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Unifying binary fluid diffuse-interface models in the sharp-interface limit

Published online by Cambridge University Press:  01 November 2013

David N. Sibley ,
Andreas Nold  and
Serafim Kalliadasis
David N. Sibley
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
Andreas Nold
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
Serafim Kalliadasis*
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: s.kalliadasis@imperial.ac.uk
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Abstract

Recent results published by Gugenberger et al. on surface diffusion (Phys. Rev. E, vol. 78, 2008, 016703), show that the sharp-interface limit of the phase field models often adopted in the literature fails to produce the appropriate boundary conditions. With this knowledge, we consider the sharp-interface limit of phase field models for binary fluids, obtained carefully, where hydrodynamic equations are coupled to phase field evolution based on Cahn–Hilliard or Allen–Cahn theories, in a variety of guises, and unify and contrast their forms and behaviours in the sharp-interface limit. In particular, a tensorial mobility model is analysed, which allows the bulk fluids in the outer region to satisfy classical Navier–Stokes type equations to all orders in the Cahn number.

JFM classification

Mathematical Foundations: General fluid mechanics Interfacial Flows (free surface): Interfacial Flows (free surface) Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 736 , 10 December 2013 , pp. 5 - 43
Copyright
©2013 Cambridge University Press 

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