UNIVERSITY OF CINCINNATI Date:___________________ I, _________________________________________________________, hereby submit this work as part of the requirements for the degree of: in: It is entitled: This work and its defense approved by: Chair: _______________________________ _______________________________ _______________________________ _______________________________ _______________________________ A Model for Dry- and Wet-Casting of Polymeric Membranes incorporating Convection due to Densification - Application to Macrovoid Formation by Hanyong Lee B.S. Yonsei University, Korea (ROK), 1996 M.S. Yonsei University, Korea (ROK), 2000 Committee Members: Dr. William B. Krantz (Chair) Dr. Sun-Tak Hwang (Co-chair) Dr. Chia-Chi Ho Dr. James E. Mark This thesis is submitted to the Faculty of the Research Committee at the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical Engineering in the year 2005. ABSTRACT The dry-casting process and the wet-casting process are two typical phase-inversion techniques for manufacturing synthetic polymeric membranes. Although extensive modeling studies have been done for both casting processes in order to achieve an optimization of a membrane recipe, all models developed heretofore allow for mass transfer only by diffusion. A proper model for membrane casting should incorporate both the diffusive and convective contributions to the mass transfer fluxes. Therefore, the objective of this thesis is the developments of a dry-casting model and a wet-casting model based on the fundamental and general approach to construct well-defined mass- transfer problems incorporating both convection and diffusion. This new more general approach produces well-defined description of wet- and dry-casting processes that are solvable with currently available PDE solvers and accurately describe the effects of density variation in the system. Non-equilibrium thermodynamics allows further generalization of this approach to multicomponent mass- transfer problems. The predictions of the dry-casting model developed with this general approach show much better agreement with experimental data in the literature for the CA/acetone/water system. The new wet-casting model predicts the presence of a metastable region in the casting solution depending on the initial thickness that is not predicted by model that incorporates only diffusive mass transfer. Low-gravity experiments using a newly developed membrane casting apparatus show that macrovoids are formed in the CA/acetone/water casting solution when a metastable region is predicted by the new wet-casting model. Furthermore, membrane casting experiments that incorporated surfactant in the precipitation bath reveal that macrovoid formation is strongly associated with the coalescence of microdoplets having a high surface energy in the metastable region of the casting solution. Therefore, both the experimental and modeling results support the coalescence-induced coalescence macrovoid formation mechanism. gÉ Åç ÑtÜxÇàá? `ç ÑtÜxÇàá@|Ç@Ätã? `ç ã|yx? TÇw gÉ Åç áÉÇá? VtàÉÇ tÇw UÜtÇwà _xx ACKNOWLEDGMENTS During all years I spent with Professor William B. Krantz and Professor Sun-Tak Hwang, they have served me as all the followings; advisors, guides, teachers, friends. The moment whenever I felt frustration, they were willing hands and gave me a very important advice for my life and for my research. Their encouragement and enthusiasm were the driving force to be what I am. Like guiding angels, they always stood at both sides of me and dragged me into the right place. I am really afraid to imagine how I was a stupid student to them. They also gave me eyes, ears, a brain and a heart to understand and to manage many cultural differences between U.S. and Korea. It was invaluable experience to learn how to manage my life from our perfect cultural spectrum from Americanized American (Professor Krantz) through Americanized Korean (Professor Hwang) to Koreanized Korean (me). They also gladly acted as the worst enemy for me. Whenever they felt my overexcitement possessed with a wrong idea, they make me frustrated without any hesitation and gave another chance to rethink from the beginning. Now I am possessed by their voices; ‘I completely agree on this, B.U.T…..’