The dynamics of a vapor embryo in a superheated liquid (characteristics of the initial growth period)

Abstract

The initial period of growth of a vapor bubble of near-critical size is studied analytically and numerically. It is demonstrated that the dynamic effects resulting from the hydrodynamics of radial liquid motion are decisive in the problem under consideration. An analytical solution for the problem is obtained, and the asymptotic solution branches are investigated. It is concluded that the dynamic inertial-controlled Rayleigh law of bubble growth is a degenerate solution branch that is applicable at sufficiently large growth times. It is demonstrated that the effect of viscous forces degenerate both in the initial period of bubble growth and for large growth times. These forces may exert a significant influence on the bubble growth dynamics only at the intermediate growth stages. The effect of viscosity is maximized in the region of near-spinodal superheating even in the case of liquids with a relatively low viscosity. For example, the corrections for the effect of viscosity in water reach hundreds of percent. The formula for estimating the duration of the initial bubble growth period (within which the viscous forces may be neglected) is derived based on the asymptotic solution. Interpolation design formulas that satisfy the needed passages to the limit are proposed. It is found that that there exists a peculiar “incubation period” of bubble growth, within which the bubble growth is not very fast. The duration of this period depends on the extent of influence of surface tension forces. The formulas for calculating the duration of this “incubation” period are derived. It is demonstrated that this duration remains finite even when the surface tension effects become degenerate.