Free streamline theory for a large gas bubble in a liquid

Abstract

The problem of predicting the shape and rising velocity of a gas bubble in an inviscid liquid of zero surface tension can be formulated by assuming there is a wake of stagnant liquid extending to infinity below the bubble. The boundary of the wake and the nose of the bubble then form a continuous free streamline whose position is determined by the required velocity distribution. This free streamline was calculated by numerical methods. The results predict a bubble whose shape is remarkably similar to that of large spherical-gap bubbles in liquids of low viscosity. The real bubbles rise about 20 per cent slower than the theoretical velocity, presumably because the pressure rise in the turbulent wake gives a higher drag coefficient.