Thermal Diffusion Shock Waves in a Linear Temperature Field and Comparison of Ultrasonic Distillation to Sparging of Liquid Mixtures by Hyeyun Jung M.Sc., Brown University 2007 B.Sc., Seoul National University 2004 A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Physics at Brown University PROVIDENCE, RHODE ISLAND May 2012 © Copyright 2012 by Hyeyun Jung This dissertation by Hyeyun Jung is accepted in its present form by The Department of Physics as satisfying the dissertation requirement for the degree of Doctor of Philosophy. Date Gerald Diebold, Ph.D., Advisor Recommended to the Graduate Council Date James Valles, Ph.D., Reader Date Xinsheng Sean Ling, Ph.D., Reader Approved by the Graduate Council Date Peter M. Weber, Dean of the Graduate School iii Vita Hyeyun Jung was born on November 29, 1980 in Daegu, Republic of Korea. She com- pleted her secondary education at Wonhwa Girls High School in Daegu in February of 1999. She then attended Seoul National University. She obtained a Bachelor of Science in Chemical Engineering and Physics in February of 2004. In September 2004, she began graduate studies in the Department of Physics at Brown University. She carried out her doctoral research under the supervision of Dr. Gerald J. Diebold. Her publications include: 1. Hyeyun Jung, Vitaly Gusev, Hyoungsu Baek, Yaqi Wang, and Gerald J. Diebold, "Ludwig-Soret Effect in a Linear Temperature Field: Theory and Experiments for Distributions at Long Times", Physics Letters A 375(19), 1917-1920, 2011 2. Hye Yun Jung, Han Jung Park, Joseph M. Calo and Gerald J. Diebold, "Com- parison of Ultrasonic Distillation to Sparging of Liquid Mixtures", Analytical Chemistry 82, 10090-10094, 2010 iv Acknowledgements I would like to especially thank my thesis advisor Prof. Gerald J. Diebold for his kind guidance during my graduate study. He has patiently waited for me until I learned how to do research and supported me in every aspect of my research. He has given me great opportunities to carry out a variety of exciting research projects in his group. From him, I learned how fun and exciting doing science can be, of his wide and deep insight in seeing scientific problems and how important it is not to lose a sense of humor and to smile while doing science. I also would like to thank Dr. Gusev E. Vitaly and Dr. Hyoungsu Baek for their collaboration in mathematics. My thanks also go to Ken Talbot and Tim Pimental in the machine shop since they helped me in making various experimental equipment. I am grateful for Alfred Tente for helping me to explore electronics. I won’t be able to forget your kind support, Al! I would like to thank Prof. John B. Marston for giving me an opportunity to work with him for one year before joining Dr. Diebold’s group. During this year, I could experience the depth and the beauty of theoretical physics. I also would like to thank Prof. James Valles and Prof. Xinsheng S. Ling for kindly serving on my thesis committee. v My labmates made my graduate life very enjoyable and more colorful. I thank Dr. Shougang Wang, Dr. Theron J. Hamilton, Dr. Guohua Cao, Dr. Clifford Frez, Dr. Cuong K. Nguyen, Dr. Hanjung Park, Binbin Wu, Yanan Liu, Katherine Phillips and Charles Beyrouthy for their friendship! I also would like to give many thanks to my postdoctoral advisor Dr. Christopher Endres for his kind consideration in allowing me to write a thesis while conducting research with him and the excellent Johns Hopkins research teams. I also would like to thank friends who helped my proofreading and who cannot be listed due to limited space and to give special thanks to Dr. Mark Smith for helping me to thoroughly proofread the second half of my thesis! I would like to give special thanks to Dr. Heekyoung Ko, Chunwoo Kim and Rozita Jalali who encouraged and supported me while I was writing my thesis. I appreciate everyone who helped directly or indirectly to get this work done. My most important acknowledgment is to my beloved family God has given me: my parents, grandmother, my three siblings, Yumi, Jiyun and Minyoon, and brother- in-law Junho and my nephew and niece Junghyun and Jungwon, who have filled my life with joy and love. Especially, my mother’s support, sacrifice and endless love have brought me this far. Her hard work, persistence, and positive thinking in achieving her dream always inspired me to live the same. I thank my lovely sister and brother, Jiyun and Minyoon, since their presence and love brought so much happiness during my graduate study. Above all, I thank my God that He has led me to Brown to meet wonderful professors and friends and given me a wonderful opportunity to grow up there. vi To my God and my family vii Abstract of “Thermal Diffusion Shock Waves in a Linear Temperature Field