A solid-liquid-gas moving contact line is considered through a diffuse-interface model with the classical boundary condition of no-slip at the solid surface. Examination of the asymptotic behaviour as the contact line is approached shows that the relaxation of the classical model of a sharp liquid-gas interface, whilst retaining the no-slip condition, resolves the stress, and pressure singularities associated with the moving contact line problem while the fluid velocity is well defined (not multi-valued). The moving contact line behaviour is analysed for a general problem relevant for any density dependent dynamic viscosity and volume viscosity, and for general microscopic contact angle and double well free-energy forms. Away from the contact line, analysis of the diffuse-interface model shows that the Navier–Stokes equations and classical interfacial boundary conditions are obtained at leading order in the sharp-interface limit, justifying the creeping flow problem imposed in an intermediate region in the seminal work of Seppecher [Int. J. Eng. Sci. 34, 977–992 (1996)]. Corrections to Seppecher's work are given, as an incorrect solution form was originally used.
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September 2013
Research Article|
September 27 2013
The contact line behaviour of solid-liquid-gas diffuse-interface models
David N. Sibley;
David N. Sibley
a)
1Department of Chemical Engineering,
Imperial College London
, London SW7 2AZ, United Kingdom
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Andreas Nold;
Andreas Nold
1Department of Chemical Engineering,
Imperial College London
, London SW7 2AZ, United Kingdom
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Nikos Savva;
Nikos Savva
1Department of Chemical Engineering,
Imperial College London
, London SW7 2AZ, United Kingdom
2School of Mathematics,
Cardiff University
, Cardiff CF24 4AG, United Kingdom
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Serafim Kalliadasis
Serafim Kalliadasis
b)
1Department of Chemical Engineering,
Imperial College London
, London SW7 2AZ, United Kingdom
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a)
Electronic mail: d.sibley@imperial.ac.uk
b)
Electronic mail: s.kalliadasis@imperial.ac.uk
Physics of Fluids 25, 092111 (2013)
Article history
Received:
February 14 2013
Accepted:
August 19 2013
Citation
David N. Sibley, Andreas Nold, Nikos Savva, Serafim Kalliadasis; The contact line behaviour of solid-liquid-gas diffuse-interface models. Physics of Fluids 1 September 2013; 25 (9): 092111. https://doi.org/10.1063/1.4821288
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