The interaction between a particle and an advancing solidi"cation front

We derive analytical expressions for the velocity of an insoluble particle near an advancing solidi"cation front when the intermolecular interactions are described by a power-law dependence between the "lm thickness and the undercooling. We predict that the maximum particle velocity, which corresponds to the lowest solidi"cation velocity at which particle trapping occurs, depends inversely on the particle radius. The critical velocity is less sensitive to the temperature gradient and the precise dependence changes with di!erent interaction types. When the critical velocity is exceeded, the particle becomes trapped within the solid region after being pushed slightly ahead of its initial position. The predicted particle displacement is typically only a fraction of the particle radius. Particle buoyancy can enhance or reduce the tendency for the particle to be captured, though it does not a!ect the parametric dependence of the critical velocity on the particle radius and the temperature gradient. ( 1999 Elsevier Science B.V. All rights reserved. PACS: 64.70.Dv; 68.15.#e; 68.45.Gd; 81.30.Fb