://scholarsmine.mst.edu/masters_theses/7792 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. NUMERICAL MODELING OF CAPILLARY-DRIVEN FLOW IN OPEN MICROCHANNELS: AN IMPLICATION OF OPTIMIZED WICKING FABRIC DESIGN by MEHRAD GHOLIZADEH ANSARI A THESIS Presented to the Faculty of the Graduate School of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE IN ENVIRONMENTAL ENGINEERING 2018 Approved by Dr. Wen Deng, Advisor Dr. Joseph Smith Dr. Jianmin Wang Dr. Xiong Zhang 2018 Mehrad Gholizadeh Ansari All Rights Reserved iii PUBLICATION THESIS OPTION This thesis has been formatted using the publication option: Paper I, pages 16-52, are intended for submission to the Journal of Computational Physics. iv ABSTRACT The use of microfluidics to transfer fluids without applying any exterior energy source is a promising technology in different fields of science and engineering due to their compactness, simplicity and cost-effective design. In geotechnical engineering, to increase the soil’s strength, hydrophilic wicking fibers as type of microfluidics have been employed to transport and drain water out of soil spontaneously by taking advantage of natural capillary force without using any pumps or other auxiliary devices. The objective of this study is to understand the scientific mechanisms of the capability for wicking fiber to drain both gravity and capillary water out of soil fills. In this work, wicking fibers were numerically modeled as open microchannels. The effect of the geometry and wettability on the spontaneous flow were analyzed. A 3D computational fluid dynamics-based model was developed to predict the transient movement of the meniscus in microchannels of different geometries. The Volume-of-Fluid (VOF) method was employed along with an in-house developed algorithm to refine the grid only at the air-water interface to reduce the computational effort. Analytical and numerical criteria were derived to determine the critical contact angle for spontaneous flow in different geometry open microchannels. It was found that the aspect ratio and channel geometry have a significant effect on the water filling velocity and mass flowrate. The study was extended to water drainage from unsaturated soils and the minimum negative inlet pressure which represents the maximum soil suction was determined numerically for spontaneous flow for different microchannel geometry. Results of this study can provide an implication in the design of wicking fibers and other microfluidic systems. v ACKNOWLEDGMENTS I would like to express my sincere gratitude to my advisor, Dr. Wen Deng, for his guidance, patience, and support. My special word of thanks goes to my committee members, Dr. Joseph Smith, Dr. Jianmin Wang and Dr. Xiong Zhang for their support of this research. I express my heart-felt gratitude to Dr. Joseph Smith for granting me access to the STAR-CCM+ license servers. His constant guidance, cooperation, motivation and support have always kept me going ahead. I owe my deepest gratitude towards my family, Farimah, Hamid and Mahta for their eternal support and understanding of my goals and aspirations. Their infallible love and support has always been my strength. A special thanks to my friends, Kiyavash, Kiarash, Behrouz and Elieh and all the other Amoos for their love, motivation and affection. vi TABLE OF CONTENTS Page PUBLICATION THESIS OPTION ............................................................................... iii ABSTRACT ................................................................................................................... iv ACKNOWLEDGMENTS ............................................................................................... v LIST OF FIGURES ...................................................................................................... viii LIST OF TABLES ........................................................................................................... x NOMENCLATURE ....................................................................................................... xi SECTION 1. INTRODUCTION .................................................................................................... 1 1.1 APPLICATIONS ............................................................................................. 1 1.2 SURFACE TENSION ..................................................................................... 5 1.3 YOUNG-LAPLACE LAW ............................................................................. 6 1.4 DIMENSIONLESS NUMBERS ..................................................................... 7 1.5 OBJECTIVES ................................................................................................. 8 2. METHODOLOGY ................................................................................................. 10 2.1 ADAPTIVE GRID REFINEMENT .............................................................. 11 2.2 ADAPTIVE TIME STEP .............................................................................. 14 PAPER I I. NUMERICAL MODELING OF CAPILLARY-DRIVEN FLOW IN OPEN MICROCHANNELS ........................................................ 16 ABSTRACT ........................................................................................................... 16 1. INTRODUCTION .......................................................................................... 17 vii 1.1 MOTIVATION ...................................................................................... 17 1.2 BACKGROUND ................................................................................... 17 1.3 SPONTANEOUS CAPILLARY-DRIVEN FLOW .............................. 22 2. NUMERICAL ANALYSIS OF CAPILLARY-DRIVEN FLOW .................. 26 2.1 GOVERNING EQUATIONS ................................................................ 26 2.2 DIFFERENCING SCHEMES ............................................................... 29 2.3 MODEL VALIDATION ....................................................................... 32 3. RESULTS AND DISCUSSION ..................................................................... 34 3.1 SCF CRITERIA ..................................................................................... 34 3.2 MOBILITY PARAMETER ................................................................... 36 3.3 NEGATIVE INLET PRESSURE .......................................................... 43 4. CONCLUSIONS ........................................................................................... 48 REFERENCES ....................................................................................................... 49 SECTION 3. CONCLUSIONS .................................................................................................... 53 4. FUTURE WORK ................................................................................................... 54 APPENDIX .................................................................................................................. 55 REFERENCES .............................................................................................................. 71 VITA ............................................................................................................................. 73 viii LIST OF FIGURES SECTION Page Figure 1.1. Blood collection device for Point Of Care Testing (POCT) [3]. ...................... 1 Figure 1.2. Schematic design of a self-pumping fuel cell[4]. ............................................. 2 Figure 1.3. Mechanism of energy transfer in a heat pipe[7]. .............................................. 3 Figure 1.4. Hydrophilic wicking fibers removing water from soil[10]. ............................. 4 Figure 1.5. Wicking fabric application to drain water from a road embankment. .............. 5 Figure 1.6. Shape equilibrium of a liquid droplet (L) on a solid surface (S), surrounded by the gas (G)................................................................................. 5 Figure 1.7. Schematic of the minimum and maximum principal osculating circle radius of the curvature at the interface [13]. ........................................... 7 Figure 2.1. Computational grid in an open circular microchannel. .................................. 12 Figure 2.2. Adaptive grid refinement algorithm. .............................................................. 13 Figure 2.3. Adaptive time step algorithm based on the maximum Co number in the computational domain. .......................................................................... 15 PAPER I Figure 1. Contact angle