The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius‐time behavior is made with experimental observations in superheated water, and very good agreement is found.

The growth of vapor bubbles in superheated liquids. report no. 26-6

The mathematical formulation of the heat input governed vapor bubble growth in a bulk of uniformly heated liquid is presented. Using the theory of dimensions, the structure of the solution was analyzed qualitatively. A historical survey of theoretical works devoted to the considered problem is presented. The set of degenerate solutions of the problem is obtained and studied systematically. The complete analytical solution of the problem is obtained for the first time. Formulas for the calculation of the bubble growth rate in the whole domain of possible variations in regime parameters are presented. The conclusion is made that the influence of permeability of the interface has a significant effect on the bubble growth rate. It is shown that the Plesset–Zwick formula, which is commonly accepted in computational practice, is not applicable at both small and large Jakob numbers and its good agreement with the experiment is determined to a large extent by a combination of the imperfectness of the theoretical analysis and the experimental error. The conclusion is made that, for many liquids, the ultimately achievable value of the dimensionless superheating parameter (Stefan number) can exceed unity. In this case, the regularities in the bubble growth acquire some features unexplored to date.

Alexander A. Avdeev

Papers

Thermally Controlled Bubble Growth