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Surface and Hydrodynamic Forces in Wetting Film Surface and Hydrodynamic Forces in Wetting Film Lei Pan Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy In Mining and Mineral Engineering Roe-Hoan Yoon, Chair Gerald H. Luttrell Gregory T. Adel Sunghwan Jung Alan R. Esker July 1, 2013 Blacksburg, Virginia Keywords: wetting film, hydrophobic force, hydrodynamic force, force apparatus for deformable surfaces (FADS), Frumkin-Derjaguin isotherm, combining rule Copyright © 2013 by Lei Pan Surface and Hydrodynamic Forces in Wetting Film Lei Pan ABSTRACT The process of froth flotation relies on using air bubbles to collect desired mineral particles dispersed in aqueous media on the surface, while leaving undesirous mineral particles behind. For a particle to be collected on the surface of a bubble, the thin liquid films (or wetting films) of water formed in between must rupture. According to the Frumkin-Derjaguin isotherm, it is necessary that wetting films can rupture when the disjoining pressures are negative. However, the negative disjoining pressures are difficult to measure due to the instability and short lifetimes of the films. In the present work, two new methods of determining negative disjoining pressures have been developed. One is to use the modified thin film pressure balance (TFPB) technique, and the other is to directly determine the interaction forces using the force apparatus for deformable surfaces (FADS) developed in the present work. The former is designed to obtain spatiotemporal profiles of unstable wetting films by recording the optical interference patterns. The kinetic information derived from the spatiotemporal profiles were then used to determine the disjoining pressures using an analytical expression derived in the present work on the basis of the Reynolds lubrication theory. The technique has been used to study the effects of surface hydrophobicity, electrolyte (Al3+ ions) concentration, and bubble size on the stability of wetting films. Further, the geometric mean combining rule has been tested to see if the disjoining pressures of the wetting films can be predicted from the disjoining pressures of the colloid films formed between two hydrophobic surfaces and the disjoining pressures of the foam films formed between two air bubbles. The FADS is capable of directly measuring the interaction forces between air bubble and solid surface, and simultaneously monitoring the bubble deformation. The results were analyzed using the Reynolds lubrication theory and the extended DLVO theory to determine both the hydrodynamic and disjoining pressures. The FADS was used to study the effects of surface hydrophobicity and approach speeds. The results show that hydrophobic force is the major driving force for the bubble-particle interactions occurring in flotation. Acknowledgement First and foremost, I would like to give my utmost appreciation to my advisor, Dr. Roe-Hoan Yoon, for his support, guidance, and inspiration throughout the course of this study. His consistent enthusiasm on research and enormous contribution to mineral engineering deeply impressed me and will continue to influence me in the future. His wisdom and extraordinary patience on me has made this work possible. He is my mentor for both career and life for my lifetime. I would also like to acknowledge my committee members, Dr. Gerald H. Luttrell and Dr. Gregory T. Adel for their invaluable advices. I appreciate the opportunities to learn the leading coal research from them. I would also like to thank Dr. Alan R. Esker for his constructive comments, which helped to improve this work. Special appreciation goes to Dr. Sunghwan Jung for his help in interfacial fluid mechanics throughout the entire course of this study. My appreciations are extended to Dr. Anbo Wang and Dr. Bo Dong at Center for Photonics Technology for their kind help and accommodation for me to learn the fiber interferometry technique in their lab. I would also like to thank Dr. Rickey Davis and his students for their help on measuring the zeta potentials. I would like to thank all the staff and peer graduate students in our Mining department. Special appreciation is given to Dr. Jialin Wang, Dr. Zuoli Li, Dr. Aaron Noble, and Dr. Jinming Zhang for the friendship and invaluable discussions. To Chris Hull, Carol Trutt, and Gwen Davis, I appreciate their care over the time of my study at Virginia Tech. I would also like to express my gratitude to Donald Leber and Jim Waddell for their technical assistant, and Kirsten Titland for editing the grammar of this dissertation. Finally, I sincerely appreciate my family for their unconditional love for all these years. I wouldn’t have received this great learning opportunity without their financial and mental support. iii Contents Chapter 1. Introduction ............................................................................................................... 1 1.1 General ...................................................................................................................... 1 1.2 Literature Review ...................................................................................................... 4 1.2.1 Static measurement of determining the disjoining pressure isotherm ................... 5 1.2.2 Dynamic methods of determining the disjoining pressure isotherm ................... 10 1.3 Dissertation Outline ................................................................................................. 14 1.4 Reference ................................................................................................................ 16 Chapter 2. Effect of Hydrophobicity on the Stability of the Wetting Films of Water Formed on Gold Surfaces .......................................................................................................... 25 2.1 Introduction ............................................................................................................. 26 2.2 Model Derivation for Disjoining Pressure ................................................................ 30 2.3 Experiment .............................................................................................................. 32 2.3.1 Materials .......................................................................................................... 32 2.3.2 Procedure ......................................................................................................... 32 2.4 Result ...................................................................................................................... 34 2.5 Discussion ............................................................................................................... 41 2.6 Summary and Conclusion ........................................................................................ 51 2.7 References ............................................................................................................... 52 Chapter 3. A Fundamental Study on the Role of Collector in the Kinetics of Bubble-Particle Interaction ............................................................................................................... 58 3.1 Introduction ............................................................................................................. 59 3.2 Experiment .............................................................................................................. 62 3.2.1 Materials .......................................................................................................... 62 iv 3.2.2 Thin Film Pressure Balance .............................................................................. 62 3.3 Result and Discussion .............................................................................................. 64 3.4 Conclusion .............................................................................................................. 72 3.5 References ............................................................................................................... 72 Chapter 4. Effect of Bubble Size on the Rate of Wetting Film Drainage .................................... 75 4.1 Introduction ............................................................................................................. 76 4.2 Experimental ........................................................................................................... 78 4.2.1 Materials .......................................................................................................... 78 4.2.2 Thin Film Pressure Balance .............................................................................. 79 4.3 Results..................................................................................................................... 81 4.3.1 Hydrophilic Surfaces ........................................................................................ 81 4.3.2 Hydrophobic Surfaces ...................................................................................... 89 4.4 Conclusions ............................................................................................................. 93 4.5 References ............................................................................................................... 94 Chapter 5. Predicting the Asymmetric Hydrophobic Interactions in Wetting Films from the Symmetric Hydrophobic Interactions in Colloid and Foam films ............................. 97 5.1 Introduction
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