The interface dynamics of a surfactant drop on a thin viscous film

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...

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Bibliographic Details
Published in:European journal of applied mathematics 2017-08, Vol.28 (4), p.656-686
Main Authors: CHUGUNOVA, MARINA, KING, JOHN R., TARANETS, ROMAN M.
Format: Article
Language:English
Subjects:
Applied mathematics
Diffusion coefficient
Functional equations
Propagation
Surface diffusion
Surfactants
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Summary: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.
ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792516000474