Mixing Fronts in Smooth Chaotic Flows

TL;DR

This paper develops a theoretical framework to predict scalar concentration fluctuations in smooth chaotic flows, accurately matching numerical simulations across various Péclet numbers, and advancing understanding of mixing processes in complex fluids.

Contribution

It introduces a novel model linking microscopic and macroscopic scalar fluctuations, enabling precise predictions of concentration variance without fitting parameters.

Findings

The model accurately predicts concentration variance across Péclet numbers.

Identification of a characteristic length scale where dispersion and diffusion balance.

Validation through direct numerical simulations without fitting parameters.

Abstract

Scalar mixing fronts develop at the interface of agitated fluids of different solute concentrations. In such fronts, scalar fluctuations form at both microscopic and macroscopic scales, due to stretching-enhanced molecular diffusion and hydrodynamic dispersion respectively. While these two elementary processes are well understood separately, predicting how their coupling governs the evolution of concentration statistics within dispersing fronts remains a challenge. Here, we propose a theoretical framework to describe scalar fluctuations in fronts mixed by smooth chaotic flows. We find that the transfer of energy between the macroscopic and microscopic scalar fluctuation scales operates at a characteristic length scale $s_i$, for which dispersion and stretching-enhanced diffusion are of equal strength. This leads to a closed expression for the concentration variance, which captures the results of direct numerical simulations with no fitting parameters, for a broad range of P\'eclet numbers. These findings open a new avenue for predicting both conservative and reactive mixing in smooth chaotic flows such as porous media or microfluidic flows.