Large cells in nonlinear marangoni convection

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Abstract

The classical problem of surface-tension-driven convection in a liquid film is considered. If the film is nearly thermally insulated, the longitudinal dimension of the convective cells is significantly greater (near the critical Marangoni number) than the film thickness. As a result one can separate horizontal and vertical space variables and so lower the dimensionality of the problem. For example, in the two-dimensional problem the dynamics of the formation and stabilization of cells is described by the following one-dimensional equation for the average temperature perturbation of the film: ∂F ∂τ+ 1 ∂4F 15 ∂π4+ ∂ ∂ξ(1- 48 35( ∂F ∂ξ)2+ 13∂2F 10∂ξ2) ∂F ∂ξ+βF=0.

Original languageEnglish
Pages (from-to)227-235
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume4
Issue number2
DOIs
StatePublished - Jan 1982

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