Nonlinear instability and dynamic bifurcation of a plane interface during solidification

By taking average over the curvature, the temperature and its gradient, the solute concentration and its gradient at the flange of planar interface pe rturbed by sinusoidal ripple during solidification, the nonlinear dynamic e quations of the sinusoidal perturbation wave have been set up. Analysis of the nonlinear instability and the behaviors of dynamic bifurcation of the s olutions of these equations shows that (i) the way of dynamic bifurcation o f the flat-to-cellular interface transition varies with different thermal g radients. The quasi-subcritical-lag bifurcation occurs in the small interfa ce thermal gradient scope, the supercritical-lag bifurcation in the medium thermal gradient scope and the supercritical bifurcation in the large therm al gradient scope. ( ii) The transition of cellular-to-flat interface is re alized through supercritical inverse bifurcation in the rapid solidificatio n area.