Investigation of bubble Dynamics in Pure Liquids and Aqueous Surfactant/Polymer Solutions under Adiabatic and Diabatic Conditions A Dissertation submitted to the Division of Graduate Studies and Research of the University of Cincinnati in partial fulfillment of the requirements for the degree of DOCTORATE OF PHILOSOPHY (Ph.D.) in the Department of Mechanical and Materials Engineering of the College of Engineering and Applied Science March 2018 by Deepak Saagar Kalaikadal B.E., Anna University, Chennai, Tamil Nadu, India M.S., University of Cincinnati, Cincinnati, Ohio, USA Committee Chair: Dr. Raj M. Manglik Committee Co-Chair: Dr. Milind A. Jog ABSTRACT The goal of this work is to gain a better understanding of the complex physics governing the growth of bubbles from orifices and cavities submerged in liquid pools of pure liquids, and aqueous solutions of surfactants and polymers through a combination of experimental, computational, and theoretical approaches. The final phase of the bubble cycle - necking and pinch-off - was investigated initially. The growth, extension, and eventual shearing of the neck is governed by a balance of buoyancy, viscous shear, and surface tension forces over four distinct stages. Understanding the nature of these forces and subsequent scaling of the same yielded a correlation capable of predicting the length of the neck at pinch-off, providing a closure criterion to a single cycle of bubble growth. Following this, the influence of the orifice/cavity size - one of the primary governing process parameters in all bubble-based applications – was studied. The positive effect of the orifice diameter on the departure bubble diameters is seen to progressively decrease with the orifice size, until a critical size, beyond which the departing bubbles are smaller than the orifice. Within the constant bubble volume region, the growth and departure of bubbles is completely governed by a balance between the capillary forces and the buoyancy forces. The resulting force balance leads to a simple correlation to predict the bubble departure size from an orifice of any size, restricted to the constant bubble volume regime. The influence of surface tension on bubble growth was further investigated in both pure liquids and aqueous surfactant solutions. Comparative studies were undertaken to investigate the effect of time-dependent surface tension relaxation in surfactant solutions as opposed to ebullience in pure liquids with the same equilibrium surface tensions. The bubble regime map in aqueous i surfactant solutions exhibited a characteristic ‘s’ shaped curve, mimicking the relaxation curve of the surfactant itself. Due to this, the slopes of the relaxation curves were found to be excellent parameters for predicting the corresponding bubble growth curves. This was followed by a computational study of thermo-capillary convection driven by the temperature and surface tension gradients at the gas-liquid interface of a bubble subjected to a stratified thermal field. This is one of the many manifestation of the surface tension forces influencing bubble growth and heat transfer in nucleate pool boiling. The effect of liquid properties, wettability, bubble size, channel depth, and temperature gradients on the strength of the thermo-capillary currents and the associated heat transfer enhancement at the bubble interface was studied. It was established that the Marangoni number, by itself, cannot capture the complexities of the transient capillary flow. The growth of bubbles in stratified temperature fields was also investigated. It was found that the effect of thermo-capillary convection on the size of bubbles growing in positive temperature gradients, diminished with an increase in the gas flow rate. The study on thermo-capillary convection was extended into a computational study of bubble induced thermo-diffuso capillary convection in the presence of surfactants and a stratified thermal field. The complex interaction between the temperature-driven and concentration-driven capillary currents were observed and related to the enhancements in heat transfer seen in the vicinity of the bubble. As before, the effects of liquid viscosity, thermal gradients, wettability, and channel depth on the thermo-diffuso Marangoni currents were investigated. Finally, the model was also used to simulate adiabatic bubble growth in surfactant solutions and compare it with the bubble growth seen in water. The interfacial variation of surface tension, due to the presence of surfactant molecules, is seen to change the shape and size of the growing bubble substantially, as ii compared to pure water. However, it was established that the micro-convective capillary currents did not have a large role in determining the size of the departing bubble. The viscosity of the liquid and its effect on bubble growth and departure dynamics was the last parameter of interest with respect to bubble growth in capillary orifices. Over the course of this study, a critical criterion was established below which viscosity ceases to have any influence on bubbles growing from orifices submerged in viscous liquids. Similarly, the existence of another regime, where surface tension plays no role in the bubble dynamics, was also recognized. In this regime, the bubble growth is seen to be regulated by a balance of viscous drag force, gas momentum force, liquid inertia, and buoyancy force. The clear demarcation of these two regimes, which form the two asymptotes of a typical bubble regime map, together with the scaling of the forces involved in each individual regime resulted in a universal correlation for predicting the departure size of bubbles growing from all sizes of capillary orifices submerged in liquids with different viscosities, surface tensions, and densities, across a wide range of flow rates within the single bubble regime. The developed correlation was compared with experimental results and was seen to be in excellent agreement. While surfactants, in aqueous solutions, are known to change the gas-liquid interfacial tension temporally and spatially through selective adsorption at the interface, solutions of polymers, on the other hand impart a non-Newtonian, pseudo-plastic (shear-thinning) characteristic to the liquid. The influence of this shear-thinning behavior on bubble growth was studied experimentally with different concentrations and grades of HydroxyEthylCellulose. The effect of decreasing viscosity was clearly seen at high flow-rates by comparing the bubble sizes with the sizes of bubbles growing in water at corresponding flow rates. iii Finally, the results derived from the experimental and computational study of surfactant solutions was applied to data available for nucleate pool boiling in aqueous surfactant solutions to propose a scaling parameter capable of estimating the heat-transfer enhancement achieved through the use of these surfactants. The enhancement in heat-transfer is shown to scale with the bubble departure diameters, and the corresponding relaxation behavior of each surfactant solutions. This, in combination with an established predictive-correlation in the literature, gave form to a relation for predicting boiling heat-transfer rates in aqueous surfactant solutions. iv v ACKNOWLEDGEMENTS This doctoral work, which took a substantial part of my twenties, would not have been possible if not for the combined orchestrated effort of several people, who I will always be grateful to. First and foremost, I would like to express my sincere gratitude to my adviser, Dr. Raj Manglik for his invaluable guidance, motivation, numerous discussions and suggestions, support (financial and otherwise) and most importantly the patience and trust that makes a doctoral student comfortable with his work. It goes without saying that this work wouldn’t have been possible without him. I would equally like to thank Dr. Milind Jog, my co-adviser, who always had his door open for clearing my doubts, running through computational methods, discussing results, and much more. I would also like to thank Dr. Je-Hyeong Bahk and Dr. Murali Sundaram, for taking time to serve on my proposal and dissertation committees, and providing me with valuable feedback, which helped in shaping this work into its final form. I am also very grateful to Frank Murrell and Dr. Bernie Rudd at the UC Simulation center for providing me with a research assistantship that enriched my doctoral experience through research-and-development interactions with several departments at Procter & Gamble. It was indeed a pleasure to work at the simulation center and interact with other students who were also a part of this brilliant collaboration. I cannot justify how thankful I am to my friends and fellow doctoral students, Sucharitha and Karthik, who were an integral part of my life at UC. They provided excellent companionship, inspiration, support, and proved to be great sounding boards for bouncing off ideas, thoughts and doubts. The same goes to the rest of my lab-mates at TFTPL – Sanjivan, An, Srivatsan, Gary, Jeewan, and DanTong. vi Acknowledgements are also due to a large community of friends, on-and-off campus, sometimes even as far as Indianapolis, Detroit, Toronto, and back home in India, who have always been a source of joy and support, during every step of my doctoral journey. I would finally like to thank my family back home, especially my mother, brother, and sister, who have always showered me with unconditional love and support. It is an understatement to state that I wouldn’t be here