Spatially patterned states in systems of interacting catalyst particles

Considering an assemblage of identical catalyst particles exposed to uniform surroundings, we show in this theoretical study that interparticle interactions give rise to spatially patterned steady states under some conditions. In such patterned states, the rate of reaction on one particle differs from the rate on all or some of the neighboring particles. Results, which are based on simple geometric configurations and on the assumption that a single nonisothermal reaction occurs, show that spatially patterned states of two types exist. The first occurs only if a single isolated particle has multiple steady states. The second type, not inferable from the behavior of a single isolated particle, is attributable to the instability of a spatially uniform state caused by particle-particle interactions. This type may occur in cases where the steady state of an isolated particle is unique and globally stable. Though the study is not extended here to complex assemblages, the results suggest that these phenomena may occur in fixed bed reactors and lead to insidious nonuniformities in reactor temperature and catalyst activity.