A numerical investigation of contact line motion

The motion of the free surface of a viscous drop is investigated. By using lubrication theory, a model is developed for the motion of the free surface which includes both the effect of slip and the dependence of the contact angle on the slip velocity. The resulting nonlinear partial differential equation is solved in several ways. First the initial motion of the drop at a non-equilibrium contact is investigated using the method of matched asymptotics. Then a pseudo-spectral method is developed to numerically solve the full nonlinear system. The dependence of the spreading rate of the drop on the various physical parameters and for different slip models is determined.; The forced motion of a drop trapped in the vertex of a cone is also studied in the lubrication limit. This problem is solved in several ways. First the nonlinear lubrication model is solved numerically using a pseudo-spectral method. The lubrication model is also linearized for small forcing amplitudes, and solved numerically with a finite difference method. A small capillary number limit of the nonlinear model is taken, resulting in a nonlinear ordinary differential equation which is solved numerically. Finally the small capillary number limit is also linearized about a small forcing amplitude and solved analytically. In addition, the viscous and contact line dissipation associated with the motion is determined in all these limits. It is found that in certain limits, the contact line dissipation can dominate the viscous dissipation.