scholarly journals The Sharp Interface Limit of a Phase Field Model for Moving Contact Line Problem

2007 ◽  
Vol 14 (3) ◽  
pp. 287-294 ◽  
Author(s):  
Xiao-Ping Wang ◽  
Ya-Guang Wang
Keyword(s):  
Contact Line ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Sharp Interface Limit ◽  
Moving Contact Line ◽  
Moving Contact

On the van der Waals–Cahn–Hilliard phase-field model and its equilibria conditions in the sharp interface limit

2010 ◽  
Vol 140 (6) ◽  
pp. 1161-1186 ◽  
Author(s):  
Wolfgang Dreyer ◽  
Christiane Kraus
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Field Model ◽  
Van Der Waals ◽  
Phase Field Model ◽  
Entropy Inequality ◽  
Sharp Interface ◽  
Energy Estimates ◽  
Sharp Interface Limit ◽  
Entropy Flux

We study the thermodynamic consistency of phase-field models, which include gradient terms of the density ρ in the free-energy functional such as the van der Waals–Cahn–Hilliard model. It is well known that the entropy inequality admits gradient and higher-order gradient terms of ρ in the free energy only if either the energy flux or the entropy flux is represented by a non-classical form. We identify a non-classical entropy flux, which is not restricted to isothermal processes, so that gradient contributions are possible.We then investigate equilibrium conditions for the van der Waals–Cahn–Hilliard phase-field model in the sharp interface limit. For a single substance thermodynamics provides two jump conditions at the sharp interface, namely the continuity of the Gibbs free energies of the adjacent phases and the discontinuity of the corresponding pressures, which is balanced by the mean curvature. We show that these conditions can be also extracted from the van der Waals–Cahn–Hilliard phase-field model in the sharp interface limit. To this end we prove an asymptotic expansion of the density up to the first order. The results are based on local energy estimates and uniform convergence results for the density.

scholarly journals Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines

2018 ◽  
Vol 849 ◽  
pp. 805-833 ◽  
Author(s):  
Xianmin Xu ◽  
Yana Di ◽  
Haijun Yu
Keyword(s):  
Boundary Condition ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Slip Boundary Condition ◽  
Sharp Interface ◽  
Navier Slip ◽  
Slip Boundary ◽  
Moving Contact ◽  
Moving Contact Lines

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for binary fluids with moving contact lines are studied by asymptotic analysis and numerical simulations. The effects of the mobility number as well as a phenomenological relaxation parameter on the boundary condition are considered. In asymptotic analysis, we consider both the cases that the mobility number is proportional to the Cahn number and the square of the Cahn number, and derive the sharp-interface limits for several set-ups of the boundary relaxation parameter. It is shown that the sharp-interface limit of the phase-field model is the standard two-phase incompressible Navier–Stokes equations coupled with several different slip boundary conditions. Numerical results are consistent with the analysis results and also illustrate the different convergence rates of the sharp-interface limits for different scalings of the two parameters.

scholarly journals Phase-field model of cell motility: Traveling waves and sharp interface limit

2016 ◽  
Vol 354 (10) ◽  
pp. 986-992 ◽  
Author(s):  
Leonid Berlyand ◽  
Mykhailo Potomkin ◽  
Volodymyr Rybalko
Keyword(s):  
Cell Motility ◽  
Traveling Waves ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Sharp Interface Limit

scholarly journals An anisotropic phase-field model for solid-state dewetting and its sharp-interface limit

Nonlinearity ◽  
2017 ◽  
Vol 30 (4) ◽  
pp. 1465-1496 ◽  
Author(s):  
Marion Dziwnik ◽  
Andreas Münch ◽  
Barbara Wagner
Keyword(s):  
Solid State ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Sharp Interface Limit ◽  
Anisotropic Phase

scholarly journals Sharp Interface Limit for a Phase Field Model in Structural Optimization

2016 ◽  
Vol 54 (3) ◽  
pp. 1558-1584 ◽  
Author(s):  
Luise Blank ◽  
Harald Garcke ◽  
Claudia Hecht ◽  
Christoph Rupprecht
Keyword(s):  
Structural Optimization ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Sharp Interface Limit

scholarly journals Sharp interface limit in a phase field model of cell motility

2017 ◽  
Vol 12 (4) ◽  
pp. 551-590 ◽  
Author(s):  
Leonid Berlyand ◽  
◽  
Mykhailo Potomkin ◽  
Volodymyr Rybalko ◽  
Keyword(s):  
Cell Motility ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Sharp Interface Limit
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