Numerical Simulation of Moving Contact Line Problems Using a Volume-of-Fluid Method

Moving contact lines are implemented in a volume-of-fluid scheme with piecewise linear interface construction. Interfacial tension is treated as a continuous body force, computed from numerical derivatives of a smoothed volume-of-fluid function. Two methods for implementing the contact angle condition are investigated. The first extrapolates the volume-of-fluid function beyond the flow domain, on the basis of the condition that its gradient is perpendicular to the interface and that the normal to the interface at the wall is determined by the contact angle. The second method treats the problem as a three-phase situation and mimics the classical argument of Young. It is found that the latter approach introduces an artificial localized flow, and the extrapolation method is preferable. Slip is a crucial factor in the spreading of contact lines; the numerical method introduces slip at the discrete level, effectively introducing a slip length on the order of the mesh size.