Evaporation convection in two-layers binary mixtures: equations, structure of solution, study of gravity and thermal diffusion effects on the motion

Abstract The theoretical approach for mathematical modeling of the evaporative convection in a multiphase system with interface based on the use of an exact solution of governing equations is discussed. The mathematical model builds on the “diffusive” laws of the transfer of matter, momentum and energy and includes the interface boundary conditions formulated with respect to the conservation laws. The carried out compatibility analysis of the equations concludes that there are three classes of exact solutions of the system under consideration. One of the possible solutions is circumstantially studied in the framework of the evaporative convection problem in a bilayer liquid – gas system, where both phases are the binary mixtures. The convection-diffusion equations are used to govern the transfer of one selected component and its vapor in the liquid and gas layers, respectively. The thermodiffusion effect is taken into account additionally for more precise description of heat transfer processes. The impact of this effect on the concentration and thermal characteristics as well as on the mass evaporation flow rate is investigated. It is shown that the utilized solution can describe convective regimes appearing on a working area of a long plane channel under thermal load distributed with respect to longitudinal coordinate by means of quadratic law. The solution correctly predicts hydrodynamical, temperature and concentration parameters of convective flows arising in the bilayer system. Basic characteristics calculated by this solution are feasible when the system is slightly deviated from the thermodynamic equilibrium state, and mass transfer through the interface is weak.

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