Bekezhanova, Victoria B.; Stepanova, Irina V. Evaporation convection in two-layers binary mixtures: equations, structure of solution, study of gravity and thermal diffusion effects on the motion. (English) Zbl 1510.76178 Appl. Math. Comput. 414, Article ID 126424, 15 p. (2022). Summary: 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. Cited in 1 Document MSC: 76T10 Liquid-gas two-phase flows, bubbly flows 35Q35 PDEs in connection with fluid mechanics 80A19 Diffusive and convective heat and mass transfer, heat flow Keywords:thermodiffusion equations; compatibility analysis; exact solutions; evaporative convection PDFBibTeX XMLCite \textit{V. B. Bekezhanova} and \textit{I. V. Stepanova}, Appl. Math. Comput. 414, Article ID 126424, 15 p. (2022; Zbl 1510.76178) Full Text: DOI References: [1] Duncan, A. B.; Peterson, G. P., Review of microscale heat transfer, Appl. Mech. Rev., 47, 9, 397-428 (1994) [2] Pacros, A.; Minster, O., The ESA contribution to space research on two-phase systems, Microgravity Sci. Tech., XIX, 3-4, 9-10 (2007) [3] Nie, Z. H.; Kumacheva, E., Patterning surfaces with functional polymers, Nat. Mater., 7, 277-290 (2008) [4] Kabov, O. A.; Kuznetsov, V. V.; Kabova, Y. O., Evaporation, dynamics and interface deformations in thin liquid films sheared by gas in a microchannel, (Thome, J. R.; Kim, J., Encyclopedia of Two-Phase Heat Transfer and Flow II: Special Topics and Applications, Volume 1: Special Topics in Boiling in Microchannels, Micro-Evaporator Cooling Systems (2015), World Scientific Publishing Company: World Scientific Publishing Company Singapore), 57-108 [5] Rosner, D. E.; Arias-Zugasti, M.; LaMantia, B., Calculation of soret-shifted dew points by continuous mixture thermodynamics, AIChE J., 51, 10, 2811-2824 (2005) [6] Bekezhanova, V. B.; Goncharova, O. N., Influence of the Dufour and Soret effects on the characteristics of evaporating liquid flows, Int. J. Heat Mass Transf., 154, 119696, 1-15 (2020) [7] Margerit, J.; Colinet, P.; Lebon, G.; Iorio, C. S.; Legros, J. C., Interfacial nonequilibrium and Benard - Marangoni instability of a liquid-vapor system, Phys. Rev. E., 68, 041601, 1-14 (2003) [8] Haut, B.; Colinet, P., Surface-tension-driven instability of a liquid layer evaporating into an inert gas, J. Colloid Interface Sci., 285, 296-305 (2005) [9] Das, K. S.; Ward, C. A., Surface thermal capacity and its effects on the boundary conditions at fluid-fluid interfaces, Phys. Rev. E., 75, 065303, 1-4 (2007) [10] [in Russian] · Zbl 07324765 [11] Iorio, C. S.; Goncharova, O. N.; Kabov, O. A., Heat and mass transfer control by evaporative thermal pattering of thin liquid layers, Comput. Therm. Sci., 3, 4, 333-342 (2011) [12] Shklyaev, O. E.; Fried, E., Stability of an evaporating thin liquid film, J. Fluid Mech., 584, 157-183 (2007) · Zbl 1123.76021 [13] Bankoff, S. G., Taylor instability of an evaporating plane interface, AlChE J., 7, 485-487 (1961) [14] [in Russian] [15] Bekezhanova, V. B.; Goncharova, O. N., Stability of the exact solutions describing the two-layer flows with evaporation at interface, Fluid Dyn. Res., 48, 6, 061408 (2016) [16] Bekezhanova, V. B.; Goncharova, O. N., Problems of the evaporative convection (review), Fluid Dyn., 53, Suppl. 