(Professor Krantz) and ‘NO!, IT IS WRONG’ (Professor Hwang). Their voices are ringing throughout my head automatically, whenever I am forcing to convince myself. However, I am deeply appreciating their intellectual and mental ‘torture’ to make me stronger. I already miss our enthusiastic discussion which, to anybody else, would look like a severe fighting. The financial support of this research was provided by NASA’s Office of Biological and Physical Sciences Research via Grant No. NAG3-2451. I would like to thank all the participants of NASA for their support of this project. Especially, I will never forget the greatest and also worst experience of flying around in front of dozens of people with an upset stomach in KC-135A low-G flight. Making the apparatus for low-G experiments was one of the challenges in this project. It would be impossible to build the excellent membrane-casting apparatus (MCA) without the great help of Dr. Paul W. Todd and Mr. Andy Kirk in Space Hardware Optimization Technology, Inc. I also would like to thank Dr. Robert L. Sani in University of Colorado at Boulder for his help to test our new idea of the MCA. I have to mention Dr. Alan R. Greenberg and Dr. Vivek P. Khare in University of Colorado at Boulder who gave me excellent advices on this project and helped to refresh Professor Krantz’s memory whenever needed. They also contributed many important advices to build FORTRAN programs. In spite of unstable stomach in low-G, Mr. Jeremiah Zartman and Mr. Chris S. Howard helped me a lot to conduct low-G experiment. My colleagues, Shaun Howard and Siladitya Ray Chaudhuri, made me happy in the lab no matter how hard and stressful things I have. I am sure that most of our chat was not constructive at all and the most subjects of our talking were not even close to our research. However, it was really nice feeling that I have two good friends who can gladly waste their time for my diversion in the lab. Also, I cannot forget to mention the nice discussions with Ray on our researches. These were really helpful to me. My friend, Yi-Chuan Chen, also contributed his time to cheer me up. I also remember the time spent on the group study with Shigao Cheng and Bo Sun. Joo-Youp Lee and Kyesang Yoo helped me a lot to accommodate myself to sudden change of my life. I also would like to thank Dr. Il Moon in Yonsei University at Korea and Seunghoon Lee, my friend, for their many good advices from Korea. Finally, I would like to thank my whole family; my parents, my wife’s parents, my wife and my sons. Their existence itself is the reason and the driving force of my life. They sacrificed many things for me to study. I cannot be too thankful for their love and confidence gave me. CONTENTS LIST OF TABLES…………………………………………………………………. 8 LIST OF FIGURES………………………………………………………………… 9 LIST OF SYMBOLS……………………………………………………………..... 21 CHAPTER I. GENERAL INTRODUCTION…………………………………………...... 26 1.1 Polymeric Membrane Industry…………………………………………. 26 1.2 Polymeric Membrane Formation………………………………………. 28 1.3 Research Challenges……………………………………………………. 32 1.4 Focus of This Research………………………………………………... 33 1.5 Organization of Thesis…………………………………………………. 36 II. CONVECTIVE TRANSPORT……………………………………………. 38 2.1 Scope of Chapter……………………………………………………….. 38 2.2 Introduction…………………………………………………………….. 39 2.3 Review of Prior Studies………………………………………………… 42 2.3.1 Diffusion………………………………………………………….. 42 2.3.2 Convection……………………………………………………….. 43 2.4 Motivation for This Study……………………………………………… 44 1 2.5 Multi-component Convection-Diffusion Mass-Transfer Problem…….. 45 2.5.1 Mass Balance for Individual Fluxes……………………………... 45 2.5.2 Equation-of-State………………………………………………… 47 2.5.3 Mass-Average Velocity…………………………………………. 47 2.5.4 Modified Peclet Number………………………………………… 49 2.5.5 Example Study 1: Rapid Unsteady-State Evaporation………….. 50 2.5.5.1 System of Interest…………………………………………. 50 2.5.5.2 Derivation of Model Equations…………………………… 53 2.5.5.3 Solution Methodology…………………………………….. 56 2.5.5.4 Results and Discussion……………………………………. 58 2.6 Generalized Flux Equation from Non-equilibrium Thermodynamics……………………………………. 68 2.6.1 Flux Equation……………………………………………………. 68 2.6.2 Example Study 2: Steady-State Binary Gas Permeation through Membrane………………………………………………………... 70 2.6.2.1 System of Interest………………………………………….. 70 2.6.2.2 Derivation of Model Equations……………………………. 73 2.6.2.3 Mass-Average Velocity and Modified Peclet Number……. 76 2.7 Summary………………………………………………………………. 77 III. DEVELOPMENT OF THE DRY-CASTING MODEL INCORPORATING CONVECTIVE TRANSPORT……………………………………………. 78 2 3.1 Scope of Chapter………………………………………………………. 78 3.2 Introduction……………………………………………………………. 79 3.3 Review of Prior Studies……………………………………………….. 80 3.4 Motivation of This Study……………………………………………… 81 3.5 Model Development…………………………………………………… 82 3.5.1 System of Interest……………………………………………….. 82 3.5.2 Thermodynamic Model………………………………………….. 84 3.5.3 Mass-Transport Model in Casting solution……………………… 85 3.5.3.1 Species-Balance Equations………………………………… 85 3.5.3.2 Equation-of-State………………………………………….. 86 3.5.3.3 Multicomponent Diffusive Flux Equations………………... 87 3.5.3.4 Mass-Average Velocity……………………………………. 88 3.5.3.5 Final Governing Equations………………………………… 90 3.5.3.6 Initial and Boundary Conditions……………………………