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Chemical reactions can have a significant impact on convective dissolution in partially miscible stratifications in porous media and are able to enhance the asymptotic flux with respect to the non-reactive case.

Convection can develop upon dissolution of a given species A in a host phase when dissolution leads to a buoyantly unstable density stratification. If A reacts with a solute B present in the host solution according to a bimolecular A + B → C reaction, convective dissolution can be enhanced or slowed down depending on the relative contribution to density of each chemical species. We study numerically the influence of differential diffusion on such reactive convective dissolution in the nonlinear regime. In particular we compute the temporal evolution of the dissolution flux, its asymptotic value and the onset time of convection as a function of the ratio of the diffusion coefficients. We find that, when B diffuses faster than C, the density profiles can exhibit a local minimum below the reaction front where a double-diffusive instability develops. This has a destabilizing effect and leads to enhanced mixing, earlier onset of convection, and increased asymptotic fluxes. On the other hand, when B diffuses slower than C, the density profiles can contain a local minimum at the reaction front followed by a local maximum below, which gives rise to two convection zones with a diffusive-layer convection instability occurring below the reaction front. The overall dynamics is stabilizing with delayed onset of convection and with smaller asymptotic fluxes. When B and C diffuse at an equal rate but differently from A, differential diffusion can accelerate or slow down convection.

A systematic study of a two-dimensional viscous flow through the straight-diverging-straight (SDS) channel defined by two straight-walled sections of different widths and a divergent section in-between is presented here. It has the plane Poiseuille flow (PPF) and the symmetric sudden expansion flow as the limiting cases. The topology of steady laminar flows and its bifurcations are characterized in the multi-parametric space formed by the divergence angle, the expansion ratio, and the Reynolds number. Three different steady flow regimes with two symmetric zones of recirculation, two asymmetric zones of recirculation, and the one with an additional third recirculation zone are observed with increasing Reynolds number. Modal stability analysis shows that the asymmetric flows remain stable at least up to Re = 300, regardless of the divergence angle and expansion ratio. Non-modal stability analyses are applied to SDS flows in the three topology regimes. A remarkable potential for transient amplification due to the Orr mechanism is found even for relatively low Reynolds numbers, which is related to the flow topology. The optimal energy amplification grows exponentially with the Reynolds number, as opposed to the substantially weaker Re2 scaling known for the lift-up mechanism dominant for PPF. This scaling holds for all divergence angles and is further increased by the expansion ratio, resulting in energy amplifications Gmax ∼ 104 for Reynolds numbers as low as Re ∼ 300. Present results suggest that the sub-critical transition due to transient growth is the most likely scenario for SDS flows at low Reynolds numbers.

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