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 J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 1, Pages 48–59 (Mi jsfu459)

Modeling of two-layer fluid flows with evaporation at the interface in the presence of the anomalous thermocapillary effect

Olga N. Goncharova, Ekaterina V. Rezanova

Altai State University, Lenina, 61, Barnaul, 656049, Russia

Abstract: Stationary convective flows of two immiscible viscous incompressible fluids (liquid and gas) under action of the transverse gravity field and longitudinal temperature gradient along the interface are studied analytically. Mathematical model of the fluid flows with the effects of evaporation at the interface is based on exact solutions to the Navier–Stokes equations in the Oberbeck–Boussinesq approximation. The effects of the thermodiffusion and diffusive heat conductivity in the gas-vapor layer are taken into consideration. The obtained solutions are used to model the flows in the two-layer gas-liquid system in the case when a liquid exhibits the anomalous thermocapillary effect. Examples of the two-layer fluid flows are presented for various values of the gas flow rate, longitudinal temperature gradient at the interface and the gravity force acceleration.

Keywords: mathematical model, interface, evaporation, exact solution, anomalous thermocapillary effect.

 Funding Agency Grant Number Russian Foundation for Basic Research 14-08-00163 Authors gratefully acknowledge the support of this work by the Russian Foundation of Basic Research, grant 14-08-00163.

DOI: https://doi.org/10.17516/1997-1397-2016-9-1-48-59

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UDC: 536.25
Accepted: 20.01.2016
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Citation: Olga N. Goncharova, Ekaterina V. Rezanova, “Modeling of two-layer fluid flows with evaporation at the interface in the presence of the anomalous thermocapillary effect”, J. Sib. Fed. Univ. Math. Phys., 9:1 (2016), 48–59

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\Bibitem{GonRez16} \by Olga~N.~Goncharova, Ekaterina~V.~Rezanova \paper Modeling of two-layer fluid flows with evaporation at the interface in the presence of the anomalous thermocapillary effect \jour J. Sib. Fed. Univ. Math. Phys. \yr 2016 \vol 9 \issue 1 \pages 48--59 \mathnet{http://mi.mathnet.ru/jsfu459} \crossref{https://doi.org/10.17516/1997-1397-2016-9-1-48-59} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000412005500006} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. S. S. Vlasova, E. Yu. Prosviryakov, “Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:3 (2016), 567–577
2. V. Sarychev, S. Nevskii, S. Konovalov, A. Granovskii, Yu. Ivanov, V. Gromov, “Model of nanostructure formation in al-si alloy at electron beam treatment”, Mater. Res. Express, 6:2 (2019), 026540
3. E. Yu. Prosviryakov, “New class of exact solutions of navier-stokes equations with exponential dependence of velocity on two spatial coordinates”, Theor. Found. Chem. Eng., 53:1 (2019), 107–114
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