Nonmonotonic depletion of phase separation under strong supercooling

We analyze the growth of a droplet of a stable phase (a plane wave front in one-dimensional case) under strong supercooling in the framework of the La ndau-Ginzburg potential for both a conserved and a nonconserved order param eter coupled to thermal diffusion. When the coupling between changes in tem perature and the order parameter is strong enough, and the heat conductivit y is sufficiently small, the following nontrivial phenomenon may occur: the latent heat released with the growth of a droplet is taken away very slowl y, and the local overheating transforms the initially overcooled state into an overheated one. As a result, the rate of droplet growth decreases, and even may change its sign, so that droplets of radius larger than the critic al one, nevertheless, may shrink. For the steady-state growth in the one-di mensional case this phenomenon was analyzed analytically, while beyond the steady regime and in the two-dimensional case, the equations were solved nu merically. The presence of a thermal bath with heat loss through thermal di ssipation narrows the areas of occurence of this phenomenon. (C) 2000 Ameri can Institute of Physics. [S0021-9606(00)50742-9].