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fluid interface

European Journal of Applied Mathematics (1)

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The interface dynamics of a surfactant drop on a thin viscous film †
MARINA CHUGUNOVA, JOHN R. KING, ROMAN M. TARANETS
Journal:

European Journal of Applied Mathematics / Volume 28 / Issue 4 / August 2017

Published online by Cambridge University Press:

08 November 2016, pp. 656-686
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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.