Note: Aris-Taylor dispersion from single-particle point of view

摘要

When a point Brownian particle diffuses in a straight circular tube in the presence of a laminar stationary flow of the liquid, its effective diffusion coefficient along the tube axis increases compared to its value in the absence of flow. The effective diffusion coefficient as a function of the average fluid velocity and the tube radius is given by the Aris-Taylor formula. We give a new derivation of this formula, which is based on consideration of the axial displacement of the particle that moves in the plane normal to the tube axis along a given trajectory. The result is obtained by averaging the displacement and its square over different realizations of the particle trajectory and analyzing the long-time asymptotic behavior of the two moments.