This study describes the behavior of bubbles rising under gravity using the Shan and Chen-type multicomponent multiphase lattice Boltzmann method (LBM) [X. H. Chen, Phys. Rev. E 47, 1815 (1993)]. Two-dimensional (2D) single bubble motions were simulated, considering the buoyancy e®ect for which the topology of the bubble was characterized by the nondimensional E€ otv€ os (Eo), and Morton (M) numbers. In this study, a new approach based on the \e®ective buoyancy" was adopted and proven to be consistent with the expected bubble shape deformation. This approach expands the range of e®ective density di®erences between the bubble and the liquid that can be simulated. Based on the balance of forces acting on the bubble, it can deform from spherical to ellipsoidal shape with skirts appearing at high Eo number. A benchmark computational case for qualitative and quantitative validation was performed using COMSOL Multiphysics based on the level set method. Simulations were conducted for 1 Eo 100 and 3 Â 10 À6 M 2:73 Â 10 À3 . Interfacial tension was checked through simulations without gravity, where Laplace's law was satis¯ed. Finally, quantitative analyses based on Int. J. Mod. Phys. C Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ DAVIS on 02/03/15. For personal use only.the terminal rise velocity and the degree of circularity was performed for various Eo and M values. Our results were compared with both the theoretical shape regimes given in literature and available simulation results.
DEDICATIONThis thesis is dedicated to my lovely wife Jacqueline Yhamen for being so supportive and understanding. I have not been able to spend time with you during this long and quite difficult moment you have been through. I hope you find here the love I was unable to share when needed.
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