Nonlinear interaction between gas bubble and free surface

Abstract

The nonlinear evolution of gas bubbles in the vicinity of a free surface is investigated numerically. The flow is assumed to be potential and a boundary-integral method is used to solve the Laplace equation for the velocity potential. The bubble content is described by an adiabatic gas law. For a bubble initiated at 1.5 maximum bubble radius from the quiescent free surface, three collapse patterns have been noticed: a downward directed Bjerknes jet for the case of weak buoyancy force; an upward directed buoyancy jet for the case of strong buoyancy force; and for the intermediate case with near-null Kelvin impulse state the bubble assumes an oblate form during collapse with no jetting. While the evolution patterns of a bubble may be different for different values of the buoyancy parameter δ, the variation of the bubble volume with time appears to be largely independent of δ. When the bubble is initiated at and less than 1.0R R m from the free surface, a much higher free surface spike is formed during the collapse phase. There are still three collapse patterns for the bubble depending on the buoyancy force imposed. The evolution of the bubbles in toroidal form is also simulated and examined. Finally, results are shown depicting the effect of initial ‘pressure’ on the evolution of the gas bubble near to the free surface.