Stretching, Coalescence and Mixing in Porous Media
Résumé
We study mixing in heterogeneous permeability fields, whose structural disorder varies from weak to strong. We propose a unified framework to quantify the overall concentration distribution predicting its shape and rate of deformation as it progresses towards uniformity in the medium. The concentation field is represented by a set of stretched lamellae whose rate of diffusive smoothing is locally enhanced by kinematic stretching. Overlap between the lamellae is enforced by confinement of the scalar line support within the dispersion area. Based on these elementary processes, we derive analytical expressions for the concentration distribution, resulting from the interplay between stretching, diffusion and random overlaps, holding for all field heterogeneities, residence times, and Peclet numbers. We discuss consequences for effective chemical reaction kinetics in heterogeneous media.