PNNL

Abstract

We investigate the effective kinetics of a reaction front for mixing limited bimolecular reaction $A+B\rightarrow C$ in a porous medium. While Fickian diffusion predicts a scaling of the cumulative mass produced as $M_C \propto t^{1/2}$, we observe two time regimes in which the total product mass evolves faster then $t^{1/2}$. At early times the invading solute is organized in fingers of high velocity. Reactions take place only at the fingers boundaries whose surface grows linearly in time. We show that this configuration leads to a mass scaling $M_C \propto t^2$. When diffusion mixes reactants and destroy these finger structures, the effective reaction rate slows down and we relate it to the longitudinal advective spreading providing $M_C \propto \sigma_x$. The transition time between these two regimes is characterized by the diffusion time over the transverse fingers cross section.