Single Bubble Bouncing on a Free Surface and a Rigid Wall with a Front-tracking Method

Abstract

Behaviors of air bubbles undergoing collisions with a free surface / rigid wall are numerically studied for various viscosities and surface tensions. The moving boundary problem is solved by means of a front-tracking method to correctly capture an exchange between the surface and kinetic energies in the bouncing process. As found in experiments by Legendre et al. (2005, Phys. Fluids, 17: 097105), the simulated contact time during the bounce normalized by the initial bubble radius and the rise velocity is proportional to the square root of the Weber number, supporting the validity of the mass-spring model proposed by Legendre et al.(2005). For the bubble-rigid wall system, the relation between the restitution coefficient (i.e. the ratio of the rebound bubble velocity to the rise velocity) and Ca/St (here, Ca is the capillary number and St is the Stokes number) is consistent with the experiments and the theoretical model of Zenit and Legendre (2009, Phys. Fluids, 21: 083306). The restitution coefficient of the bubble-free surface system is found to be larger than that of the bubble-rigid wall system, implying the smaller viscous dissipation during the bounce, as a result of the smaller vorticity generation on the free surface.