Spherical phase growth in superheated liquids

Abstract

The growth of vapor bubbles in a superheated liquid has been treated as a series of rate phenomena governed by an equation of continuity for the vapor, the Knudsen equation for interfacial evaporation, the modified Rayleigh equation describing the radial hydrodynamic behavior and a heat diffusion equation representing the temperature distribution in the liquid—these transport equations have been converted into a coupled set of nonlinear integral equations which have been solved numerically on a high-speed digital computer to generate bubble growth curves starting with a nucleus containing saturated vapor. In the period of 10 −10−10 −6 sec the vapor bubble does not grow significantly but surface evaporation and heat transfer at the bubble wall cause the vapor pressure and temperature to build up internally until in the region 10 −6 to nearly 10 −5 sec the radius begins to increase slowly, the rate of increase being retarded by surface tension and liquid inertial forces described by the hydrodynamic equation. At 10 −5−10 −3 sec the bubble size increases quite rapidly, the rate determining processes being the combined effects of liquid inertia and heat transfer at the interface. The liquid inertial terms in the hydrodynamic equation become negligible at about 10 −3 sec and the asymptotic growth at large times becomes increasingly dependent upon heat transfer in the liquid around the bubble, the growth curves in the period 10 −3−10 −2 sec being virtually independent of the initial nucleus size. The agreement, within experimental error, of the computed growth curves with the photographic measurements by Dargarabedian of steam bubbles at times of 10 −3−10 −2 sec indicates that the present heat transport model, based on a localized source-sink combination at the interface, represents a realistic approximation to the physical behavior of the liquid at the bubble wall.