Mixing-Induced Bimolecular Reactive Transport in Rough Channel Flows: Pore-Scale Simulation and Stochastic Upscaling

Mixing and reaction in rough channel flows govern various applications in engineering and natural processes such as microfluidic mixers and fracture flows, where channel wall roughness and flow inertia can vary widely. The combined effects of channel roughness and flow inertia induce complex flow structures such as recirculating flows, which along with diffusion-reaction processes, lead to a wide range of reactive transport behaviors. Currently, we lack a mechanistic understanding of mixing-induced reactive transport in rough channel flows. To establish a comprehensive understanding of bimolecular reactive transport in rough channel flows, we conduct a simulation-based study with varying channel roughness, Reynolds number (Re), and Peclet number (Pe). The simulation results reveal the distinctive effects of roughness, inertia (Re), and diffusion (Pe) on reactive transport. It is found that first passage time distributions between conservative and reactive tracers are significantly different, especially in mixing-limited pre-asymptotic regimes. The interplay between roughness and inertia leads to complex flow structures, which determines a spatially heterogeneous fluid stretching field. We show that the fluid stretching field together with solute diffusion leads to a spatially non-uniform chemical reactivity field, and the non-uniform chemical reactivity explains the distinctive transport behaviors between conservative and reactive tracers. Furthermore, we characterize the non-uniform reactivity with a reaction probability model that is parameterized with Lagrangian velocity magnitudes, and upscale reactive transport by incorporating the velocity-dependent reaction model into a spatial Markov model.