Speaker
Description
Mixing induced reactions play a key role in a wide range of applications, including contaminant transport and remediation, carbon and hydrogen storage, etc. The stretching of the resulting front developed at the interface between two miscible and reacting fluids caused by flow heterogeneities plays a central role in controlling the spatial extent of reaction and its effective rate. Since shear flows act as the fundamental building blocks for more complicated scenarios pertaining to stratified or fully heterogeneous fronts in natural porous media, reaction kinetics subject to uniform stretching (shear flow) is a cornerstone towards understanding the front's spatiotemporal evolution. The effective kinetics of reactive fronts under shear deformation have only been studied under the assumption of a constant diffusion coefficient. However, when describing solute transport in porous media at the Darcy scale, the proper mathematical description for diffusive spreading of the reactants and products is hydrodynamic dispersion. This so-called dispersion arises at the Darcy scale from pore-scale coupling between heterogeneous advection and molecular diffusion. It is generally expressed using a second rank tensor linearly dependent on the local Darcy velocity.
In this work, we investigated the influence of hydrodynamic dispersion on a bimolecular type reaction between miscible solutions subjected to uniform stretching. We derived approximate analytical solutions for the reaction rate and product mass across various spatiotemporal regimes, from which we obtain phase diagrams showing the scaling’s of these reaction metrics as functions of time and the Peclet and Damkohler numbers. To validate our theoretical predictions, we also performed numerical simulations of the associated advection-dispersion-reaction equations. Our results show that depending on the relative strength of dispersion and diffusion, distinct dispersion- and diffusion-dominated regions emerge within the front and evolve over time. Further, the analytical temporal scaling’s and the associated pre-factors of the reaction metrics deduced in the presence of dispersion differ notably from those obtained under a constant diffusion coefficient. We consider that these findings provide significant new insights on the combined impact of fluid deformation and dispersive transport on the dynamics of homogeneous reactions in porous media flow.
| Country | India |
|---|---|
| Acceptance of the Terms & Conditions | Click here to agree |
