Enhanced Mixing and Reaction in Converging Flows: Theory and Pore‐Scale Imaging

Abstract

Mixing fronts at the interface of opposing flows are compressed at a constant rate. The resulting exponential stretching of fluid elements leads to enhanced chemical gradients and biogeochemical processes. This process is similar as what occurs in the pore space of 3D chaotic flows. However, it is so far not known how such fluid compression controls the amplitude of mixing and reaction rates in porous media. Here we derive analytical predictions for the mixing width, the maximum reaction rate and the reaction intensity in compressed mixing fronts as a function of the Péclet and Damköhler numbers. We developed an experimental setup providing pore scale measurements of mixing and reaction rates in mixing fronts at the interface of converging flows. The theory accurately predicts the scaling of mixing and reaction with the Péclet number both in porous micromodels and simple Hele‐Shaw cells. Additionally, we found that the presence of pore scale heterogeneities in the porous micromodels enhances reaction rates by a factor of 4 compared to the Hele‐Shaw cells. Using numerical simulations of pore scale velocity fields, we attributed this phenomenon to the enhancement of pore‐scale compression due to the presence of grains in accelerating flows. These findings provide new insights into the dynamics of mixing‐induced reactions in porous media.

Microscale Chaotic Mixing as a Driver for Chemical Reactions in Porous Media

“…Close to the lamella, the velocity field that leads to a steady elongation and compression is expressed as v ζ = γζ ; v η = − γη . Therefore, by neglecting the gradients on the elongation direction ζ (much smaller than in the compression direction η), the transport is represented by the Lagrangian compression-diffusion-reaction equation: ∂ a ∂ t = D ∂ 2 a ∂ η 2 + γ η ∂ a ∂ η − k r a b The scaling laws resulting from this model for reactive mixing in a steady front are summarized in Table . The mean stretching rate can be expressed as a nondimensional Lyapunov exponent as λ = γ d v z …”

“…The scaling laws resulting from this model for reactive mixing in a steady front 47 are summarized in Table 3. The mean stretching rate can be expressed as a nondimensional Lyapunov exponent as , where ϕl is the initial front length.…”