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University of Kentucky UKnowledge Theses and Dissertations--Physics and Astronomy Physics and Astronomy 2021 Predicting Material Properties: Applications of Multi-Scale Multiphysics Numerical Modeling to Transport Problems in Biochemical Systems and Chemical Process Engineering Tom Pace University of Kentucky, [email protected] Author ORCID Identifier: https://orcid.org/0000-0003-3364-5123 Digital Object Identifier: https://doi.org/10.13023/etd.2021.162 Right click to open a feedback form in a new tab to let us know how this document benefits ou.y Recommended Citation Pace, Tom, "Predicting Material Properties: Applications of Multi-Scale Multiphysics Numerical Modeling to Transport Problems in Biochemical Systems and Chemical Process Engineering" (2021). Theses and Dissertations--Physics and Astronomy. 84. https://uknowledge.uky.edu/physastron_etds/84 This Doctoral Dissertation is brought to you for free and open access by the Physics and Astronomy at UKnowledge. It has been accepted for inclusion in Theses and Dissertations--Physics and Astronomy by an authorized administrator of UKnowledge. For more information, please contact [email protected]. STUDENT AGREEMENT: I represent that my thesis or dissertation and abstract are my original work. Proper attribution has been given to all outside sources. I understand that I am solely responsible for obtaining any needed copyright permissions. I have obtained needed written permission statement(s) from the owner(s) of each third-party copyrighted matter to be included in my work, allowing electronic distribution (if such use is not permitted by the fair use doctrine) which will be submitted to UKnowledge as Additional File. I hereby grant to The University of Kentucky and its agents the irrevocable, non-exclusive, and royalty-free license to archive and make accessible my work in whole or in part in all forms of media, now or hereafter known. I agree that the document mentioned above may be made available immediately for worldwide access unless an embargo applies. I retain all other ownership rights to the copyright of my work. I also retain the right to use in future works (such as articles or books) all or part of my work. I understand that I am free to register the copyright to my work. REVIEW, APPROVAL AND ACCEPTANCE The document mentioned above has been reviewed and accepted by the student’s advisor, on behalf of the advisory committee, and by the Director of Graduate Studies (DGS), on behalf of the program; we verify that this is the final, approved version of the student’s thesis including all changes required by the advisory committee. The undersigned agree to abide by the statements above. Tom Pace, Student Dr. Peter M. Kekenes-Huskey, Major Professor Dr. Christopher B. Crawford, Director of Graduate Studies PREDICTING MATERIAL PROPERTIES: APPLICATIONS OF MULTI-SCALE MULTIPHYSICS NUMERICAL MODELING TO TRANSPORT PROBLEMS IN BIOCHEMICAL SYSTEMS AND CHEMICAL PROCESS ENGINEERING DISSERTATION A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the College of Arts and Sciences at the University of Kentucky By Thomas G. Pace Lexington, Kentucky Co-Directors: Dr. Peter M. Kekenes-Huskey, Associate Professor of Cell and Molecular Physiology and Dr. Ribhu K. Kaul, Professor of Physics and Astronomy Lexington, Kentucky Copyright © Thomas G. Pace 2021 https://orcid.org/0000-0003-3364-5123 ABSTRACT OF DISSERTATION PREDICTING MATERIAL PROPERTIES: APPLICATIONS OF MULTI-SCALE MULTIPHYSICS NUMERICAL MODELING TO TRANSPORT PROBLEMS IN BIOCHEMICAL SYSTEMS AND CHEMICAL PROCESS ENGINEERING Material properties are used in a wide variety of theoretical models of material be- havior. Descriptive properties quantify the nature, structure, or composition of the material. Behavioral properties quantify the response of the material to an imposed condition. The central question of this work concerns the prediction of behavioral properties from previously determined descriptive properties through hierarchical multi-scale, multiphysics models implemented as numerical simulations. Applica- tions covered focus on mass transport models, including sequential enzyme-catalyzed reactions in systems biology, and an industrial chemical process in a common reaction medium. KEYWORDS: Finite Element Method, Homogenization, Transport, Zeolites Thomas G. Pace May 12, 2021 PREDICTING MATERIAL PROPERTIES: APPLICATIONS OF MULTI-SCALE MULTIPHYSICS NUMERICAL MODELING TO TRANSPORT PROBLEMS IN BIOCHEMICAL SYSTEMS AND CHEMICAL PROCESS ENGINEERING By Thomas G. Pace Peter M. Kekenes-Huskey Co-Director of Dissertation Ribhu K. Kaul Co-Director of Dissertation Christopher B. Crawford Director of Graduate Studies May 12, 2021 and lean not on your own understanding ACKNOWLEDGMENTS I thank Dr. Pete Kekenes-Huskey for his support and guidance, for introducing me to the area of multiphysics models in mass transport systems, for helping me learn to the technique of Molecular Dynamics, for introducing me to asymptotic