Effect of an interface undulation on convective dissolution of CO2

Abstract

When a partially miscible fluid dissolves into a host phase below it, buoyancy-driven fingering develops when the diffusive boundary solution created is denser than the underlying solvent. In many situations, the interface between the two fluids may present level variations introduced by geometrical irregularities. We study here numerically the influence of this interface undulation on the properties of the convective dissolution and on the resulting transfer flux. Two-dimensional time dependent numerical simulations are performed, assuming that the flow is governed by Darcy’s law, along with the Boussinesq approximation, to account for buoyancy effects introduced by a concentration dependent density. The velocity field is modeled by a vorticity–stream function formulation. The resulting equations are solved through the Taylor–Galerkin Finite Element Method, using a Crank–Nicolson time discretization. It is observed that the onset of the fingering instability is delayed in the inclined regions between the peaks and valleys of the undulation and that the fingers develop mainly in the horizontal regions. Additionally, at the valleys, there is an accumulation of the solute and a thickening of the boundary layer caused by the recirculation which induces the nucleation and by the anchoring of the fingering process at that location. This anchoring is maintained up to the later shutdown stages for cases with large interface undulations. While the flux is larger during the diffusive and initial fingering stages, the asymptotic flux is not strongly influenced by the undulation.