A gradient stable scheme for a phase field model for the moving contact line problem

2012 ◽  
Vol 231 (4) ◽  
pp. 1372-1386 ◽  
Author(s):  
Min Gao ◽  
Xiao-Ping Wang
Keyword(s):  
Contact Line ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Stable Scheme

Numerical Approximations for Allen-Cahn Type Phase Field Model of Two-Phase Incompressible Fluids with Moving Contact Lines

2017 ◽  
Vol 21 (3) ◽  
pp. 867-889 ◽  
Author(s):  
Lina Ma ◽  
Rui Chen ◽  
Xiaofeng Yang ◽  
Hui Zhang
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Contact Line ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Two Phase ◽  
Navier Boundary Conditions ◽  
Moving Contact ◽  
Type Phase

AbstractIn this paper, we present some efficient numerical schemes to solve a two-phase hydrodynamics coupled phase field model with moving contact line boundary conditions. The model is a nonlinear coupling system, which consists the Navier-Stokes equations with the general Navier Boundary conditions or degenerated Navier Boundary conditions, and the Allen-Cahn type phase field equations with dynamical contact line boundary condition or static contact line boundary condition. The proposed schemes are linear and unconditionally energy stable, where the energy stabilities are proved rigorously. Various numerical tests are performed to show the accuracy and efficiency thereafter.

A phase-field-based lattice Boltzmann method for moving contact line problems on curved stationary boundaries in two dimensions

2019 ◽  
Vol 30 (06) ◽  
pp. 1950044
Author(s):  
Weifeng Zhao
Keyword(s):  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Two Dimensions ◽  
Curved Boundaries ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Boltzmann Method

In this work, we propose a phase-field-based lattice Boltzmann method to simulate moving contact line (MCL) problems on curved boundaries. The key point of this method is to implement the boundary conditions on curved solid boundaries. Specifically, we use our recently proposed single-node scheme for the no-slip boundary condition and a new scheme is constructed to deal with the wetting boundary conditions (WBCs). In particular, three kinds of WBCs are implemented: two wetting conditions derived from the wall free energy and a characteristic MCL model based on geometry considerations. The method is validated with several MCL problems and numerical results show that the proposed method has utility for all the three WBCs on both straight and curved boundaries.

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