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.

Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice

Smooth transportation has drawn the attention of many researchers and practitioners in several fields. In the present study, we propose a modified model of a totally asymmetric simple exclusion process (TASEP), which includes multispecies of particles and takes into account the sequence in which the particles enter a lattice. We investigate the dependence of the transportation time on this "entering sequence" and show that, for a given collection of particles, group sequence in some cases minimizes the transportation time better than a random sequence. We also introduce the "sorting cost" necessary to transform a random sequence into a group sequence and show that when this is included a random sequence can become advantageous in some conditions. We obtain these results not only from numerical simulations but also by theoretical analyses that generalize the simulation results for some special cases.

Generalized exclusion processes: Transport coefficients

A class of generalized exclusion processes with symmetric nearest-neighbor hopping which are parametrized by the maximal occupancy, k≥1, is investigated. For these processes on hypercubic lattices we compute the diffusion coefficient in all spatial dimensions. In the extreme cases of k=1 (symmetric simple exclusion process) and k=∞ (noninteracting symmetric random walks) the diffusion coefficient is constant, while for 2≤k<∞ it depends on the density and k. We also study the evolution of the tagged particle, show that it exhibits a normal diffusive behavior in all dimensions, and probe numerically the coefficient of self-diffusion.