Abstract

The spatial distribution of reactants in heterogeneous media plays a central role in chemical reactions, which, as contact processes, depend on mixing. For fast reactions, diffusion is unable to smooth out structure in reactant distributions on scales relevant for reaction, leading to incomplete mixing. Thus, well-mixed reaction models tend to overestimate reaction rates, as they assume that all solute is available for reaction and do not take into account mass-transfer limitations. Although different models have been proposed to capture this phenomenon, linking pore-scale structure, flow heterogeneity, and local reaction kinetics to upscaled effective kinetics remains a challenging problem. We develop a novel theoretical framework to quantify these dynamics for fluid--solid reactions, with the fluid phase undergoing advective--diffusive transport. Our approach is based on the concept of inter-reaction times, which result from the waiting times between contacts of transported reactants with the solid phase. We use this formulation to quantify the time evolution of total mass for a catalytic degradation reaction, and test its predictions against numerical simulations of advective--diffusive transport in stratified channel flow and Stokes flow through a beadpack.