A theory for the interaction of particles with a solidifying front

Bolling, G. F.; Cissé, J.

doi:10.1016/0022-0248(71)90046-7

Cited by 236 publications

(111 citation statements)

References 7 publications

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“…When the solidi"cation velocity is too rapid or the particle is too large, the separation decreases below this threshold and the particle becomes trapped in the growing solid. In a re"nement of these ideas, Bolling and CisseH [5] noted that the viscous drag accompanying #uid motion around the particle is a!ected by the deformation of the ice}liquid interface as the local melting temperature is lowered by the presence of the particle.…”

Section: Introductionmentioning

confidence: 99%

The interaction between a particle and an advancing solidification front

Rempel

Worster

1999

Journal of Crystal Growth

142

172

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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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Section: Introductionmentioning

confidence: 99%

The interaction between a particle and an advancing solidification front

Rempel

Worster

1999

Journal of Crystal Growth

142

172

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“…[1][2][3][4][5][6][7][8] In the experiments the velocity and shape of the interface around a particle are in-situ measured using an optical microscope for transparent materials 1,2) and an X-ray transmission microscope for metals 3) and the critical interface velocity for the pushing/engulfmant transition is determined. Theoretical investigations have also been done to estimate the critical velocity.…”

Section: Introductionmentioning

confidence: 99%

“…Theoretical investigations have also been done to estimate the critical velocity. 4,5) In the theory, it is defined as the velocity at which the dragging force becomes equal to the pushing force. In case of pure materials the dragging force is due to the viscosity flow of liquid and the pushing force is due to the difference of interface energies when the particle contacts with solid.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of the Critical Velocity for Particle Pushing/Engulfment Transition in Fe-C alloys Using a Phase-field Model.

et al. 2000

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The particle/interface problem is numerically analyzed using a phase-field model in thin interface limit. A new double-well potential function in free energy density of the alloy is defined using a dilute solution approximation. With the function, a negative value of double-well potential height is usable and the mesh size restriction is largely relaxed. A pushing force for alloy systems is also introduced so as to relate to the interface energy change caused by the deformation of interface shape. With the pushing and drag forces calculated from the interface shape, the acceleration and velocity of the particle are estimated and the particle movement relative to the interface is analyzed. Using the model, the particle pushing and engulfment behaviors are successfully reproduced for the system of Fe-C alloys and an alumina particle. The critical velocities for the pushing/engulfment transition are determined for the particles with different diameters. The effect of initial carbon content on critical velocity is also examined and discussed in terms of the pushing force.KEY WORDS: phase-field model; thin interface limit; particle-interface problem; critical velocity for pushing/engulfment transition; Fe-C alloy.

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“…Boiling and Cisse [73] have proposed a model which concentrates mainly on the shape of the solid/liquid interface behind the particles, and which is good for predicting the particle entrapment. Predictions of Zubkovs model [74], based on the thermal conductivity of the particles and the melt, and the Surappa and Rohatgi model [75] which employs a heat diffusivity criterion, agree with the experimental observations.…”

Section: Effect Of Sic P On the Precipitation Kineticsmentioning

confidence: 99%

L effet des niveaux de refroidissement (temperature de du moule) et des traitements thermiques sur les proprietes mecaniques et sur la microstructure des deux alliages composites Al-Si-Mg/SiC/10p

Labib¹

1993

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A theory for the interaction of particles with a solidifying front

Cited by 236 publications

References 7 publications

The interaction between a particle and an advancing solidification front

The interaction between a particle and an advancing solidification front

Numerical Simulation of the Critical Velocity for Particle Pushing/Engulfment Transition in Fe-C alloys Using a Phase-field Model.

L effet des niveaux de refroidissement (temperature de du moule) et des traitements thermiques sur les proprietes mecaniques et sur la microstructure des deux alliages composites Al-Si-Mg/SiC/10p

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