Linking Mixing Interface Deformation to Concentration Gradients in Porous Media

TL;DR

This paper links pore-scale concentration gradients to mixing interface deformation in porous media, revealing persistent fluctuations at high Peclet numbers and developing a model to predict mixing-limited reaction kinetics.

Contribution

It introduces a new perspective connecting pore-scale gradients to mixing interfaces and develops a validated model for mixing-limited reactions in porous media.

Findings

Pore-scale fluctuations persist at high Peclet numbers.

Advection rapidly generates and sustains concentration fluctuations.

Incomplete mixing remains indefinitely at Pe > 1.

Abstract

We study the pore-scale transport of a conservative scalar forming an advancing mixing front, which can be re-interpreted to predict instantaneous mixing-limited bimolecular reactions. We investigate this using a set of two-dimensional, high-resolution numerical simulations within a poly-disperse granular porous medium, covering a wide range of Peclet numbers. The aim is to show and exploit the direct link between pore-scale concentration gradients and mixing interface (midpoint concentration isocontour). We believe that such a perspective provides a complementary new lens for better understanding mixing and spreading in porous media. We develop and validate a theoretical model that quantifies the temporal elongation of the mixing interface and the upscaled reaction kinetics in mixing-limited systems accounting for pore-scale concentration fluctuations. Contrary to the classical belief that, given sufficient time, pore-scale fluctuations would eventually be washed out, we show that for $Pe>1$ advection generates pore-scale concentration fluctuations more rapidly than they can be fully dissipated. For such P'eclet numbers, once incomplete mixing is established, it will persist indefinitely.