We consider the fast irreversible bimolecular chemical reaction A+B→C in the Poiseuille flow through a channel, in which A displaces B. This system allows to systematically study the impact of the interaction of interface deformation and diffusion on mixing and reactive transport. At early times, the reaction is diffusion controlled. With increasing time, advection begins to dominate and we find enhanced reaction efficiency due to the deformation of the interface between the two reactants. For times larger than the characteristic diffusion time across the channel, mixing and reaction are quantified by the Taylor dispersion coefficient. Predictions based on Taylor dispersion may significantly overestimate the reaction efficiency at preasymptotic times, when the system is characterized by incomplete mixing. This type of behaviors of incomplete mixing and reaction have been observed in heterogeneous systems across different scales. Channel flow allows to study them in detail for a well‐controlled system. We propose a dispersive lamella approach based on the concept of effective dispersion which accurately predicts the full evolution of the product mass. Specifically, this approach captures the impact of interface deformation and diffusive coalescence, which marks the transition to the Taylor regime. It gives insight into the mechanism of incomplete mixing and its consequences for reactive transport in more general porous media flows.

We present a reactive random walk particle‐tracking approach to describe bimolecular chemical reactions and show its equivalence with the advection‐diffusion‐reaction equation. The method is able to efficiently simulate reactions in d‐dimensional systems with homogeneous and spatially variable advection. Reactions among particles are determined by the reaction probability that is given in terms of the reaction rate coefficient, the total number of particles, and an interaction radius that describes the well‐mixed support volume at which all particles have the same probability to interact. The method is meshless and free of numerical dispersion. The method is validated for the bimolecular irreversible chemical reaction A + B→C in scenarios characterized by slow and fast chemical kinetics under diffusion and heterogeneous advection and diffusion.