Although particle coarsening has been studied for over a century, it remains an active area of materials science research. The current work presents a theoretical analysis of the degradation of regular arrays of spherical particles through diffusional interaction. In order to understand the onset of coarsening, a linear stability analysis is performed on a simple square lattice of particles. It is predicted that particles will dissolve in a spatially ordered manner. The active transport mechanism plays a strong role in the selection of the coherent growth modes.