Purdue University Purdue e-Pubs Open Access Dissertations Theses and Dissertations January 2014 On the theory of Brownian aggregation in colloidal dispersions Aniruddha Kelkar Purdue University Follow this and additional works at: https://docs.lib.purdue.edu/open_access_dissertations Recommended Citation Kelkar, Aniruddha, "On the theory of Brownian aggregation in colloidal dispersions" (2014). Open Access Dissertations. 1072. https://docs.lib.purdue.edu/open_access_dissertations/1072 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. !"#$"%&'()*++,'-+!.' 30 /0&123&# 08 414 5' PURDUE UNIVERSITY GRADUATE SCHOOL Thesis/Dissertation Acceptance 6*23'23'%+')&!%278'%*"%'%*&'%*&3234#233&!%"%2+9':!&:"!&#' ;8' Aniruddha V. Kelkar <9%2%,&#''ON THE THEORY OF BROWNIAN AGGREGATION IN COLLOIDAL DISPERSIONS ' Doctor of Philosophy -+!'%*&'#&=!&&'+7''' >3'"::!+1&#'?8'%*&'729",'&@".2929=')+..2%%&&A' Elias I. Franses 'David ' S. Corti Osman A. Basaran Chongli Yuan Carl Wassgren Jr. To the best of my knowledge and as understood by the student in the Thesis/Dissertation Agreement, Publication Delay, and Certification/Disclaimer (Graduate School Form 32), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy on Integrity in Research” and the use of ' copyrighted material. David S. Corti B::!+1&#'?8'C"D+!'E!+7&33+!/35A'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' Elias I. Franses ''''''''FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' 'B::!+1&#'?8A John A. Morgan 09/16/2014 G&"#'+7'%*&' Department !"#$"%&'E!+=!".' '''H"%& ON THE THEORY OF BROWNIAN AGGREGATION IN COLLOIDAL DISPERSIONS A Dissertation Submitted to the Faculty of Purdue University by Aniruddha V. Kelkar In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2014 Purdue University West Lafayette, Indiana ii To those who came before and to those that brought me here. iii ACKNOWLEDGMENTS “If I have seen a little further, it is by standing on the shoulders of Giants.” - Sir Isaac Newton. The scientific tradition, having shunned superstition and mysticism, has gone on to shape human progress and will continue to do so. It has imbued humility and optimism, and piqued in me that innate curiosity that characterizes the human condition. I am most grateful to my PhD advisers, Profs. David S. Corti and Elias I. Franses, for inducting me into this rich institution. Their patience, guidance, and constant encouragement made working under them a pleasure. I was given the freedom, other graduate students pine for, to pursue my interests both in and outside of research. They provided me with an environment conducive to growth as a person and a researcher. Having these nurturing educators and thorough gentlemen in my corner, fills me with confidence. The coursework in graduate school has been challenging. I thoroughly enjoyed the Advanced Thermodynamics and Statistical Thermodynamics courses taught by Prof. Corti, and the Transport Phenomena course taught by Prof. Ramkrishna. I have also benefited tremendously from courses taught by Profs. Thomson, Morgan, Won, Lit- ster, Kais (Chemistry), and Lynall (Krannert School of Management). Some of these courses — Metabolic Engineering, Quantum Computing & Information, and Consult- ing Methods, were not related to my research area, but helped broaden my perspective and have ultimately proven to be useful. I must also thank Prof. Boudouris, who kindly agreed to mentor my team in several business plan competitions. His drive and attention to detail are superlative. I am grateful to my committee members — Profs. Basaran, Wassgren, and Yuan, for their time and suggestions. iv I owe thanks to my fellow research group members — Dr. Mark Uline, Dr. Ko- rosh Torabi, Dr. Jiannan Dong, Betty Yang, Sree Panuganty, and Qiufei Hu. Jiannan helped me immensely in my early days and was patient with me during my exper- imental training. Mark was very generous with his time and helped me with the density functional theory calculations. I have enjoyed the many research discussions I have had with Betty, and it has been a pleasure to work on some collaborative projects. Finally, I have had the opportunity to mentor Sree and Qiufei, who both joined the group as undergraduates. Their inquisitiveness, diligence, and enthusiasm make them ideal students. My life as a graduate student was made immensely easy by the excellent staff members at the School of Chemical Engineering. I would be remiss if I did not acknowledge the role of Deb Bowman, whose patience, knowledge, and efficiency, made stepping into her office a pleasure. I have always found a helping hand in the business office and I owe thanks to Amy Hayden and Courtney Eddy, in particular. I am also grateful to Cristina Farmus, Jeff Valley, Jason