Aw. Rempel et Mg. Worster, Particle trapping at an advancing solidification front with interfacial-curvature effects, J CRYST GR, 223(3), 2001, pp. 420-432
We predict the maximum solidification rate, or critical velocity, V-c at wh
ich an insoluble particle suspended in a melt is pushed ahead of an advanci
ng solidification front by intermolecular forces. At higher solidification
rates the particle is incorporated within the solid. The net intermolecular
force pushing the particle and the viscous resistance opposing it are both
significantly influenced by the shape of the front as it conforms to the p
article in response to interfacial premelting. We predict the entire shape
of the front, within a thin-film approximation, accounting for the freezing
-point depression due to curvature. We show how the interface shape varies
with the magnitude of the surface energy and the closeness of the particle,
and compare these to previous, ad hoc representations of the interface. We
confirm the scaling results of previous, more approximate, analyses for th
e case in which the intermolecular forces are dominated by nonretarded van
der Weals interactions, and provide new results for other power-law interac
tions. We examine how the particle behaviour changes as its radius increase
s so that the effect of interfacial curvature is diminished. (C) 2001 Elsev
ier Science B.V. All rights reserved.