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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

MARINA CHUGUNOVA ,
JOHN R. KING  and
ROMAN M. TARANETS
MARINA CHUGUNOVA
Affiliation:
Institute of Mathematical Sciences, Claremont Graduate University, 150 E. 10th St., Claremont, California 91711, USA email: chugunovamar@yahoo.ca
JOHN R. KING
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK email: john.king@nottingham.ac.uk
ROMAN M. TARANETS
Affiliation:
Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Donetsk, 83114, Ukraine UCLA Department of Mathematics, Los Angeles, CA 90095, USA email: taranets_r@yahoo.com
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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.

Keywords

35K5535K3535K6576A2076D4576D08System of parabolic equationsthin liquid filmssurfactant spreadingfree boundaryfluid interfacewaiting-time phenomenonfinite speed of support propagation
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 4 , August 2017 , pp. 656 - 686
Copyright
Copyright © Cambridge University Press 2016 

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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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