Diffusive evolution of stable and metastable phases. II. Theory of nonequilibrium behavior in colloid-polymer mixtures

By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of nonequilibrium behavior in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics therefore impinges on many areas of thermodynamics and phase ordering. An exact solution is found for the motion of a single, planar interface separating a growing phase of uniform high density from a supersaturated low-density phase, whose diffusive depletion drives the interfacial motion. In addition, an approximate solution is found for the one-dimensional evolution of two interfaces, separated by a slab of a metastable phase at intermediate density. The theory predicts a critical supersaturation of the low-density phase, above which the two interfaces become unbound and the metastable phase grows ad infinitum. The growth of the stable phase is suppressed in this regime.