Dynamics of a bubble in oscillating viscous liquid.

This article is devoted to the investigation of gaseous bubble dynamics in oscillating viscous liquids of different density values. The study is conducted numerically using the level-set method with a non-stationary approach. The bubble is initially located near the upper wall of the container. The effects of the inclusion and host liquid viscosities on interaction of the bubble with the wall are analysed. The calculations show that in the absence of gravity, for low-viscosity fluids the bubble is attracted to the nearest wall, which is consistent with previous analytical and experimental results. With increasing viscosity, the vibrational attraction to the wall becomes weaker and is then replaced by repulsion, which can be explained by the decelerative effect of viscosity in the boundary layer near the rigid surface, where the average flow becomes less intensive. The dependencies of the repulsion force on the parameter values are obtained by using the balance method (investigation of the gravity level needed to attain the quasi-equilibrium state at a certain distance between the bubble and the wall). The calculations show that the repulsion force grows with decreasing Reynolds number (increase of the viscosity). This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.