The late stages of model B dynamics for asymmetric quenches, where the initial condition places the post-quench system just inside and quite near to the coexistence curve, exhibit characteristic features. For an asymmetric system, ψ0 is a measure of the extent of off-criticality of the system. For ψ0 > 0 the majority phase equilibrates at ψ+ = +1 and the minority phase at ψ–= –1. At late times, the minority-phase clusters have a characteristic radius R(τ) which is much larger than the interface width ξ. An important coupling exists between the interface and the majority phase through the surface tension σ. The conservation law dictates that the minority phase will occupy a much smaller “volume” fraction than the majority phase in the final equilibrium state. The dynamics is governed by interactions between the different domains of the minority phase. At late times, these domains have spherical and circular shapes for three- and twodimensional systems, respectively. Late-stage coarsening is referred to as Ostwald ripening.

The late-stage dynamics may be mapped onto a diffusion equation with sources and sinks (domains) whose boundaries are time dependent. The classic papers by Lifshitz and Slyozov (1961) and Wagner (1961) form the theoretical cornerstone for the description of domain coarsening dynamics for model B. The Lifshitz– Slyozov–Wagner (LSW) theory of coarsening is based on the assumption that each interface between a minority phase domain and the majority phase background is infinitely sharp. It describes the diffusive interactions between the domains through a mean-field treatment with precisely defined boundary conditions at each of the interfaces.