Geodesic
The loss of stability equilibrium between two liquids in cylinder the presence of interface
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 558-565

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The arising convection problem in a two-layers cylindrical system was considered. To seek for it solution the method of variables separation was used. As result obtained the homogeneous differential equation of sixth order with constant coefficients of the complicated boundary conditions. For the case of weightlessness and the monotonic disturbances the analytical expression for the critical Marangoni numbers were found. It is proved that with increasing radius of the cylinder, these numbers tend to well-known Marangoni number for a system of two flat layers.
Mots-clés : interface
Keywords: weightlessenss, critical Marangoni number. 
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     author = {Eugeny P. Magdenko},
     title = {The loss of stability equilibrium between two liquids in cylinder the presence of interface},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {558--565},
     publisher = {mathdoc},
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     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a11/}
}
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Eugeny P. Magdenko. The loss of stability equilibrium between two liquids in cylinder the presence of interface. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 558-565. http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a11/