Asymptotic analysis of particle engulfmemt

Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Nov;60(5 Pt B):6180-3. doi: 10.1103/physreve.60.6180.


An asymptotic analysis is conducted on the interaction between an insoluble spherical particle and an advancing solid-liquid interface when the particle is in the near-contact region (gap thickness is much smaller than the particle's radius). The analysis considers only thermal effects in a pure substance. The interface equilibrium temperature includes the undercooling effects due to the front curvature and to the long-range intermolecular forces in the thin melt film behind the particle. An expression for the crystal-particle gap thickness is derived and used to calculate the threshold value for the front velocity V(T) which separates pushing from engulfment.