Thermal force induced by the presence of a particle near a solidifying interface

The presence of a foreign particle in the melt, ahead of a solid-liquid interface, leads to the onset of interfacial deformations if the thermal conductivity of the particle, k(p), differs from that of the melt, k(l). In this paper, the influence of the thermal conductivity contrast on the interaction between the solidifying interface and the particle is quantified. We show that the interface distortion gives rise to a thermal force whose expression is given by F(th)=2piLGa3(1-alpha)/(2+alpha)T(m), where L is the latent heat of fusion per unit volume, T(m) is the melting point, a is the particle's radius, G the thermal gradient in the liquid phase and alpha=k(p)/k(l). The derivation makes use of the following assumptions: (i) the particle is small compared to the horizontal extent of the interface, (ii) the particle is placed in the near proximity of the deformable solid-liquid interface, and (iii) the interface is practically immobile in the calculation of the thermal field, i.e., V<