Year: 2025
Type: preprint
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 Péclet 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.
Source: arXiv (Cornell University)
Authors: Joris, Heyman, Tanguy, Le Borgne, Daniel, Lester
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415333637
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