Rate equation approach to the late stages of cluster ripening

Off-critical phase separation processes are frequently described in literature on the basis of a set of rate equations describing the change rate of number of clusters of given size. This approach works very well for nucleation, but computational limitations and the complexity of processes impede its applicability in the early stages of cluster growth. Late stage clustering in mass conserved systems, which starts much later during the evolution of the morphology of the system, is well understood on the basis of the Lifshitz–Slyozov–Wagner (LSW) theory. In this paper both concepts are connected analytically, showing that identical predictions resulted for the same (simplified) assumptions. Significance of the equivalency of both models has been further explored, particularly in bridging the early stage of clustering, which is not well understood.