Anti-dispersion in flows in leaky channels

Solute transport in a channel has important implications in industrial processes, biomechanics, and drug delivery. When flow is driven down a channel by a pressure gradient, solute is spread axially by shear and laterally by molecular diffusion. The combination causes the effective axial diffusivity to exceed the molecular diffusivity, a phenomenon known as Taylor dispersion. Here we show, however, that if the channel walls are permeable to the fluid but not to the solute, solute in the channel can be consolidated, making the effective axial diffusivity negative, a phenomenon we call "anti-dispersion." We present a theoretical model, with numerical validation, to study anti-dispersion, demonstrating that it occurs both with boluses of solute and with moving solute fronts. We determine the conditions in which anti-dispersion exceeds dispersion: high dimensionless permeability, moderate dimensionless flow speed, and concentration gradients that are not too steep. Our findings may inform understanding of biological circulation systems and design of systems for controlling solute concentration, as in drug delivery and desalination.