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Determination of the Thickness and Composition Profiles for aFilm of Binary Mixture on a Solid Substrate

Published online by Cambridge University Press:  09 June 2010

L. Fraštia ,
U. Thiele  and
L. M. Pismen
L. Fraštia*
Affiliation:
Department of Mathematical Sciences, Loughborough University Loughborough, Leicestershire, LE11 3TU, UK
U. Thiele
Affiliation:
Department of Mathematical Sciences, Loughborough University Loughborough, Leicestershire, LE11 3TU, UK
L. M. Pismen
Affiliation:
Minerva Center for Nonlinear Physics of Complex Systems Technion–Israel Institute of Technology, 32000 Haifa, Israel
*
* Corresponding author. E-mail:L.Frastia@lboro.ac.uk
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Abstract

We determine the steady-state structures that result from liquid-liquid demixing in afree surface film of binary liquid on a solid substrate. The considered model correspondsto the static limit of the diffuse interface theory describing the phase separationprocess for a binary liquid (model-H), when supplemented by boundary conditions at thefree surface and taking the influence of the solid substrate into account. The resultingvariational problem is numerically solved employing a Finite Element Method on an adaptivegrid. The developed numerical scheme allows us to obtain the coupled steady-state filmthickness profile and the concentration profile inside the film. As an example wedetermine steady state profiles for a reflection-symmetric two-dimensional droplet forvarious surface tensions of the film and various preferential attraction strength of onecomponent to the substrate. We discuss the relation of the results of the present diffuseinterface theory to the sharp interface limit and determine the effective interfacetension of the diffuse interface by several means.

Keywords

Cahn-Hilliard theorymodel-Hphase separationdiffuse interfacephase-field modeldemixing coupled to dewettingsurface evolutionvariational methodFEM
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 1: Instability and patterns. Issue dedicated to the memory of A. Golovin , 2011 , pp. 62 - 86
Copyright
© EDP Sciences, 2010

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