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Unifying binary fluid diffuse-interface models in the sharp-interface limit
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DOI：10.1017/jfm.2013.521.png)
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Abstract
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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.
Keywords:
general fluid mechanics
interfacial flows (free surface)
multiphase flow
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