Aris-Taylor dispersion with drift and diffusion of particles on the tube wall

A laminar stationary flow of viscous fluid in a cylindrical tube enhances the rate of diffusion of Brownian particles along the tube axis. This so-called Aris-Taylor dispersion is due to the fact that cumulative times, spent by a diffusing particle in layers of the fluid moving with different velocities, are random variables which depend on the realization of the particle stochastic trajectory in the radial direction. Conceptually similar increase of the diffusivity occurs when the particle randomly jumps between two states with different drift velocities. Here we develop a theory that contains both phenomena as special limiting cases. It is assumed (i) that the particle in the flow can reversibly bind to the tube wall, where it moves with a given drift velocity and diffusivity, and (ii) that the radial and longitudinal diffusivities of the particle in the flow may be different. We derive analytical expressions for the effective drift velocity and diffusivity of the particle, which show how these quantities depend on the geometric and kinetic parameters of the model.