Solute dispersion in channels with periodic square boundary roughness

Abstract

Transport of solutes through channels with rough boundaries is abundant in natural and engineered settings. However, it is not known currently what the consequences of an abruptly alternating boundary are for the solute dispersion, in particular when advected by inertial fluid flow. To investigate this, we compute numerically the time-asymptotic longitudinal dispersion coefficient of a passive solute advected by fluid flow through a two-dimensional channel with square boundary roughness. We determine how the effective diffusion coefficient depends on the boundary amplitude, Péclet number and Reynolds number. For creeping flow, the effective diffusion coefficient is found to be enhanced significantly through the recirculation zones. Increasing fluid inertia reduces the effective diffusion coefficient by up to a factor of two for high Péclet numbers. We interpret this behaviour by analysing residence times computed from Lagrangian particle simulations.