Stability of Two-Layer Fluid Flow
A. V. Rodionova1, E. V. Rezanova2,3
1Institute of Mathematics and Fundamental Informatics, Siberian Federal University, Krasnoyarsk, 660041, Russia
2Altai State University, Barnaul, 656049, Russia
3Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: двухслойные течения, уравнения Обербека -- Буссинеска, испарение, линейная устойчивость, длинноволновая асимптотика, two-layer flows, Oberbeck-Boussinesq equations, evaporation, linear stability, long-wave asymptotic behavior
Abstract
The problem of two-layer convective flow of viscous incompressible fluids in a horizontal channel with solid walls in the presence of evaporation is considered in the Oberbeck-Boussinesq approximation assuming that the interface is a thermocapillary surface which is not deformed and taking into account the Dufour effect in the upper layer which is a mixture of gas and liquid vapor. The effects of longitudinal temperature gradients at the boundaries of the channel and the thicknesses of the layer on the flow pattern and the evaporation rate are studied under specified gas flow conditions with no vapor flow on the upper boundary of the channel. It is shown that the long-wavelength asymptotic behavior for the decrement is determined from the flow characteristics, the long-wave perturbations occurring in the system decay monotonically, and the thermal instability mechanism is not potentially the most dangerous.
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