A level-set method for two-phase flows with moving contact line and insoluble surfactant. (English) Zbl 1349.76554
Summary: A level-set method for two-phase flows with moving contact line and insoluble surfactant is presented. The mathematical model consists of the Navier-Stokes equation for the flow field, a convection-diffusion equation for the surfactant concentration, together with the Navier boundary condition and a condition for the dynamic contact angle derived by the second author et al. [Phys. Fluids 22, No. 10, Paper No. 102103, 19 p. (2010; Zbl 1308.76082)]. The numerical method is based on the level-set continuum surface force method for two-phase flows with surfactant developed by the first author, Y. Yang and J. Lowengrub [J. Comput. Phys. 231, No. 17, 5897–5909 (2012; Zbl 1522.76105)] with some cautious treatment for the boundary conditions. The numerical method consists of three components: a flow solver for the velocity field, a solver for the surfactant concentration, and a solver for the level-set function. In the flow solver, the surface force is dealt with using the continuum surface force model. The unbalanced Young stress at the moving contact line is incorporated into the Navier boundary condition. A convergence study of the numerical method and a parametric study are presented. The influence of surfactant on the dynamics of the moving contact line is illustrated using examples. The capability of the level-set method to handle complex geometries is demonstrated by simulating a pendant drop detaching from a wall under gravity.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 76Txx | Multiphase and multicomponent flows |
Keywords:
two-phase flow; moving contact line; insoluble surfactant; level-set method; continuum surface force; slip boundary conditionSoftware:
IIMPACKReferences:
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