Linking mixing interface deformation to concentration gradients in porous media

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 P & eacute;clet (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 P & eacute;clet numbers, once incomplete mixing is established, it will persist indefinitely. We identify critical P & eacute;clet 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 P & eacute;clet numbers, demonstrating its applicability to more realistic systems.