Previous work in the mathematical modelling of particulate (or heterogeneous) reactors has used either the segregated model or the number balance. There has been no mention of the effects of micro- mixing, nor mention of the relationship between these two approaches. This work shows that the relationship between these two equations is concerned with the micro-mixing in a particulate reactor. The number balance for the extremes of micro-mixing is derived. These models are the segregated model and the maximum-mixedness model. Analytical solutions to these equations are obtained for the case in which the order of reaction with respect to the concentration in the gas or liquid phase is zero. It was shown that if the concentration in the gas or liquid phase remains unaffected by the course of the reaction, then the segregated and maximum-mixedness models are identical. In all other cases the performance calculations yield results which depend on the conditions of micro-mixing in the reactor. Numerical solutions for other cases are also discussed. It is shown that the segregated model predicts greater conversions than the maximum-mixedness model for shrinking-particle kinetics (e.g. roasting or leaching).