1, S69-S102 (2018) · Zbl 1425.76228 [17] [in Russian] [18] [in Russian] [19] Birikh, R. V., Thermocapillary convection in a horizontal layer of liquid, J. Appl. Mech. Tech. Phys., 3, 35-45 (1966) [20] [in Russian] [21] Goncharova, O. N.; Resanova, E. V., Example of an exact solution of the stationary problem of two-layer flows with evaporation at the interface, J. Appl. Mech. Tech. Phys., 55, 2, 247-257 (2014) · Zbl 1297.76174 [22] Bekezhanova, V. B.; Goncharova, O. N., Analysis of characteristics of two-layer convective flows with diffusive type evaporation based on exact solutions, Microgravity Sci. Technol., 32, 139-154 (2020) [23] Shefer, I. A., Influence of the transverse temperature drop on the stability of two-layer fluid flows with evaporation, Fluid Dyn., 54, 5, 603-613 (2019) · Zbl 1434.76044 [24] Shefer, I. A., Effect of the system geometry on the flow stability of an evaporating liquid, Fluid Dyn., 53, Suppl.1, S59-S68 (2018) · Zbl 1425.76088 [25] Bekezhanova, V. B.; Shefer, I. A., Influence of gravity on the stability of evaporative convection regimes, Microgravity Sci. Technol., 30, 543-560 (2018) [26] Goncharova, O. N.; Kabov, O. A., Investigation of the two-layer fluid flows with evaporation at the interface on the basis of the exact solutions of the 3D problems of convection, J. Phys. Conr. Ser., 754, 032008 (2016) [27] Bekezhanova, V. B.; Goncharova, O. N., Numerical study of the evaporative convection regimes in a three-dimensional channel for different types of liquid-phase coolant, Int. J. Thermal Sci., 156, 1-15 (2020) [28] Andreev, V. K.; Stepanova, I. V., Unidirectional flows of binary mixtures within the framework of the Oberbeck-Boussinesq model, Fluid Dyn., 51, 2, 136-147 (2016) · Zbl 1342.76116 [29] Stepanova, I. V., Construction and analysis of exact solution of Oberbeck-Boussinesq equations, J. Sib. Fed. Univ.: Math and Phys, 12, 5, 590-597 (2019) · Zbl 07325537 [30] Stepanova, I. V., On influence of geometrical parameters and flow rate on mass transfer through interface of two binary mixtures, Interfacial Phenom. Mass Transf., 8, 4, 273-290 (2020) [31] Landau, L. D.; Lifshitz, E. M., Course of Theoretical Physics, Fluid Mechanics, Vol. 6 (1987), Butterworth-Heinemann [32] Andreev, V. K.; Gaponenko, Y. A.; Goncharova, O. N.; Pukhnachov, V. V., Mathematical Models of Convection (de Gruyter Studies in Mathematical Physics) (2012), De Gruyter: De Gruyter Berlin, Boston · Zbl 1257.76001 [33] Polyanin, A. D.; Zaitsev, V. F., Handbook of Exact Solutions for Ordinary Differential Equations (2003), Chapman and Hall/CRC Press: Chapman and Hall/CRC Press Boca Raton · Zbl 1015.34001 [34] Lyulin, Y.; Kabov, O., Measurement of the evaporation mass flow rate in a horizontal liquid layer partly opened into flowing gas, Tech. Phys. Lett., 39, 795-797 (2013) [35] Königer, A.; Meier, B.; Köhler, W., Measurement of the Soret, diffusion, and thermal diffusion coefficients of three binary organic benchmark mixtures and of ethanol-water mixtures using a beam deflection technique, Phyl. Mag., 89, 10, 907-923 (2009) [36] Chemical Engineers’ Handbook, (Perry, R. H.; Chilton, C. H.; Kirkpatrick, S. D. (1963), McGraw-Hill: McGraw-Hill New York, NY) [37] Lyulin, Y.; Kabov, O., Evaporative convection in a horizontal liquid layer under shear-stress gas flow, J. Heat Mass Transf., 70, 599-609 (2014) [38] Machrafi, H.; Lyulin, Y.; Iorio, C. S.; Kabov, O.; Dauby, P. C., Numerical parametric study of the evaporation rate of a liquid under a shear gas flow: experimental validation and the importance of confinement on the convection cells and the evaporation rate, Int. J. Heat Fluid Flow, 72, 8-19 (2018) [39] Scheid, B.; Margerit, J.; Iorio, C. S., Onset of thermal ripples at the interface of an evaporating liquid under a flow of inert gas, Exp. Fluids, 52, 5, 1107-1119 (2012) [40] [in Russian] This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.