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

Abstract

Various spatial density profiles can develop in partially miscible stratifications, when a phase A dissolves with a finite solubility into a host phase containing a dissolved reactant B. We investigate theoretically the impact of an A+B → C reaction on such density profiles in the host phase and classify them in a parameter space spanned by the ratios of relative contributions to density and diffusion coefficients of the chemical species. While the density profile is either monotonically increasing or decreasing in the non reactive case, reactions combined with differential diffusivity can create eight different types of density profiles featuring up to two extrema in density, at the reaction front or below it. We use this framework to predict various possible hydrodynamic instability scenarios inducing buoyancy-driven convection around such reaction fronts when they propagate parallel to the gravity field.

Enhanced steady-state dissolution flux in reactive convective dissolution

“…5b-c. At early times < 8000, theĀ profile ( Fig. 5b) looks like its RD counterpart [12][13][14] as convection is not large enough to significantly affect the concentration profiles, while laterĀ is deformed due to the apparition of fingering. At t = 28000, we observe a plateau between z ≈ 80 and 420 in whichĀ ≈ 0.3.…”

“…C(x, z,t = 0) = 0, (12) where β = B 0 /A 0 is the ratio between the initial concentration B 0 of reactant B and the solubility A 0 of A in the host phase. When β = 0, the non-reactive case is recovered; when β → ∞, reactant B is in large excess with regard to A so that the reaction can be considered first-order at early times [21][22][23][24][25][26][27]32 .…”

“…We therefore analyze two main classes of dissolving species A, taking R A =+1 (-1) representing a component increasing (respectively decreasing) the density of the host phase upon dissolution. Fixing thus |R A | = 1 and only varying the sign of R A affects the type of density profile above the reaction front 12,14 : increasing downwards if R A = −1 (stable non-reactive counterpart) or decreasing downwards if R A = 1 (unstable non-reactive counterpart). For each case, we vary ∆R CB , which corresponds to scanning various possible reactant B and product C pairs.…”

“…When R A < 0, the non-reactive case is stable and A+B → C reactions can be at the origin of buoyancy-driven convection as soon as ∆R CB > 0 because a maximum, corresponding to a locally unstable stratification, then develops in the density profile 12,14 . Therefore we expect a stable boundary layer just below the interface followed further away at a given distance from the interface by a locally unstable zone generating fingers sinking down.…”

“…Understanding the impact of chemical reactions on such dynamics has recently gained interest because of the potential effect of geochemistry on the efficiency of CO 2 geological sequestration 5,10 . Reactions can indeed affect convection because they modify solute concentrations affecting fluid properties such as the density of the solution, leading to different possible scenarios for the development of convection 11,12 .…”