Asymptotic analysis of the crystal-melt interface profile near a foreign particle

Mathematics Department, The University of Alabama Tuscaloosa, Alabama 35487-0350, USA

Corresponding author: lhadji@euler.math.ua.edu

Received: 2 May 2000
Accepted: 21 June 2000

Abstract

During the directional solidification of a pure substance, the presence in the melt of an inert particle is known to induce local deformations in the solid-liquid interface before the particle is either pushed or engulfed by the moving front. In this work, an axisymmetric model, which accounts for fluid flow effects and heat conduction in the solid and particle, is considered. The interface temperature accounts for the undercoolings due to the Gibbs-Thomson effect and to the long-range intermolecular forces in the melt film separating the particle from the front. An asymptotic analysis has been carried out to derive a uniformly valid representation for the crystal-melt interface profile when the disjoining pressure is the sole cause of interfacial deformation. Thus, the dependence of the interface morphology on the dimensionless groupings governing the problem is revealed.