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- Title
Dispersion Versus Diffusion in Mixing Fronts.
- Authors
Rousseau, Gauthier; Izumoto, Satoshi; Le Borgne, Tanguy; Heyman, Joris
- Abstract
Mixing fronts form when fluids with different chemical compositions are brought into contact. They influence a large range of biogeochemical processes in hydrological systems. An important mechanism governing mixing rates in such fronts is stretching by non‐uniform flows that accelerates diffusive mass transfer by enhancing concentration gradients. In a range of systems, including porous media at Darcy scale, hydrodynamic dispersion dominates over diffusion to control local mixing rates. As it differs from diffusion through its velocity‐dependent dispersion tensor, it is not known how local dispersion interacts with macroscopic mixing front stretching. Here, we investigate the impact of local dispersion versus diffusion on the properties of steady mixing fronts created by both uniform and non‐uniform flows. We derive analytical solutions for the concentration profile, mixing scale and mixing rate across the fronts. We validate these predictions by comparison with numerical simulations and experiments performed in quasi two‐dimensional tanks over a broad range of Péclet numbers. Without porous media, the mixing scale is governed by local diffusion coupled with flow: it increases diffusively along streamlines in uniform flows while it is constant in converging flows due to the balance between fluid compression and local diffusion. With porous media, the Batchelor scale is no longer sustained and the mixing scale grows with dispersion in non‐uniform flows. In addition, the coupling between flow acceleration and dispersion results in a flow rate independent mixing interface, in contrast with the local diffusion scenario. We discuss the consequences of these findings on mixing rates in mixing fronts. Plain Language Summary: This study explores mixing in fluids with and without the presence of a dispersive matrix such as porous media. It highlights the difference of mixing rates in miscible solutes interfaces in the presence or absence of hydrodynamic dispersion, in uniform and non‐uniform flow fields. We find that the mixing scales and mixing rates in the presence of dispersion media follows different laws than their well‐known diffusive counterparts. These findings provide new insights into mixing and reaction processes controlling a range of applications, such as contaminant transport and remediation, water quality, and subsurface energy storage and extraction. Key Points: The effect of diffusive versus local dispersion on mixing front dynamics is studied under uniform and non‐uniform flowsAnalytical solutions for the mixing width and flux are derived for all scenarios and validated through simulations and experimentsWhile diffusion and local dispersion produce similar mixing front dynamics in uniform flows, they fundamentally differ in non‐uniform flows
- Subjects
NON-uniform flows (Fluid dynamics); DISPERSION (Chemistry); POROUS materials; UNDERGROUND storage; CONCENTRATION gradient
- Publication
Water Resources Research, 2023, Vol 59, Issue 11, p1
- ISSN
0043-1397
- Publication type
Article
- DOI
10.1029/2023WR035848