The interaction between a particle and an advancing solidification front

We derive analytical expressions for the velocity of an insoluble particle near an advancing solidification front when the intermolecular interactions are described by a power-law dependence between the film thickness and the undercooling. We predict that the maximum particle velocity, which corresp onds to the lowest solidification velocity at which particle trapping occur s, depends inversely on the particle radius. The critical velocity is less sensitive to the temperature gradient and the precise dependence changes wi th different interaction types. When the critical velocity is exceeded, the particle becomes trapped within the solid region after being pushed slight ly ahead of its initial position. The predicted particle displacement is ty pically only a fraction of the particle radius. Particle buoyancy can enhan ce or reduce the tendency for the particle to be captured, though it does n ot affect the parametric dependence of the critical velocity on the particl e radius and the temperature gradient. (C) 1999 Elsevier Science B.V. All r ights reserved.