, Volume 63, Issue 5, pp 122-128
Date: 08 Nov 2008

Solitary waves in a viscous liquid film flowing down a thin vertical cylinder

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Abstract

Several equations to describe the flow of a viscous liquid film on a thin cylinder are derived. The solitary-wave solutions to these equations are studied. The families of solutions are constructed for the first two eigenvalues that correspond to single-humped and double-humped waves. It is found that these families become similar as the similarity parameter increases. The dependencies of phase velocities and wave amplitudes on the free parameters of the problem are analyzed. The resulting solutions are compared with solitary waves in films on a flat surface.

Original Russian Text © V.Ya. Shkadov, A.N. Beloglazkin, S.V. Gerasimov, 2008, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2008, Vol. 63, No. 5, pp. 39–45.