Dynamics of Bubbles in an Infinite Volume of Liquid

Abstract

We solve the fundamental problems of dynamic growth, collapse and pulsations of bubbles under the influence of the inertia, surface tension and viscosity forces. For all these problems it proved possible to obtain analytic solutions, study the degenerate (asymptotic) branches, and use them to construct practical interpolation formulas. In this way we build the solution of the gas bubble collapse problem, give a detailed analysis of the laws of variation of its radius and of the pressure distribution in the liquid. The surface tension forces are shown as having predominant influence on the dynamics of a bubble in terms of the variation of the initial pressure drop. A general solution of the dynamic bubble growth problem is obtained with allowance for the viscosity and surface tension forces. It is shown that, in the absence of the viscosity and surface tension forces (the dynamic-inertia-controlled growth law), the bubble growth rate increases in time, in the initial period, according to the linear law, and only then asymptotically turns to the concluding stage, in which the growth rate is constant. An analysis is given of the initial growth period duration of vapour nucleus in equilibrium with the ambient superheated liquid as a function of the initial perturbation. A conclusion is made that there exists a peculiar “incubation period” of bubble growth, within which the bubble growth is not very fast. The effect of the viscosity forces on the bubble growth process is studied. The effect of viscosity is shown to degenerate both in the initial stages of bubble growth and for large growth times. Nevertheless, in the intermediate growth stages the effects of viscosity may have a substantial effect on the bubble growth even for relatively low-viscous liquids like water. The effect of viscosity exhibits the most powerful manifestation when a vapour nucleus grows in the regions of liquid superheats close to spinodal.