Reactive fronts dynamics under joint shear deformation and hydrodynamic dispersion

Reactive fronts driven by fluid flow and mixing in porous media are central to a wide range of applications, including contaminant transport, CO and hydrogen storage, and soil remediation. Because flow in porous media exhibits significant spatial variability, the deformation of reactive fronts by flow heterogeneity plays a crucial role in enhancing solute mixing and driving chemical reactions. To date, the kinetics of reactive fronts undergoing fluid deformation have mostly been studied under the assumption of a constant diffusion coefficient. However, at the Darcy scale, solute transport in porous media is primarily governed by hydrodynamic dispersion, rather than by molecular diffusion. As such, in this work, we investigate the influence of hydrodynamic dispersion on a bimolecular reaction front subject to homogeneous shear flow. Assuming the dispersion coefficient to be linearly dependent on the local fluid velocity, we derive approximate analytical estimates for the various reaction metrics, which are subsequently validated against numerical simulations. We show that both the temporal scalings and prefactors for the reaction metrics obtained with dispersion differ notably from those obtained under molecular diffusion. In particular, pure longitudinal dispersion yields a reduced scaling for the product mass beyond the shear time, whereas pure transverse dispersion produces an accelerated scaling prior to this time. Such contrasting scalings are driven by the dispersion tensor’s anisotropy, which dynamically alters the effective dispersion experienced by the front as it stretches and rotates with the flow. Furthermore, unlike pure diffusion where a clear transition in the reaction’s effective kinetics takes place at the characteristic shear time, the transition time in the presence of dispersion varies depending on the region under consideration. These findings provide new insights on the joint effect of fluid deformation with hydrodynamic dispersion on mixing and reaction in porous media.