On Approaches to Solving the Problem of an Interface Deformation in a Two-Layer System with Evaporation
Abstract
Mathematical modeling of the two-layer convective fluid flows is performed by the Oberbeck — Boussinesq equations and relations at the thermocapillary interface. Special attention should be paid to the problems with mass transfer at the interfaces. In particular, mass transfer can be a result of evaporation or condensation. Also, the problems with the vapor diffusion and thermodiffusion and diffusive thermal conductivity effects in the gas-liquid layers should be considered. The new solutions of the convection equations are presented to model two-layer flows. The flows are induced by the action of a longitudinal temperature gradient in the transversely directed gravity field. The interface assumed to be rectilinear when developing the analytical solution. The problem of finding the real interface position is solved with the help of the interface conditions. A derivation of the kinematic and dynamic conditions in terms of stream function and vorticity and an equation for the tangential velocity at interface is presented. A method of determination of a smooth deformable interface is discussed.
DOI 10.14258/izvasu(2018)1-12
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