Hydrodynamic separation of colloidal particles in tubes: Effective one-dimensional approach.

We investigate diffusion of colloidal particles carried by flow in tubes of variable diameter and under the influence of an external field. We generalize the method mapping the three-dimensional confined diffusion onto an effective one-dimensional problem to the case of nonconservative forces and use this mapping for the problem in question. We show that in the presence of hydrodynamic drag, the lowest approximation (the Fick-Jacobs approximation) may be insufficient, and inclusion of at least the first-order correction is desirable to obtain more reliable results. As a practical application, we use the method for investigation of separation of colloidal particles carried by a fluid flow according to their size, using flotation and centrifugation.