Linear rate law for the decay of the excess surface area of a coalescing solid particle

Abstract

A linear rate law has been derived for the final stages of decay of the excess surface area of a spheroidal solid particle approaching a spherical shape. Solid-state diffusion within the particle, driven by stress gradients resulting from nonsphericity, is assumed to be the controlling mechanism. The derivation is based on a solution to Laplace's equation for the chemical potential inside the solid particle, which satisfies the boundary condition for the chemical potential on the particle surface. The characteristic frequency for the decay is 16${\mathit{v}}_{\mathit{m}}^{2}$L\ensuremath{\sigma}/${\mathit{R}}^{3}$ where ${\mathit{v}}_{\mathit{m}}$ is the molecular volume, \ensuremath{\sigma} the surface tension, and R the radius of the sphere. The phenomenological coefficient L appears in the diffusional flux, driven by the chemical-potential gradient.