THE EFFECT OF SOLUTAL CONVECTION ON THE MORPHOLOGICAL STABILITY OF A BINARY ALLOY
THE EFFECT OF SOLUTAL CONVECTION ON THE MORPHOLOGICAL STABILITY OF A BINARY ALLOY
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DOI：
10.1111/j.1749-6632.1983.tb19479.x
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发表时间：
1983-05
影响因子：
5.2
通讯作者：
D. Hurle;E. Jakeman;A. Wheeler
中科院分区：
文献类型：
--
作者：
D. Hurle;E. Jakeman;A. Wheeler
The effects of the coupling between the morphological stability of a planar, horizontal crystal-melt interface of a growing crystal and the solutal convection in the melt are investigated using a linear stability analysis. Our results are given for physical parameters appropriate to a lead-tin alloy, with the realistic assumptions that there is no density change upon solidification of the alloy and that the thermal field is unperturbed by the flow in the melt. As a consequence of the latter, we set the Prandtl number, Pr ( = Y / K L ) . and Pr, ( = Y / K ~ ) both to zero, where u is the kinematic viscosity of the melt and K~ and K, are the thermal diffusivities of the liquid and solid phase, respectively. The results are compared with the Mullins and Sekerka criterion for morphological stability’ and with a recent numerical study by Coriell et a1.’ We will first consider the onset of instability through stationary modes. It is found that there is a critical value of the solutal Rayleigh number defined on the length scale of the solute field that depends only upon the segregation coefficient and the Schmidt number. For values of the solutal Rayleigh number above this critical value, the system is unstable due to solutal convection induced by the unstable density profile associated with the solute distribution in the melt. At this critical solutal Rayleigh number, the interface is undeformed at the onset of instability. For values of the solutal Rayleigh number below this critical value, solutal convection acts to stabilize the system. This effect is most pronounced at low values of the wavenumber. The most unstable state, which is associated with morphological instability, occurs a t larger values of the wavenumber, where this stabilizing effect is insignificant. Hence, the Mullins and Sekerka criterion for instability is not significantly affected in this regime. Exceptions to this are the cases when the temperature gradient is small or the effect of capillarity is made to be large, in which case the critical wavenumber for the morphological instability is reduced to such a degree that the stabilizing effect of convection becomes significant. As a consequence of the above, the marginal stability curve for stationary stability given in the ( V , , C , ) parameter space, where Vo is the interface velocity and C, is the far-field solute concentration, consists of two branches: a convective branch, corresponding to the critical Rayleigh number, from which there is a bifurcation to a morphological branch, which depends upon the melt temperature gradient a t the interface and, i n general, differs negligibly from the case when convection is neglected. The results in this case compare well with those of Coriell et al.’
