Rising bubble in the presence of a wall or a flat free surface

The dynamics of a gas/vapor bubble rising under the action of gravity in an isochoric, inviscid liquid bounded by flat solid wall or free surface is investigated by developing simplified analytical models, based on the assumption that the bubble remains spherical during its motion. The bounding surface is assumed orthogonal to the gravity. Effects of viscosity are neglected and the fluid is initially at rest, so that the resulting flow is a potential one. Suitable forms of the classical Rayleigh-Plesset equation for the time evolution of radius and center of mass are deduced. The bubble dynamics resulting from the models is compared with numerical simulation performed with a boundary integral code, in which the bubble shape is assumed symmetric about an axis aligned with gravity.