The Growth and Collapse of Vapor Bubbles

Abstract

A theory is developed which describes the behavior of a vapor bubble in a liquid. Its physical basis is the assumption that the heat transfer effects which accompany the evaporation occurring at the bubble wall when the bubble grows, 0r the condensation that occurs there when the bubble collapses, are dynamically important. The basic equations of hydrodynamics are shown to reduce, for the problem under consideration, to a dynamic equation which describes the behavior of the bubble wall, and a heat convection equation for the liquid which is coupled to the dynamic equation by a boundary condition at the bubble surface. A solution for the heat problem is obtained under the assumption that significant temperature variation in the liquid occurs only in a thin thermal boundary layer surrounding the bubble wall. An estimate of the correction to the temperature solution is also derived. Once the temperature at the bubble wall is given, the vapor pressure within the bubble is known and the dynamic problem becomes determinate. The theory is applied to the cases of the growth of a vapor bubble in a superheated liquid, and the collapse of a vapor bubble in a liquid below its boiling temperature at the external pressure. The simplifying physical assumptions made in the course of the investigation are justified for the specific example of vapor bubble behavior in water. A comparison of the theory with experiment is given for the observable range of bubble growth in superheated water, and the agreement is found to be very good.