ABSTRACT
In numerical simulation, it is possible to model the local transient flows as quasi steady state processes and use explicit time integration. Then, free boundary conditions [Eqs. (5a) and (6a, b)] can be used in a similar way to the macroscopic flow. The capillary pressure is thus introduced on the known surface (known curvature) together with the other static conditions. In the first step of this procedure, there will be an error, unless implicit time integration is used. The reason for this error can be demonstrated. Consider the example of capillary rise or depression in a vertical capillary. Starting from the flat liquid surface, there will be no capillary pressure to originate the motion. To avoid it, it would also be possible to initially adjust the contact angle. This error and the error from the explicit time integration is not very important for our purpose because in our case, the hydrodynamic pressure gradient will always originate the flow and then the capillary pressure effect will add to it after a curvature is already formed at the interface. Small inaccuracies in the resin surface are not important in our case and some oscillation are expected for very low capillary numbers [19].
