Utilizing Curved Channels to Either Enhance or Diminish Diffusion

Solute transport in diverse fluid systems (e.g., medicine in blood, chemicals in microchannels, river pollutants) involves significant boundary layer formation, dispersing solute concentration and creating gradients impacting diffusion dynamics. We develop and employ an effective diffusion equation with a diffusivity parameter to model this phenomenon. This study focuses on sinusoidal boundary perturbations' role in the long time limit using homogenization, specifically exploring the lubrication approximation and Stokes flow regimes. By using the lubrication approximation, we identify a threshold where perturbations transition from enhancing to diminishing diffusion relative to a flat wall. However, in Stokes flow, any wall perturbation only reduces diffusivity compared to a flat wall. Our model is validated through Monte Carlo simulations and full advection-diffusion simulations.