A disaggregation theory for predicting concentration gradient distributions in heterogeneous flows

International audienceMany transport processes occurring in fluid flows depend on concentration gradients, including a wide range ofchemical reactions, such as mixing-driven precipitation, and biological processes, such as chemotaxis. A generalframework for predicting the distribution of concentration gradients in heterogeneous flow fields is proposed basedon a disaggregation theory. The evolution of concentration fields under the combined action of heterogeneous advectionand diffusion is quantified from the analysis of the development and aggregation of elementary lamellarstructures, which naturally form under the stretching action of flow fields. Therefore spatial correlations in concentrationscan be estimated based on the understanding of the lamellae aggregation process that determine theconcentration levels at neighboring spatial locations. Using this principle we quantify the temporal evolution ofthe concentration gradient Probability Density Functions in heterogeneous Darcy fields for arbitrary Peclet numbers.This approach is shown to provide accurate predictions of concentration gradient distributions for a range offlow systems, including turbulent flows and low Reynolds number porous media flows, for confined and dispersingmixtures