Ostwald ripening — Marqusee and Ross type analysis

Abstract

The Wagner-analysis rests on the introduction of a critical radius and the assumption that the volume fraction is a conserved quantity. This is inconsistent since the small supersaturation decays during coarsening and thus the volume also varies with time. It is possible to remove this inconsistency using instead the more general mass or enthalpy conservation laws¹. The asymptotic analysis employs a power series representation for the particle size distribution in time and shows that asymptotically a time independent state is reached under the appropriate scaling, which is unique and independent of the initial conditions. This analysis was performed by Marqusee and Ross and is especially suitable to incorporate effects beyond simple mass diffusion. Moreover, the analysis is self-consistent unlike the Wagner-analysis. We therefore present their approach in some detail. We first treat coarsening due to interface kinetics in a supersaturated matrix and then treat coarsening due to diffusional heat transfer.