Generalized Taylor dispersion theory for particle transport in wide channels with different surface topographies

In both microfluidic and natural applications, solid boundaries may have rough surface topographies. Hydrodynamic interactions between the rough surface and the flow influence the motion of particles in these environments. Here we generalize the classical Taylor dispersion theory (Taylor, 1953) to include surface roughness, deriving an asymptotic long-time convective diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our theory captures dispersion over general surface shapes of small amplitude expressible as a Fourier series. We demonstrate that the leading-order correction to the diffusion tensor is a superposition of the contributions of each surface mode. Surface corrugations can result in anisotropic diffusion with an increase in dispersion along the main flow direction and potential enhancement or reduction in dispersion perpendicular to the flow direction depending on surface characteristics. We also investigate the effects of symmetric bumpy surfaces and random surfaces, finding enhancement of 30% relative to standard Taylor dispersion for some flow conditions. Overall, these effects demonstrate that it is possible to influence dispersion and steer particles through surface topography.