A general theory for the formation of a new phase. Static cavitation in a nonvolatile liquid

The rate of formation of cavities in a nonvolatile liquid subjected to negative pressure is calculated. The pressure is assumed to be sufficiently moderate, so that the critical bubble (hole) can be treated macroscopically. If this condition is satisfied one may apply the Zel'dovich saddle-point method. However, in distinction from that method, the present paper makes use of a construction of Gibbs grand canonical ensemble, which allows one to avoid the ambiguities that appear in the calculation of the microscopic initial stage of formation of the hole and yields a more accurate value of the kinetic (preexponential) factor. A more accurate value of the work required to form a critical hole, the value which occurs in the exponent, is obtained by taking into account the dependence of the surface tension of the hole on the curvature of the surface. For this purpose we use an expansion of the surface tension in powers of the curvature of the surface of the hole. Since the surface tension occurs in the exponent of the expression for the probability or rate of cavitation, it is necessary to retain the expansion terms which are linear or quadratic in the curvature, whereas the correction factors to the cavitation rate, due to higher-order terms tend to unity as the expansion of the liquid decreases, in contradistinction from the first terms. It is important that for large expansions, and hence for small curvatures of the surface of the critical hole, the series for the surface tension diverges.