An Interface Stretching-Diffusion Model for Mixing-Limited Reactions During Convective Mixing

Abstract:

We study the behavior of mixing-limited dissolution reactions under the unstable flow conditions caused by a Rayleigh-Bénard convective instability in a two fluids system. The reactions produce a dissolution pattern that follows the ascending fluids's interface where the largest concentration gradients and maximum mixing are found. Contrary to other chemical systems, the mixing history engraved by the dissolution does not map out the fingering geometry of the unstable flow. The temporal scaling of the mixing Χ and the reaction rate r are explained by a stretching-diffusion model of the interface between the fluids. The model accurately reproduces the three observed regimes: a diffusive regime at which Χ, r ~ t^-1/2; a convective regime of at which the interface contracts to the Batchelor scale resulting in a constant Χf and r independent of the Rayleigh number; and an attenuated convection regime in which Χ and r decay faster than diffusion as t^-3/2 and t^-1, respectevely, because of the decompression of the interface and weakened reactions caused by the accumulation of dissolved fluid below the interface.