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The conventional no-slip boundary condition leads to a non-integrable stresssingularity at a moving contact line. This makes numerical simulationschallenging, especially when capillary effects are essential for the dynamicsof the flow. This paper presents a new boundary methodology, suitable fornumerical simulation of flow of two immiscible and incompressible fluids in thepresence of moving contact points. The methodology is based on combining arelation between the apparent contact angle and the contact point velocity withthe similarity solution for Stokes flow at a planar interface. The relationbetween angle and velocity can be determined by theoretical arguments, or fromsimulations using a more detailed model. The approach here uses the phase fieldmodel in a micro domain, with physically relevant parameters for moleculardiffusion and interface thickness. The methodology is used to formulate a newboundary condition for the velocity. Numerical results illustrate theusefulness.

A Computational Multiscale Model for Contact Line Dynamics