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 present 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 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 chemical control of convective dissolution.

Density profiles around A+B→C reaction-diffusion fronts in partially miscible systems: A general classification

“…In the case of partially miscible interfaces, so-called "dissolution-driven" convection can also develop when the transfer of one phase to the other one locally changes the density of the host solution upon dissolution [23,24]. This is for instance the case during dissolution from above of less dense CO 2 into brine [12][13][14][15][16][17][18], or upon dissolution from below of methanol into cyclohexane [25].…”

“…If the non reactive profile can be buoyantly unstable, i.e. the density of the solution increases upon dissolution, a minimum of density is formed when C contributes less to density than B, which slows down the growth of buoyancydriven fingering [15][16][17]. If C is sufficiently denser than B, the density profile remains monotonic and the reaction can accelerate the development of the instability [15,16].…”

“…The number of possible density profiles increases up to four when a reaction A+B → C takes place in the host phase [15,16]. If the non reactive profile can be buoyantly unstable, i.e.…”

“…For partially miscible stratifications, the possible density profiles have been classified in the case where all species diffuse at the same rate [15,16]: without reaction, only two density profiles can build up, monotonically increasing or decreasing [16]. The number of possible density profiles increases up to four when a reaction A+B → C takes place in the host phase [15,16].…”

“…Such stratifications are typically composed of a reservoir phase A dissolving with a finite solubility into a host phase, containing chemicals that may react with A. The dissolution of A is limited by its solubility in the host phase, where most of the dynamics occurs [12][13][14][15][16][17][18]. Upon dissolution and reaction, various concentration profiles can develop and thereby affect the physical properties of the host phase.…”