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 J. Sib. Fed. Univ. Math. Phys., 2020, Volume 13, Issue 2, Pages 197–212 (Mi jsfu831)

Rotationally-axisymmetric motion of a binary mixture with a flat free boundary at small Marangoni numbers

Victor K. Andreevab, Natalya L. Sobachkinab

a Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation
b Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: Rotationally-axisymmetric motion of a binary mixture with a flat free boundary at small Marangoni numbers is investigated. The problem is reduced to the inverse linear initial-boundary value problem for parabolic equations. Using Laplace transformation properties the exact analytical solution is obtained. It is shown that a stationary solution is the limiting one with the growth of time if there is a certain relationship between the temperature of the solid wall and the external temperature of the gas. If there is no connection, the convergence to the stationary solution is broken. Some examples of numerical reconstruction of the temperature, concentration and velocity fields are given, which confirm the theoretical conclusions.

Keywords: binary mixture, free boundary, inverse problem, the pressure gradient, the stationary solution, Laplace transformation, thermal Marangoni number.

DOI: https://doi.org/10.17516/1997-1397-2020-13-2-197-212

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UDC: 519.21
Accepted: 06.02.2020
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Citation: Victor K. Andreev, Natalya L. Sobachkina, “Rotationally-axisymmetric motion of a binary mixture with a flat free boundary at small Marangoni numbers”, J. Sib. Fed. Univ. Math. Phys., 13:2 (2020), 197–212

Citation in format AMSBIB
\Bibitem{AndSob20} \by Victor~K.~Andreev, Natalya~L.~Sobachkina \paper Rotationally-axisymmetric motion of a binary mixture with a flat free boundary at small Marangoni numbers \jour J. Sib. Fed. Univ. Math. Phys. \yr 2020 \vol 13 \issue 2 \pages 197--212 \mathnet{http://mi.mathnet.ru/jsfu831} \crossref{https://doi.org/10.17516/1997-1397-2020-13-2-197-212} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000526181200007}