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.
Received: 06.11.2019 Accepted: 06.02.2020
Bibliographic databases:
Document Type:
Article
UDC:519.21
Language: English
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
\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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000526181200007}
Linking options:
https://www.mathnet.ru/eng/jsfu831
https://www.mathnet.ru/eng/jsfu/v13/i2/p197
This publication is cited in the following 1 articles:
Sergey V. Ershkov, Evgeniy Yu. Prosviryakov, Natalya V. Burmasheva, Victor Christianto, “Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review”, Symmetry, 15:10 (2023), 1825
Citation in format AMSBIB
Contact us: