  We study the mixing in the presence of convective flow in a porous medium.
Convection is characterized by the formation of vortices and stagnation points,
where the fluid interface is stretched and compressed enhancing mixing. We
analyze the behavior of the mixing dynamics in different scenarios using an
interface deformation model. We show that the scalar dissipation rate, which is
related to the dissolution fluxes, is controlled by interfacial processes,
specifically the equilibrium between interface compression and diffusion, which
depends on the flow field configuration. We consider different scenarios of
increasing complexity. First, we analyze a double-gyre synthetic velocity
field. Second, a Rayleigh-B\'enard instability (the Horton-Rogers-Lapwood
problem), in which stagnation points are located at a fixed interface. This
system experiences a transition from a diffusion controlled mixing to a chaotic
convection as the Rayleigh number increases. Finally, a Rayleigh-Taylor
instability with a moving interface, in which mixing undergoes three different
regimes: diffusive, convection dominated, and convection shutdown. The
interface compression model correctly predicts the behavior of the systems. It
shows how the dependency of the compression rate on diffusion explains the
change in the scaling behavior of the scalar dissipation rate. The model
indicates that the interaction between stagnation points and the correlation
structure of the velocity field is also responsible for the transition between
regimes. We also show the difference in behavior between the dissolution fluxes
and the mixing state of the systems. We observe that while the dissolution flux
decreases with the Rayleigh number, the system becomes more homogeneous. That
is, mixing is enhanced by reducing diffusion. This observation is explained by
the effect of the instability patterns.
