Chemical control of dissolution-driven convection in partially miscible systems: theoretical classification

Abstract

Dissolution-driven convection occurs in the host phase of a partially miscible system when a buoyantly unstable density stratification develops upon dissolution. Reactions can impact such convection by changing the composition and thus the density of the host phase. Here we study the influence of A + B → C reactions on such convective dissolution when A is the dissolving species and B a reactant initially in solution in the host phase. We perform a linear stability analysis of related reaction-diffusion density profiles to compare the growth rate of the instability in the reactive case to its non reactive counterpart when all species diffuse at the same rate. We classify the stabilizing or destabilizing influence of reactions on the buoyancy-driven convection in a parameter space spanned by the solutal Rayleigh numbers R_A,B,C of chemical species A, B, C and by the ratio β of initial concentrations of the reactants. For R_A > 0, the non reactive dissolution of A in the host phase is buoyantly unstable. In that case, we show that the reaction is enhancing convection provided C is sufficiently denser than B. Increasing the ratio β of initial reactant concentrations increases the effect of chemistry but does not significantly impact the stabilizing/destabilizing classification. When the non reactive case is buoyantly stable (R_A ≤ 0), reactions can create in time an unstable density stratification and trigger convection if R_C > R_B. Our theoretical approach allows classifying previous results in a unifying picture and developing strategies for the chemical control of convective dissolution.