Numerical calculation of the drag force applied to particle pushing

The interaction of solid particles with a solidifying interface is studied with numerical and analytical models for the drag and pushing forces. The numerical results of the drag force on a spherical particle and planar interface were compared with the forces given by both, the Stokes and modified Stokes equations. The pushing force was calculated employing the Casimir–Lifshitz–van der Waals force. The results show the range and degree of validity of the Stokes and modified Stokes equations for large and small separations.From this, it is shown that the particle–interface separations for steady pushing obtained numerically, for the same particle radius and solidification velocity. In addition, the critical velocities obtained with the present hybrid model are compared with experimental results published in the literature.