Toroidal bubble dynamics near a solid wall at different Reynolds number

The bubble dynamics in a viscous liquid have significant applications, but the influence of viscosity on bubble dynamics near a solid wall are still not fully understood, especially for the toroidal bubble. In this paper, a numerical method is presented to study toroidal bubble dynamics near a solid wall in the viscous liquid. The liquid phase is assumed to be incompressible and separated from the gas by a free surface. Based on the finite volume method, the incompressible and viscous Navier-Stokes equations are discretized on the staggered grids, which are solved using the explicit projection method. A Lagrange multiplier method is used to deal with the additional constrain that the tangential stress equals zero, and the bubble surface is advected using a front tracking method. The numerical method is compared with the Rayleigh-Plesset solution for a single bubble with multi-oscillations, and the results between them are favorable with regard to bubble radius history. Finally, the toroidal bubble dynamics near a solid wall with different stand-off parameter (γ= 1.5, 0.95 and 0.6, respectively, where γ= d/Rmax, d is the distance between the solid wall and the bubble center at the moment of formation and Rmax is the maximum bubble radius) at different Reynolds number are studied, including water jet, peak pressure induced by water jet, water layer, bubble rupture, bubble migration, etc, where some important conclusions are obtained.