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The interface dynamics of a surfactant drop on a thin viscous film†
Published online by Cambridge University Press: 08 November 2016
Abstract
We study a system of two coupled parabolic equations that models the spreading of a drop of an insoluble surfactant on a thin liquid film. Unlike the previously known results, the surface diffusion coefficient is not assumed constant and depends on the surfactant concentration. We obtain sufficient conditions for finite speed of support propagation and for waiting-time phenomenon by application of an extension of Stampacchia's lemma for a system of functional equations.
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- Copyright © Cambridge University Press 2016
Footnotes
The research of Roman Taranets leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement No PIIF-GA-2009-254521 - [TFE]. This work was partially supported by a grant from the Simons Foundation (#275088 to Marina Chugunova).
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