Effect of far field flow on the stability of thespherical crystal in undercooled melt

The effect of far-field uniform flow on the morphological evolution of a spherical particle in a supersaturated solution affected by a far-field uniform flow is studied by using the matched asymptotic expansion method. The analytical solution for the interface shape, concentration field, and interface velocity of the particle growth shows that the convection induced by the far-field uniform flow facilitates the growth of the spherical particle, the upstream flow imposed on the particle enhances the growth velocity of the interface when the flow comes in, the downstream flow lowers the growth velocity of the surface when the flow goes out, and the interface morphology evolves into a peach-like shape.

Section: Introductionmentioning

confidence: 99%

Interface evolution of a particle in a supersaturated solution affected by a far-field uniform flow

Chen

Wang

2013

“…In our previous work, [19] we used perturbation series to obtain the solutions of temperature field and solute field under far-field flow. In our another paper, [20] the influence of a three-dimensional (3D) shear flow on morphological stability of a globular crystal interface was investigated.…”

Section: Introductionmentioning

confidence: 99%

The effect of two-dimensional shear flow on the stability of a crystal interface in a supercooled melt

Cao¹,

Lin²,

Wang³

et al. 2012

A model is developed based on the time-related thermal diffusion equations to investigate the effects of two-dimensional shear flow on the stability of a crystal interface in the supercooled melt of a pure substance. Similar to the three-dimensional shear flow as described in our previous paper, the two-dimensional shear flow can also be found to reduce the growth rate of perturbation amplitude. However, compared with the case of the Laplace equation for a steady-state thermal diffusion field, due to the existence of time partial derivatives of the temperature fields in the diffusion equation the absolute value of the gradients of the temperature fields increases, therefore destabilizing the interface. The circular interface is more unstable than in the case of Laplace equation without time partial derivatives. The critical stability radius of the crystal interface increases with shearing rate increasing. The stability effect of shear flow decreases remarkably with the increase of melt undercooling.

“…[15] We found that the shear flow around the crystal can enhance the stability of the spherical interface. In another paper, [16] we used a perturbation series to obtain the solutions of the temperature and the solute fields.…”

Section: Introductionmentioning

confidence: 99%

Linear stability analysis on a spherical particle growing from a binary melt under the far-field flow

Cao¹,

Lin²,

Wang³

et al. 2012

The solutions of temperature and solute fields around a spherical crystal growing from a binary melt under the far-field flow are obtained. Based on the results, a linear stability analysis on the spherical interface growing from the binary melt under the far-field flow is performed. It is found that the constitutional supercooling effect ahead of the spherical crystal interface under the far-field flow is enhanced compared with that without the flow. The growth rate of the perturbation amplitude at the up-wind side of the spherical crystal interface is larger than that at the down-wind side. The critical stability radius of the crystal interface decreases with the increasing far-field flow velocity. Under the far-field flow, the whole spherical interface becomes more unstable compared with that without the flow.