Separation of dense colloidal suspensions in narrow channels: A stochastic model

The flow of a colloidal suspension in a narrow channel of periodically varying width is described by the one-dimensional generalized asymmetric exclusion process. Each site admits multiple particle occupancy. We consider particles of two different sizes. The sites available to particles form a comblike geometry: entropic traps due to variation of channel width are modeled by dead ends, or pockets, attached individually to each site of a one-dimensional chain. This geometry, combined with periodically alternating external driving, leads to a ratchet effect which is very sensitive to particle size, thus enabling particle sorting. A typical behavior is reversal of the current orientation when we change the density of small and big particles. In an optimal situation, the two types of particles move in opposite directions, and particle separation is in principle perfect. We show that in the simplest situation with one type of particles only, this model is exactly soluble. In the general case we use enhanced mean-field approximation as well as direct numerical simulations.