Effect of shrinkage flow on particle engulfment

Lubrication theory is used to derive an expression for the lubrication force experienced by a spherical particle as it approaches a directionally solidified interface. The analysis focuses on the effect of shrinkage flow. We show that for liquid substances that expand upon solidification, such as water, the lubrication force can act to push the particle away from the interface. Thus, the present analysis proposes a new mechanism for particle rejection that enters into play at distances that are greater than those at which the Van der Waals forces act.