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The engulfment of foreign particles by a freezing interface


The interactions of second-phase particles, liquid droplets or gas bubbles with a solidification front form the basis of various materials synthesis and purification processes and the design of microstructures in cast metal-matrix composites, as well as frost heaving and biological cell interactions. The physical mechanisms of this interaction phenomenon are based upon surface thermodynamic factors, solidification parameters, and fluid dynamic effects such as fluid drag and buoyancy. An overview is presented of the role of various factors which determine the nature as well as the kinetics of foreign particle-solidification front interactions, and the current status and limitations of the various theoretical models of the phenomenon.

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V :

Critical velocity for particle engulfment

L :

Latent heat of fusion

a 0 :

Atomic radius


Atomic volume

D 1 :

Diffusion coefficient in the liquid

T :


R :

Particle radius

ΔS :

Entropy of fusion

ρs :

Density of the solid

ρ1 :

Density of the liquid

ρp :

Density of the particle

k :

Boltzmann's constant

Δv :

Difference in the specific volumes of solid and liquid

G :

Temperature gradient

h 0 :

Critical gap thickness

R b :

Radius of surface bump on particle

σsl :

Surface energy of solid-liquid interface

σpl :

Surface energy of particle-liquid interface

σsp :

Surface energy of solid-particle interface


Viscosity of the melt

g :

Acceleration due to gravity


Density difference between particle and liquid

A :

Hamaker constant

B :


K p :

Thermal conductivity of the particle

K l :

Thermal conductivity of the liquid

C :

Bulk concentration of the liquid

m l :

Slope of liquidus line

K c :

Partition coefficient

C p :

Specific heat of the particle

C 1 :

Specific heat of the liquid


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Asthana, R., Tewari, S.N. The engulfment of foreign particles by a freezing interface. JOURNAL OF MATERIALS SCIENCE 28, 5414–5425 (1993).

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  • Physical Mechanism
  • Dynamic Effect
  • Cell Interaction
  • Purification Process
  • Liquid Droplet