Modeling the interaction of convex solidifying interfaces with spherical particles

The phenomenon of pushing during solidification is modeled for the case of particles producing a convex interface. The thermal and fluid fields generated by the particle-melt-solid system are calculated in a decoupled way determining in the first place the shape of the interface and then, the two main forces acting during pushing; the drag and repulsion forces. The thermal and fluid flow fields were calculated using finite element methods. Both, the drag and repulsion forces are integrated at each step and compared until both are equal and the steady state of pushing is reached. The repulsion force is integrated using the Casimir-Lifshitz-Van der Waals interaction. The model predicts the equilibrium distance in a steady state of pushing for spherical particles and a convex solidifying interface. It is shown that the equilibrium separation distance for a convex interface results in a larger solidification velocity for trapping with respect to an ideal planar interface. The model results were in good agreement with experimental results for the critical velocity reported in the literature.