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Particle engulfment and pushing by solidifying interfaces: Part II. Microgravity experiments and theoretical analysis

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Results of the directional solidification (DS) experiments on particle engulfment and pushing by solidifying interfaces (PEP), conducted on the space shuttle Columbia during the Life and Microgravity Science (LMS) Mission, are reported. Two pure aluminum (99.999 pct) 9 mm cylindrical rods, loaded with about 2 vol pct 500µm-diameter zirconia particles, were melted and resolidified in the microgravity (µg) environment of the shuttle. One sample was processed at a stepwise increased solidification velocity and the other at a stepwise decreased velocity. It was found that a pushing/engulfment transition (PET) occurred in the velocity range of 0.5 to 1 µm/s. This is smaller than the ground PET velocity of 1.9 to 2.4 µm/s. This demonstrates that natural convection increases the critical velocity. A previously proposed analytical model for PEP was further developed. A major effort to identify and produce data for the surface energy of various interfaces required for calculation was undertaken. The predicted critical velocity for PET was 0.775 µm/s.

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a :

coefficient (0 for no contact and 1 for perfect contact)

a O :

atomic diameter

A :

Hammaker constant

B :

constant defining the disjoining pressure (CTM model)

d :

equilibrium distance

d cr :

critical distance

D :

liquid diffusivity

E vdW :

van der Waals energy

F g :

gravity force

F D :

drag force

F L :

life force

F vdW :

van der Waals force

F γσ :

interaction force between the particle and the SL interface

G :

temperature gradient in the liquid (CTM model)

ΔH f :

latent heat of fusion

ΔH vap :

heat of sublimation

kB :

Boltzman’s constant

K O :

material constant


ratio between the thermal conductivity of the particle (K P) and of the liquid (K L)

n :

exponent between 2 and 7 (UCJ and SAS models)

R :

particle radius

ΔS f :

entropy of fusion

T :


V :


V cr :

critical velocity

V L :

fluid velocity at the SL interface parallel to the interface

V SL :

solidification velocity

W ad :

work of adhesion

γ :

surface energy

η :

liquid viscosity

ϑ :

contact angle

σ :

surface tension

Δσ O :

surface tension difference

Δγ0 :

surface energy difference


atomic volume

Ω (∞):

function with value of 0.34

L :

liquid (matrix)

P :


S :

solid (matrix)


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Stefanescu, D.M., Juretzko, F.R., Catalina, A. et al. Particle engulfment and pushing by solidifying interfaces: Part II. Microgravity experiments and theoretical analysis. Metall Mater Trans A 29, 1697–1706 (1998).

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