A disaggregation theory for predicting concentration gradient distributions in heterogeneous flows
Abstract
Many transport processes occurring in fluid flows depend on concentration gradients, including a wide range of
chemical reactions, such as mixing-driven precipitation, and biological processes, such as chemotaxis. A general
framework for predicting the distribution of concentration gradients in heterogeneous flow fields is proposed based
on a disaggregation theory. The evolution of concentration fields under the combined action of heterogeneous advection
and diffusion is quantified from the analysis of the development and aggregation of elementary lamellar
structures, which naturally form under the stretching action of flow fields. Therefore spatial correlations in concentrations
can be estimated based on the understanding of the lamellae aggregation process that determine the
concentration levels at neighboring spatial locations. Using this principle we quantify the temporal evolution of
the 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 of
flow systems, including turbulent flows and low Reynolds number porous media flows, for confined and dispersing
mixtures.