| Abstract: |
| In this talk, we consider a phase field 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. is adopted. We discretize model equations using a continuous finite element method in space and a modified midpoint scheme in time. A discrete energy law which is a good approximation of the continuous energy law is derived for the scheme. 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 computed using a relatively coarse grid. We also derive the discrete energy law for the droplet displacement case, which is a slightly different problem due to the boundary condition. Accuracy and stability of the scheme are validated through some test computations. |
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