Geodesic
Rotationally-axisymmetric motion of a binary mixture with a flat free boundary at small Marangoni numbers
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 2, pp. 197-212

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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, thermal Marangoni number.
Mots-clés : Laplace transformation 
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     author = {Victor K. Andreev and Natalya L. Sobachkina},
     title = {Rotationally-axisymmetric motion of a binary mixture with a flat free boundary at small {Marangoni} numbers},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {197--212},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a6/}
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Victor K. Andreev; Natalya L. Sobachkina. Rotationally-axisymmetric motion of a binary mixture with a flat free boundary at small Marangoni numbers. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 2, pp. 197-212. http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a6/