Nucleation stage with nonsteady growth of supercritical gas bubbles in a strongly supersaturated liquid solution and the effect of excluded volume.

An approach to the kinetics of barrier formation of supercritical gas bubbles in a strongly supersaturated liquid solution is presented. A common assumption of uniform reduction of a dissolved gas supersaturation in a liquid solution via stationary diffusion to nucleating gas bubbles is shown to be not applicable to the case of high gas supersaturations. The approach recognizes that the diffusion growth of supercritical bubbles at high gas supersaturation is essentially nonstationary. Nonstationary growth of an individual gas bubble is described by a self-similar solution of the diffusion equation which predicts a renormalized growth rate and thin highly nonuniform diffusion layer around the bubble. The depletion of a dissolved gas due to intake of gas molecules by the bubble occurs only within this thin layer. An integral equation for the total volume of an ensemble of supercritical gas bubbles within a liquid solution is derived. This equation describes the effect of excluding a total volume of the depleted diffusion layers around the growing bubbles nucleated at all previous moments of time until nucleation of new bubbles ceases due to elimination of the nondepleted volume of the solution. An analytical solution of this equation is found. The swelling of the liquid solution, the number of gas bubbles nucleated, the distribution function of bubbles in their sizes, and the mean radius of the bubbles are determined in their dependence on time.