Substrate degradation in high-Rayleigh-number reactive convection

We study buoyancy-induced convection of a solute in an ideal two-dimensional fluid-saturated porous medium, where the solute undergoes a second-order reaction with a chemical substrate that is fixed in the underlying matrix. Numerical simulations at high Rayleigh number show how a flow is established in which a thin dynamic boundary layer beneath the solute source feeds slender vertical plumes beneath. We examine how the substrate is reactively degraded, at a rate enhanced by convective mixing. For the case when the substrate is abundant, we derive a reduced-order model describing the slow degradation of the substrate, which is formulated as a novel one-dimensional free-boundary problem. Numerical simulations and the reduced model reveal how, when the reaction is rapid compared to the convective time scale, the plumes propagate deep into the flow domain with reaction confined to a narrow region at their base. In contrast, slow reaction allows plumes to fill the domain before degradation of the substrate proceeds homogeneously. An alternative model with a thin reaction front captures the rapid degradation of the substrate when the solute concentration is relatively high. (C) 2015 AIP Publishing LLC.