The growth model of a spherical crystal in the undercooled melt including the surface energy, interfacial kinetics and convective flow is established. The effect of the convective flow induced by a small far field flow on the evolution and morphological stability of the interface of the spherical crystal is studied. The interface shape of the spherical crystal, which is affected by the far field flow, and the dispersion relation of the growth rate of amplitude of the perturbed interface are derived. It is shown that the convection induced by the far field flow makes the interface of the growing spherical crystal further grow in the upstream direction of the far field flow and inhibit growth in the downstream direction; the interface of the decaying spherical crystal further decays in the upstream direction and inhibits decay in the downstream direction. The theoretical result suggests that both the growth of the sphere in the upstream direction and the decay of the sphere in the downstream direction make the spherical crystal tend to evolve into an oval; the morphological stability of the interface depends on a certain radius R c such that the spherical crystal is unstable when its radius is greater than R c and stable when its radius is less than R c . The surface energy and interfacial kinetics have strong stabilizing effects on the growth of the spherical crystal. In the meantime interfacial kinetics is a table factor of the interface when the interface of the sphere is growing; it is an unstable factor of the interface when the interface is decaying.
CHEN MingWen1,2, WANG ZiDong2 & XU JianJun3,4 1 School of Applied Sciences, University of Science and Technology Beijing, Beijing 100083, China
The directional solidification in the undercooled pure melt influenced by a transverse far field flow was studied by using the multiple scale method. The result shows that in the boundary layer near the liquid-solid interface, when affected by a transverse far field flow, the temperature distribution in the direction of crystal growth presents an oscillatory and decay front in the side of liquid phase. The crucial distinguishing feature of a temperature pattern due to the transverse convection is the additional periodic modulation of the pattern in the growth direction. The wave number and eigenvalue that satisfy the Mullins-Sekerka dispersion relation are suppressed by the transverse far field flow.
Mingwen ChenZidong WangWei YangRenji SunXinfeng Wang
The steady-state dendritic growth from the undercooled binary alloy melt with the far field flow is considered. By neglecting the interface energy, interface kinetics and buoyancy effects in the system, we obtaine the steady-state solution for the case of the large Schmidt number, in terms of the multiple variable expansion method. The changes of the temperature and concentration fields, the morphology of the interface, the normalization parameter and the Peclet number of the system induced by uniform external flow are derived. The results show that, compared with the system of dendritic growth from undercooled pure melt, the convective flow in the system of growth from undercooled binary alloy has stronger effects on the morphology of the interface. Nevertheless, the shape of the interface still remains nearly a paraboloid.
CHEN MingWen1,2, WANG ZiDong2 & XU JianJun2,3,4 1 School of Applied Sciences, University of Science and Technology Beijing, Beijing 100083, China
