A dynamic model for the interaction between a solid particle and an advancing solid/liquid interface

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 subcritical velocities. The model was tested for three systems: aluminum-zirconia particles, succinonitrile-polystyrene particles, and biphenyl-glass particles. The calculated values for critical velocity of the pushing/engulfment transition were in the same range with the experimental ones.

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