Axial dispersion via shear-enhanced diffusion in colloidal suspensions

The familiar example of Taylor dispersion of molecular solutes is extended to describe
colloidal suspensions, where the fluctuations that contribute to dispersion arise from hydrodynamic
interactions. The generic scheme is illustrated for a suspension of particles in a pressure-driven
pipe flow, with a concentration-dependent diffusivity that captures both the shear-induced and
Brownian contributions. The effect of the cross-stream migration via shear-induced diffusion is
shown to dramatically reduce the axial dispersion predicted by classical Taylor dispersion for a
molecular solute. Analytic and numerical solutions are presented that illustrate the effect of the
concentration dependence of this nonlinear hydrodynamic mechanism.