and Comparison of Ultrasonic Distillation to Sparging of Liquid Mixtures”by Hyeyun Jung, Ph.D., Brown University, May 2012 The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of mixtures in a temperature gradient. Thermal diffusion is governed by a pair of coupled differential equations which reduce to a nonlinear partial differential equa- tion when the temperature profile is specified. Here two solutions are given to the partial differential equation describing thermal diffusion in a linear temperature field where the components are constrained in space. The first solution considers thermal diffusion without the effects of mass diffusion and shows the underlying motion of the components of the mixture to be that of shock waves. The second solution is an exact solution of the Ludwig-Soret equation that includes both the effect of the thermal gradient and mass diffusion. An additional solution is found for the problem of thermal diffusion in unbounded space. A new experimental method was devel- oped to monitor distributions of components of the mixture in a linear temperature field based on probing a cell containing fluorescent nanoparticles with a confocal microscope. The nanoparticles were chemically synthesized and labeled with a flu- orophore that absorbed 488 nm radiation and fluoresced at a 520 nm peak. The temperature gradient in the cell was generated by cooling one surface of the cell, a sapphire plate, with flowing water and electrically heating the other surface, which was an indium tin oxide coated glass plate. The dynamics of the separation of the mixture was recorded by monitoring fluorescence from the particles with the scan- ning confocal microscope. Data were fitted to a new numerical solution to the full partial differential equation for thermal diffusion with mass diffusion included. The method developed here is shown to provide Soret parameters, including the thermal diffusion factor and the Soret coefficient, based on either a single recording of the terminal density fraction profile, or by fitting the density profile at several times with the results of numerical integration. Ultrasonic distillation was investigated. Experiments were carried out to verify the recently reported, perfect separation of ethanol from water by ultrasonic dis- tillation. Ultrasonic distillation refers to the application of intense ultrasound to a liquid resulting in the formation of an ultrasonic fountain that generates both mist and vapor. Here, the composition of the vapor and aerosol above an ultra- sonic fountain was determined as a function of irradiation time and compared with the results of sparging for five different solutions. The experimental apparatus for determining the efficiency of separation consists of a glass vessel containing a piezo- electric transducer driven at either 1.65 or 2.40 MHz. Dry nitrogen was passed over the ultrasonic fountain to remove the vapor and aerosol. The composition of the liquid solutions remaining in the apparatus were recorded following irradiation us- ing gas chromatography, refractive index measurement, nuclear magnetic resonance, or spectrophotometry as diagnostics for the concentrations of the components of the mixtures. Experiments were carried out with ethanol-water and ethyl acetate- ethanol solutions, cobalt chloride in water, colloidal silica, and colloidal gold. The data show that ultrasonic distillation produces separations that are somewhat less complete than what is obtained using sparging. No evidence for the perfect separa- tion of ethanol from water-ethanol mixtures was found. Contents I Thermal Diffusion Shock Waves in the Linear Temperature Field 1 1 Thermal Diffusion and Non-equilibrium Thermodynamics 2 1.1 History of the Soret Effect(Thermal Diffusion) . .2 1.1.1 Three Postulates on Non-equilibrium Thermodynamics . .4 1.2 Conservation Laws . .6 1.2.1 Mass Flow and Chemical Reactions . .6 1.2.2 General Conservation Laws . .8 1.2.3 Conservation of Mass . .9 1.2.4 Equation of Motion . 10 1.2.5 Energy Transport Equation . 12 1.3 The Assumption of Local Equilibrium . 13 1.3.1 First Law Heat Flux . 15 1.3.2 Second-law Heat Flux . 17 1.3.3 Entropy Law and Entropy Balance Equation . 18 ix 1.4 The Linear Laws . 21 1.5 Onsager Theory . 22 1.6 Soret Effect . 25 2 Analytical Solution for the Dynamics of the Soret Effect 28 2.1 Equation of Motion For a Linear Temperature Field . 29 2.1.1 Exact Solution Using Hopf-Cole Transformation . 31 2.1.2 Solution without Mass Diffusion . 37 2.1.3 Shock Waves with Moving Coordinates in the Infinite Domain without Boundary . 40 2.1.4 Long Time (Terminal) Solution for Soret Equation . 44 3 Experiments and Results 47 3.1 Different Techniques to Measure the Soret Coefficient . 47 3.1.1 The Standard Soret Cell .