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Numerical Simulation for Moving Contact Line with Continuous Finite Element Schemes

Part of: Two-phase and multiphase flows Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  03 July 2015

Yongyue Jiang ,
Ping Lin ,
Zhenlin Guo  and
Shuangling Dong
Yongyue Jiang*
Affiliation:
School of Mathematics and Physics, University of Science and Technology, Beijing 100083, P.R. China
Ping Lin
Affiliation:
Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, United Kingdom
Zhenlin Guo
Affiliation:
Department of mathematics, University of California Irvine, CA 92697-3875, 540H Rowland Hall, Irvine, USA
Shuangling Dong
Affiliation:
School of Aerospace Engineering, Tsinghua University, Beijing 100084, P.R. China
*
*Corresponding author. Email addresses: [email protected] (Y. Jiang), [email protected] (P. Lin)
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Abstract

In this paper, we compute a phase field (diffuse interface) model of Cahn-Hilliard type for moving contact line problems governing the motion of isothermal multiphase incompressible fluids. The generalized Navier boundary condition proposed by Qian et al. [1] is adopted here. We discretize model equations using a continuous finite element method in space and a modified midpoint scheme in time. We apply a penalty formulation to the continuity equation which may increase the stability in the pressure variable. Two kinds of immiscible fluids in a pipe and droplet displacement with a moving contact line under the effect of pressure driven shear flow are studied using a relatively coarse grid. We also derive the discrete energy law for the droplet displacement case, which is slightly different due to the boundary conditions. The accuracy and stability of the scheme are validated by examples, results and estimate order.

Keywords

Two-phase flowgeneralized Navier boundary conditioncontinuous finite elementsmoving contact line

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 76T10: Liquid-gas two-phase flows, bubbly flows
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 1 , July 2015 , pp. 180 - 202
Copyright
Copyright © Global-Science Press 2015 

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