Self-similar solution of a nonsteady problem of nonisothermal vapor condensation on a droplet growing in a diffusion regime

A. P. Grinin, G. Yu Gor, F. M. Kuni

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3 Scopus citations

Abstract

This paper presents a mathematically exact self-similar solution to the joint nonsteady problems of vapor diffusion toward a droplet growing in a vapor-gas medium and of removal of heat released by a droplet into a vapor-gas medium during vapor condensation. An equation for the temperature of the droplet is obtained, and it is only at that temperature that the self-similar solution exists. This equation requires the constancy of the droplet temperature and even defines it unambiguously throughout the whole period of the droplet growth. In the case of a strong display of heat effects, when the droplet growth rate decreases significandy, the equation for the temperature of the droplet is solved analytically. It is shown that the obtained temperature fully coincides with the one that settles in the droplet simultaneously with the settlement of its diffusion regime of growth. At the obtained temperature of the droplet, the interrelated nonsteady vapor concentration and temperature profiles of the vapor-gas medium around the droplet are expressed in terms of initial (prior to the nucleation of the droplet) parameters of the vapor-gas medium. The same parameters are used to formulate the law in accordance with which the droplet is growing in diffusion regime and also to define the time that passes after the nucleation of the droplet till the settlement of the diffusion regime of droplet growth, when the squared radius of the droplet becomes proportionate to time. For the sake of completeness, the case of weak display of heat effects has been studied.

Original languageEnglish (US)
Pages (from-to)19069-19079
Number of pages11
JournalJournal of Physical Chemistry C
Volume112
Issue number48
DOIs
StatePublished - Dec 4 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Energy(all)
  • Physical and Theoretical Chemistry
  • Surfaces, Coatings and Films

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