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

Abstract

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.

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

“…When proceeding to the higher-order terms, we obtain the asymptotic solution in Eqs. ( 10)- (12). It is noticed that the solution obtained in Eqs.…”

“…[7] Though various experimental observations and numerical simulations explicitly suggest the significant effect of the convection on the interface microstructure formation, theoretical investigations of the morphological evolution of interface during crystallization in the stirred melt and solution are still very limited due to the complicated effects of convection. [2,[8][9][10][11][12][13][14][15][16][17] Hence, there is a strong need for the common analytical method to predict the experimentally observed particle morphologies developed under different flow conditions. A feasible way is to model the growth of spherical particles in the complex flow of the stirred liquid as a singularly perturbed free boundary problem and find its asymptotic solution by using the matched asymptotic expansion method.…”

Effect of far-field flow on a columnar crystal in the convective undercooled melt

“…Buchholz and Engler [8] found that the deformation of the solute layer around the dendrites tips caused by the forced convection makes the columnar dendrites tips incline in the upstream direction. [9,10] In the solidification, the crystal growth will be affected by many factors, such as undercooling, [11] interface kinetics, [12] anisotropic surface tension, [13,14] flow, [15][16][17][18][19] etc. These experiments and numerical simulations deepen the understanding of the crystal growth.…”