The interaction between a particle and an advancing solidification front

Abstract

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.

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“…If the physical mechanisms controlling the interactions are relatively well understood for single large particles, the solidification behaviour of colloidal suspensions is a matter of great interest, but highly challenging. Conclusions derived from single large particles experiments [1][2][3][4][5][6] can hardly be extrapolated to smaller particles (<1 microns) where Brownian motion is dominating and segregation effects are negligible. The analysis is further complicated by the necessity to take into account the various interactions between particles, which could be of different natures: electrostatic, Van der Waals, steric, etc… Additional deviations from the ideal situation, which could be modelled, such as the distribution of particle size, their surface state, charge and roughness, could have a major influence over the general behaviour and stability of the system but are difficult to take into account theoretically.…”

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