Linking mixing interface deformation to concentration gradients in porous media

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 Péclet (Pe) 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 to better understand 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 Péclet numbers, once incomplete mixing is established, it will persist indefinitely. We identify critical Péclet thresholds (Pe=18 for Poiseuille flow, Pe=48 for porous media) where reaction efficiency is minimized. Finally, our developed model accurately reproduces the reaction product mass in a three-dimensional porous media column over a wide range of Péclet numbers, demonstrating its applicability to more realistic systems.

This research was funded by National Science Foundation Grant No. EAR2049688 and by the European Commission (MixUp, MSCA-101068306). The authors gratefully acknowledge the Center for Research Computing (CRC) at the University of Notre Dame for providing the computational resources used to conduct the simulations in this work.

Peer Reviewed

Postprint (author's final draft)