Modelling and asymptotic analysis of particle-interface interaction

An asymptotic study of the interaction between a foreign particle and a solidifying interface is undertaken. The analysis focuses primarily on the influence of the disjoining pressure on particle pushing or engulfment. The analysis considers only thermal effects in a pure substance in which a neutrally buoyant spherical particle, whose thermal conductivity is equal to that of the melt, is positioned near the solid-liquid interface. The interface equilibrium temperature includes the undercooling effects due to both the front curvature (the Gibbs-Thomson effect) and the long-range intermolecular forces (nonretarded van der Waals interactions) in the thin film behind the particle. A uniformly valid asymptotic representation for the front shape is derived and used to infer the gap width separating the particle from the solid front. The latter is utilized to calculate the growth rate that results from a balance of the van der Waals and Stokes forces. An attempt is also made at deriving an expression for the critical velocity for continuous pushing from the balance of forces.