A model is developed based on the time-related thermal diffusion equations to investigate the effects of twodimensional shear flow on the stability of a crystal interface in the supercooled melt of a pure substance. S...A model is developed based on the time-related thermal diffusion equations to investigate the effects of twodimensional 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.展开更多
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 gr...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.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 50771083 and 50901061)the National Basic Research Program of China (Grant No. 2011CB610402)+1 种基金the Fund of the State Key Laboratory of Solidification Processing in Northwestern Polytechnical University,China (Grant Nos. 02-TZ-2008 and 36-TP-2009)the Program of Introducing Talents of Discipline to Universities,China (Grant No. 08040)
文摘A model is developed based on the time-related thermal diffusion equations to investigate the effects of twodimensional 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.
基金Project supported by the National Natural Science Foundation of China(Grants Nos.50771083 and 50901061)the National Basic Research Program of China(Grant No.2011CB610402)+1 种基金the Fund of the State Key Laboratory of Solidification Processing in NWPU,China(Grants Nos.02-TZ-2008 and 36-TP-2009)the Programme of Introducing Talents of Discipline to Universities, China(Grant No.08040)
文摘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.
