Point mixing rate potential in heterogeneous velocity fields

Abstract:

Adequately predicting multi-component chemical reaction rates requires a quantitative understanding of mixing, the process that brings different species together through transport. In the presence of a heterogeneous background velocity field, solute parcels may be stretched and compressed in such a way as to enhance mixing. To quantify this effect, we study the time evolution of the local dilution index, which measures the entropy of the concentration field. We depart from an Ornstein-Uhlenbeck description of the transport, under the assumption of advective-dispersive transport and employing a local linearization of the velocity field. We employ a combination of analytical techniques and numerical particle tracking to relate the evolution of the dilution index to the local stress, and highlight fundamental differences between two and three dimensional flows.