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Conference publicationsAbstractsXXIII conferenceSelf-pressing solutions of the problem by thermal convection with averaging on a thin layer346 720, Aksay, Rostov region, Maxim Gorky Street, №9 1 pp. (accepted)Тhe object of study is the process of building a self-similar solutions of the problem of thermal convection, averaged on a thin layer. The problem arises in the modeling of the films disposed on a horizontal base, with which surface the liquid is vaporized. It has a significant application in medical diagnostics, protein crystallography, to stretch of DNA and RNA, production of nanostructures creating structured surfaces, printing, etc. The purpose of modeling is to identify the self-organization processes occurring during the evaporation of droplets of body fluids. Model evaporation of the liquid containing solid impurity, built using averaging equations Oberbeck-Boussinesq on the basis of "lubrication» (Lubrication theory) and includes partial differential equations derived for the averaged unknown function of two coordinates and time: the function of the film surface, the flux density fluid flow heat impurity concentration. Depending on the physical formulation of the problem equations are supplemented by the boundary conditions to be determined by physical and chemical properties of the liquid, the horizontal surface and the environment. For the problem of self-proposed replacement, allowing to reduce the two-dimensional to three-dimensional problem. In particular, the analytical solution for the replacement of the self, including the exponential time dependence of a damping parameter.
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