The filamentary structure of mixing fronts and its control on reaction kinetics in porous media flows

The mixing dynamics resulting from the combined action of diffusion, dispersion, and advective stretching of a reaction front in heterogeneous flows leads to reaction kinetics that can differ by orders of magnitude from those measured in well-mixed batch reactors. The reactive fluid invading a porous medium develops a filamentary or lamellar front structure. Fluid deformation leads to an increase of the front length by stretching and consequently a decrease of its width by compression. This advective front deformation, which sharpens concentration gradients across the interface, is in competition with diffusion, which tends to increase the interface width and thus smooth concentration gradients. The lamella scale dynamics eventually develop into a collective behavior through diffusive coalescence, which leads to a disperse interface whose width is controlled by advective dispersion. We derive a new approach that quantifies the impact of these filament scale processes on the global mixing and reaction kinetics. The proposed reactive filament model, based on the elementary processes of stretching, coalescence, and fluid particle dispersion, provides a new framework for predicting reaction front kinetics in heterogeneous flows.