Front Tracking Computation of Trijunction Solidification with Volume Change

We test a front-tracking/finite difference method for simulation of axisymmetric drop solidification, where the melt is confined by its own surface tension. The problem includes temporal evolution of three interfaces, i.e. solid–liquid, solid–air, and liquid–air, that are explicitly tracked. The solid–liquid interface is propagated with a normal velocity that is calculated from the normal temperature gradient across the front and the latent heat. The liquid–air front is advected by the velocity interpolated from nearest bulk fluid flow velocities, while constant growth angle is assumed at the three-phase “trijunction”. Method validation is carried out by comparing computational results with related experiments on a drop solidifying on a cold plate in which there exists volume expansion due to density difference between the solid and liquid phases.