Mixing in Heterogeneous Media Across Spatial and Temporal Scales: From Local Non-Equilibrium to Anomalous Chemical Transport and Dynamic Uncertainty
Transport, mixing and reaction of solutes and particles in natural media are of central importance in many fields of science and engineering, ranging from contaminant dispersion in geophysical flows to diffusion in living cells. Transport in these intrinsically heterogeneous media is characterized by early and late solute and particle arrivals, tailed spatial distributions, and scale effects in measured parameters. These behaviors cannot be explained by available models based on Fick’s law and are called anomalous, despite their ubiquity. The origin of such phenomena lies in heterogeneity-induced mixing processes that lead to fluctuations in chemical concentration, or, in other words, to physical non-equilibrium. Current transport formulations based on the advection-dispersion-reaction equation or phenomenological non-equilibrium models lack the relation to the heterogeneity controls, fail to describe mixing and concentration variability and thus are not suited for the quantification of chemical reactions. The main objective of this project is to establish a global predictive framework that quantifies mixing across scales, anomalous transport and reaction, and dynamic uncertainty for heterogeneous media. We propose an integrated approach that links the interrelated phenomena of mixing, anomalous transport and chemical reaction. In short, the idea consists in quantifying microscale heterogeneity-induced mixing in terms of the flow kinematics and heterogeneity structure and linking it to transport through its relation to Lagrangian particle dynamics. These dynamics will be quantified stochastically by a novel generalized continuous time random walk approach and used to model chemical reactions under physical non-equilibrium.