Dynamics of solid/liquid interface shape evolution near an insoluble particle—An X-ray transmission microscopy investigation

Sen, S.; Curreri, Peter A.; Kaukler, William F.; Stefanescu, Doru M.

doi:10.1007/s11661-997-0170-y

Cited by 55 publications

(62 citation statements)

References 11 publications

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“…This causes the bulk melting temperature isotherm to curve outwards towards the particle if the particle is more insulating than the melt, while a particle made of a good thermal conductor causes the ¹ isotherm to deform in the opposite sense. Experimental evidence suggests that such thermal e!ects can in#uence the critical velocity < by promoting the capture of high-conductivity particles and reducing the tendency of insulating particles to be trapped within the melt [15]. We defer analysis of this complicated thermal problem to future research, and treat the thermal conductivities of the particle, the melt, and the solid as equal while the temperature gradient is assumed constant.…”

Section: The Forces On a Particlementioning

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: The Forces On a Particlementioning

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%

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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“…This, in turn, introduces a small deformation in the profile of the interface. The difference in the thermal conductivities of the melt and particle stands out as the cause for this interfacial deflection [7,8,9,10]. Imagine a situation wherein a solid is growing antiparallel to the direction of the heat flux and toward an inclusion that is less heat conducting than the melt in which it is immersed.…”

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confidence: 99%

Morphological instability induced by the interaction of a particle with a solid-liquid interface

Hadji

2003

The European Physical Journal B - Condensed Matter

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We show that the interaction of a particle with a directionally solidified interface induces the onset of morphological instability provided that the particle-interface distance falls below a critical value. This instability occurs at pulling velocities that are below the threshold for the onset of the Mullins-Sekerka instability. The expression for the critical distance reveals that this instability is manifested only for certain combinations of the physical and processing parameters. Its occurence is attributed to the reversal of the thermal gradient in the melt ahead of the interface and behind the particle.PACS numbers: 81.05. Ni, 81.30.Fb, 81.10.Mx,81.10.Dn, 81.20.Dn The freezing of a liquid with a dispersed phase takes place in numerous natural and industrial processes. Some examples include the formation of ice lenses that result from the freezing of soil water [1], the freezing of biological cell suspensions in a cryopreservation experiment [2], the decontamination of metallic pollutants from soils [3], the growth of Y123 superconductors by the undercooling method [4] and the manufacture of particulate reinforced metal matrix composites (PMMC) [5]. The properties of these composite materials are enhanced by the addition of the dispersed elements.The freezing of a liquid suspension is associated with the interaction of the constituents of the dispersed phase with a solidifying interface. The first systematic study of this interaction was carried out by Uhlmann et al.[6]. They demonstrated the existence of a critical value for the growth rate below which the inclusions are pushed by the moving interface, and above which they are engulfed by the interface and incorporated into the solid. Consequently, very low growth rates are conducive to particles being pushed by the interface, while high growth rates are conducive to particle engulfment.The presence of an inclusion in the melt near a solid-liquid interface introduces locally a change, albeit small, in the thermal gradient ahead of the solid front. This, in turn, introduces a small deformation in the profile of the interface. The difference in the thermal conductivities of the melt and particle stands out as the cause for this interfacial deflection [7,8,9,10]. Imagine a situation wherein a solid is growing antiparallel to the direction of the heat flux and toward an inclusion that is less heat conducting than the melt in which it is immersed. Then, as the width of the gap separating the inclusion from the solid front decreases, heat becomes more easily evacuated from the solid phase than from ahead, leading to a local reversal of the thermal gradient and, consequently, to the local destabilization of the interface. As long as the particle remains pushed, the disturbance grows and propagates radially with decreasing magnitude. FIG. 1: Sketch of a particle of radius a immersed in a melt near a deformable solid-liquid interface; aH0 is the particleinterface distance measured from the particle's center to the planar solid front, V is the interface growth...

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Dynamics of solid/liquid interface shape evolution near an insoluble particle—An X-ray transmission microscopy investigation

Cited by 55 publications

References 11 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.

Morphological instability induced by the interaction of a particle with a solid-liquid interface

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