A mathematical approach to Ostwald ripening due to diffusion and deformation in liquid bridge

Abstract

From many experiments with mixtures of small and large grains, it can be concluded that during liquid phase sintering, smaller grains partially dissolve and a solid phase precipitates on the larger grains and grain coarsening occurs. The growth rate can be controlled either by the solid-liquid phase boundary reaction or by diffusion through the liquid phase. The microstructure may change either by larger grains growing during the Ostwald ripening process or by shape accommodation. In this study, two-dimensional mathematical approach for simulation of grain coarsening by grain boundary migration based on a physical and corresponding numerical modeling of liquid phase sintering will be considered. A combined mathematical method of analyzing viscous deformation and solute diffusion in liquid bridge between two grains with different sizes will be proposed. The viscous FE method will be used for calculating meniscus of the liquid bridge, with the interfacial tensions taken into consideration. The FE method for diffusion will be also implemented by using the same mesh as the deformation analysis.