Optimizing Mixing in Porous Media with Automatic Differentiation

Dispersion in porous media is a fundamental process in many industrial settings. Prediction of mixing behavior in a porous medium for a given flow geometry is well-understood. However, the inverse problem of systematically designing the flow (i.e. porous medium geometry, fluid properties, etc.) to target specific mixing behavior is computationally extremely expensive. The advent of efficient automatic differentiation algorithms has made such optimization possible. In this work, we combine a fully differentiable CFD solver that accounts for the presence of solid obstacles with a differentiable Brownian dynamics solver to enable Lagrangian studies of fluid flows that include the effects of molecular diffusion. We use this technique to simulate and quantify mixing in periodic structured porous media. By differentiating through the entire simulation, we identify optimum array arrangements that maximize mixing in porous media across a range of Péclet numbers, Reynolds numbers, and solid packing fractions. More broadly, our results demonstrate the versatility of using automatic differentiation for the design and optimization of fluid systems to target specific flow properties.