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Journal of Siberian Federal University. Mathematics & Physics, 2018, Volume 11, Issue 2, Pages 194–205
DOI: https://doi.org/10.17516/1997-1397-2018-11-2-194-205 (Mi jsfu649) 		 
The motion of a binary mixture with a cylindrical free boundary at small Marangoni numbers

Viсtor K. Andreevab, Natalya L. Sobachkinab

a Institute of Computational Modelling RAS SB, Akademgorodok, 50/44, Krasnoyarsk, 660036, Russia
b Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
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DOI: https://doi.org/10.17516/1997-1397-2018-11-2-194-205
Abstract: We studied the problem of axisymmetric motion of a binary mixture with a cylindrical free boundary at small Marangoni numbers. 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 satisfy certain conditions imposed on the external temperature. Some examples of numerical reconstruction of the velocity, temperature and concentration fields are considered, which correspond well with the theoretical results.
Keywords: binary mixture, free boundary, stationary solution, Laplace transformation, the Marangoni number.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00067_а
This work was supported by a grant from the Russian Foundation for basic research no. 14-01-00067.
Received: 19.08.2017
Received in revised form: 28.08.2017
Accepted: 06.12.2017
Bibliographic databases:
Document Type: Article
UDC: 532.516
Language: English
Citation: Viсtor K. Andreev, Natalya L. Sobachkina, “The motion of a binary mixture with a cylindrical free boundary at small Marangoni numbers”, J. Sib. Fed. Univ. Math. Phys., 11:2 (2018), 194–205
Citation in format AMSBIB
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\by Viсtor~K.~Andreev, Natalya~L.~Sobachkina
\paper The motion of a binary mixture with a cylindrical free boundary at small Marangoni numbers
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2018
\vol 11
\issue 2
\pages 194--205
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\crossref{https://doi.org/10.17516/1997-1397-2018-11-2-194-205}
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