homogenization, and for the opportunity to use and further develop my skills with the Finite Element Method. I also thank him for his patience and understanding during the time of our work together. I thank Dr. Ribhu Kaul for his support and encouragement over the years, through the many ups and downs of my doctoral studies, and his willingness to help me work through the complexity of my situation as a returning student. I thank the other members of my committee for their helpful comments and sug- gestions. This includes Dr. Douglas Strachan from Physics, Dr. Jason DeRouchey from Chemistry, and Dr. Christoph Brehm from Mechanical Engineering. I thank Dr. Kate Ponto from Mathematics for her participation as the committee member appointed by the Graduate School. I thank my fellow students Dylan Colli and Hadi Rahmaninejad for their con- tributions to our mutual projects. I am also grateful to the other members of our research group for beneficial conversations and camaraderie. The Director of Graduate Studies, Dr. Christopher Crawford, also fielded many questions about the requirements of the doctoral program with great patience. I thank him for doing the extra work to understand and explain the rules that apply in unusual situations like mine. I know that I am not the only student for whom he has been a stabilizing force during difficult times. I thank also Dr. David Singh and Dr. Madhu Menon. Along with Dr. Ribhu Kaul, they helped me gain experience in Density Functional Theory. Even though iii my experience with Density Functional Theory is mostly not discussed herein, I hope to return to problems of electronic structure and computational chemistry at some point in my career. I also thank my Stantec supervisors, Greg Yankey and Dr. Alan Rauch, for their support and patience during the eight years I was a part-time graduate student and part-time employee. I am also grateful to my other colleagues at Stantec for their willingness to work around my schedule. Most of this thesis was compiled during the COVID-19 pandemic. Accordingly, I wish to thank all the workers in health care and other occupations who faced the greatest risk to their own safety during this time. I also thank Kentucky’s Governor, Andy Beshear, for his courageous leadership throughout this ongoing crisis. I am exceptionally grateful to my wife and children, who have made many sacri- fices, over many years, so that this could be possible. I cannot describe how important to me their encouragement and support have been. I would also like to thank my parents, brothers, and extended family for their support as well. Above all, I am grateful to that boundless and eternal Power that once created and still sustains all things, that is stronger even in defeat than evil is even in triumph, and that is available in each of us if sought. One final acknowledgement: the work you are now reading is certainly an imper- fect, incomplete one. As in all endeavors, I have learned things in doing this work that I wish I had known when I first began it. While this document marks the end of my education in an official capacity, learning truly is a lifelong commitment. In this spirit, whatever the future may hold for me, I hope that I may always be considered a student. iv TABLE OF CONTENTS Acknowledgments . iii Table of Contents . v List of Tables . vii List of Figures . viii Chapter 1 Introduction . 1 1.1 Objective, Organization, and Notation . 1 1.2 Multi-scale Models . 2 1.3 Multiphysics Models . 3 1.4 Heat and Diffusion Equations . 4 1.5 Fickian Diffusion . 6 1.6 The Nernst-Planck and Smoluchowski Equations . 7 1.7 Diffusion Coefficient . 8 1.8 Other Diffusion Models . 11 Chapter 2 Principal Methods . 14 2.1 Overview . 14 2.2 Electronic Structure Calculations . 14 2.3 Molecular Simulations . 17 2.4 The Finite Element Method . 19 2.5 Periodic Homogenization . 21 2.6 Stochastic Homogenization . 23 Chapter 3 Sequential Enzymes in a Nanoscale Domain . 26 3.1 Background . 26 3.2 Geometry of a Nanoporous Membrane . 26 3.3 Fickian Diffusion in a Nanoscale Pore . 29 3.4 Electro-diffusion in a Nanoscale Pore . 32 3.5 Diffusion-Limited Reaction Kinetics of a Single Enzyme . 39 3.6 Diffusion-Limited Kinetics of Sequential Enzyme-Catalyzed Reactions 41 3.7 Discussion and Conclusion . 43 Chapter 4 Transport Properties of Zeolites and Other Porous Silicates . 45 4.1 Background . 45 4.2 Theoretical Model . 46 4.3 Silicate Channel System . 48 4.4 Methods . 50 4.5 Validation Analyses for Molecular Simulations . 53 v 4.6 Validation Analyses for Homogenization of Fickian Diffusion . 57 4.7 Validation Analyses for the Homogenized Smoluchowski Equation . 59 4.8 Results of Homogenization for Zeolites . 60 4.9 Results of Molecular Simulations in Silicate Channel . 62 4.10 Effective Diffusion Coefficients for the Silicate Channel . 69 4.11 Discussion and Conclusion . 71 Chapter 5 Summary, Conclusions, and Speculation . 73 5.1 Summary and Review: Successes and Limitations of the Methods .

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