An analytical theory of the stage of nonisothermal nucleation of supercritical droplets in a vapor with instantly created supersaturation is formulated with taking into account the vapor concentration and temperature inhomogeneities arising as a result of nonstationary diffusion onto growing droplets and condensation heat release. This theory extends our recent excluded volume approach to isothermal nucleation theory1 and assumes that the intensity of the nucleation of new droplets is suppressed in spherical non-stationary diffusion regions of a certain size surrounding previously nucleated droplets, and stays at the initial level in the remaining volume of the vapor-gas environment. The value of excluded from nucleation volume depends on the explicit forms of the vapor concentration and temperature profiles in the vapor-gas environment around the growing droplet. To find the excluded volume we use the self-similar solutions of time-dependent diffusion and thermal conductivity equations. The main characteristics of the phase transition at the end of the nucleation stage are found and compared with those in the isothermal and nonisothermal theory of nucleation with homogeneous vapor consumption (the theory of mean-field vapor supersaturation and temperature). It is shown that applicability of the mean-field approach depends on smallness of the square root of ratio of the densities of metastable and stable phases. With increasing the temperature of the vapor-gas environment or for nucleation in liquid or solid solutions, this smallness weakens, and then the excluded volume approach gives a more profound result.
This work was supported by the Russian Foundation for Basic Research (grant 13-03-01049-a) and St. Petersburg State University (grant 11.37.183.2014).
References
1A.Kuchma, M. Markov, A. Shchekin, Physica A, 402, 255 (2014).
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