Homogenization of a Shrinking Core Model for Gas--Solid Reactions in Granular Particles

Reactions between gases and solid particles are commonly modeled using a shrinking core framework, where a sharp interface between an inner unreacted core and an outer product shell moves inward until the reaction is complete. However, for some physical systems this sharp divide is not present, and so a better model is needed to capture a transition region for the reaction. We are interested in large particles made of many small grains where there are strong interactions between microscale granular and macroscale particulate effects, and where a shrinking core model represents behavior at the microscale level. We obtain homogenized equations for macroscale behavior by exploiting the small ratio of granular to particle lengthscales. These macroscale equations allow for a diffuse reaction front, as well as a sharp interface between reacted and unreacted solid material. We analyze the resulting model asymptotically in the limits where the reaction time is rate-limited by chemical kinetics, and separately by ...