A Dynamic Model for the Interaction Between an Insoluble Particle and an Advancing Solid/Liquid Interface

Abstract

Most models that describe the interaction of an insoluble particle with an advancing solid-liquid interface are based on the assumption of steady state. However, as demonstrated by experimental work, the process does not reach steady state until the particle is pushed for a while by the interface. In this work, a dynamic mathematical model was developed. The dynamic model demonstrates that this interaction is essentially non-steady state and that steady state eventually occurs only when solidification is conducted at sub-critical velocities. The model was tested for three systems: aluminum-zirconia particles, succinonitrilepolystyrene particles, and biphenyl-glass particles. The calculated values for critical velocity of the pushing/engulfment transition were in same range with the experimental ones.