By taking average over the curvature, the temperature and its gradient, the solute concentration and its gradient at the flange of planar interface perturbed by sinusoidal ripple during solidification, the nonlinear d...By taking average over the curvature, the temperature and its gradient, the solute concentration and its gradient at the flange of planar interface perturbed by sinusoidal ripple during solidification, the nonlinear dynamic equations of the sinusoidal perturbation wave have been set up. Analysis of the nonlinear instability and the behaviors of dynamic bifurcation of the solutions of these equations shows that (i) the way of dynamic bifurcation of the flat-to-cellular interface transition varies with different thermal gradients. The quasi-subcritical-lag bifurcation occurs in the small interface thermal gradient scope, the supercritical-lag bifurcation in the medium thermal gradient scope and the supercritical bifurcation in the large thermal gradient scope. (ii) The transition of cellular-to-flat interface is realized through supercritical inverse bifurcation in the rapid solidification area.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 49634120) Visiting Scholar Foundation of Key Lab in University. We thank Prof. Huang Weidong and Dr. Li Fanglin for their instruction and help.
文摘By taking average over the curvature, the temperature and its gradient, the solute concentration and its gradient at the flange of planar interface perturbed by sinusoidal ripple during solidification, the nonlinear dynamic equations of the sinusoidal perturbation wave have been set up. Analysis of the nonlinear instability and the behaviors of dynamic bifurcation of the solutions of these equations shows that (i) the way of dynamic bifurcation of the flat-to-cellular interface transition varies with different thermal gradients. The quasi-subcritical-lag bifurcation occurs in the small interface thermal gradient scope, the supercritical-lag bifurcation in the medium thermal gradient scope and the supercritical bifurcation in the large thermal gradient scope. (ii) The transition of cellular-to-flat interface is realized through supercritical inverse bifurcation in the rapid solidification area.
