The interaction between a particle and an advancing solidification front is studied using a multi-scale computational model developed in Part I. The flow and temperature fields are solved separately at two disparate scales, i.e. at the overall system scale ("outer region") and in the thin melt layer ("inner region") between the particle and the front. The solutions from the inner and outer regions are coupled at a matching region. The coupled dynamics of the particle and phase boundary motion, including lubrication and disjoining pressure effects in the premelted film between the particle and the front is captured in the simulations. Results show that particle pushing (as opposed to particle engulfment) can occur when the ratio of thermal conductivity of the particle to the melt, k(p)/k(l) < 1. The velocity of the solidification front at which the transition from particle pushing to particle engulfment occurs, i.e. the critical velocity for particle engulfment, is naturally obtained from the coupled dynamics. No ad hoc assumptions to identify the critical velocity need be made. The results also provide insights into the physics of particle-solidification front interactions. (C) 2007 Elsevier Ltd. All rights reserved.