Davenport, and Catherine Field for their assistance at various times during the past four years. I gratefully acknowledge Chevron Energy Technology Company (ETC) for spon- soring this research project. Interactions with the Flow Assurance & Production Systems group were invaluable; in particular, Dr. Hariprasad J. Subramani’s assis- tance on both technical and professional fronts is highly appreciated. Additionally, I had the opportunity to spend the summer in 2013 as an intern at the Chevron ETC’s Richmond Technology Center, CA. I have learnt tremendously from this experience and would like to thank my supervisors — Drs. Alice He and Lin Li, and the entire Process & Products R&D team. Whatever flaws exist in the Indian education system, my experience at ICT, Mum- bai was largely world-class. I am ever grateful to Profs. A. B. Pandit, S. S. Bhagwat, V. G. Gaikar, V. V. Mahajani, A. W. Patwardhan and G. D. Yadav. They taught me my craft and provided me with opportunities that have allowed me to excel. Several v friendships made in those days have stood the test of time — the reunions with my classmates have been thoroughly enjoyable. Life as a graduate student can at times be hard but I was lucky to find solace in the company of the kindred. I could count on the guidance and friendship of senior graduate students — Vishesh, Anirudh (Andy), Krishna, Mayank, Meenesh, Dhairya, Harsha, Ranjita, Kartik, and Jay. Atish, Anshu, Anuj, and Kaiwalya made the journey through grad school with me, and their friendship has made it enjoyable. I am also thankful to Dharik, Vinod, Sumeet, Chinmay, Gautam, Anuradha, Kavitha, Tej, Pritish, Shankali, Rohit, Agnes, and Ravi. Sharing an office with Anand and Nicholas was always exciting — full of conversations both intellectual and trivial. Anand played the roles of mentor and friend ably, and I have learned tremendously from his experiences. It was at ICT, seven years ago that I first met Prerna. I am grateful to her for her love, patience, and encouragement. I always looked forward to her visits, and especially in the cold of winter, to escape to Tampa to meet her. She is also duly acknowledged here for helping me improve the quality of my figures. Outside of fleeting visits, I have been away from my family for the past four years. I owe thanks to them all for their unconditional love, support, and affection. The few weeks of vacation that I spent with them, made the midwest winters tolerable. My grandmother, Smt. Sunita Kulkarni, is my hero, she is a testament to the indefatigable human spirit and she inspires me every day. I fondly remember my late grandmother, Smt. Padma Kelkar, who will always be missed. I am grateful to my aunt, Vandana Kulkarni, who taught me that discipline and dedication go a long way. She shaped my taste in music and football, and has always had more confidence in me than myself. Like the north star to a weary sailor, my parents, Sangita (Ammu) and Vasudeo (Baba) have always been there to guide and support me. They have worked tirelessly to make sure that I had the best education. It is impossible to express my gratitude toward them; I owe them everything. vi TABLE OF CONTENTS Page LIST OF TABLES ................................ ix LIST OF FIGURES ............................... x ABSTRACT ................................... xxi 1 Thesis Overview and Chapter Synopsis ................... 1 1.1 Motivation and Summary ....................... 1 1.2 Thesis Goals ............................... 5 1.3 Synopsis ................................. 6 References ................................ 22 2 Review of the current understanding of Colloidal Dispersion Stability . 26 2.1 Abstract ................................. 26 2.2 Introduction ............................... 27 2.2.1 Interparticle potential energy functions ............ 30 2.2.2 Hydrodynamic interactions ................... 33 2.2.3 Aggregate Structure ...................... 36 2.3 The Smoluchowski model for Brownian aggregation of hard spheres 37 2.4 The Fuchs-Smoluchowski model for Brownian aggregation of interact- ing spheres ................................ 41 2.5 Population balances for colloidal dispersions ............. 44 2.6 Models for Orthokinetic aggregation .................. 47 2.7 Effects of gravity on colloidal dispersions ............... 49 2.8 Brownian dynamics simulations of colloidal dispersions ....... 53 2.9 Experimental methods for studies on colloidal dispersion stability . 59 References ................................ 61 3 Unsteady-State Effects in Brownian Aggregation Kinetics of Hard Spheres 67 3.1 Abstract ................................. 67 3.2 Introduction ............................... 68 3.3 Theory .................................