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.

中文翻译：

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狭窄通道中稠密胶体悬浮液的分离：随机模型

一维广义不对称排斥过程描述了胶体悬浮液在周期性变化宽度的狭窄通道中的流动。每个站点允许多个粒子占用。我们考虑两种不同大小的粒子。粒子可用的位点形成梳状几何形状：由于通道宽度变化而引起的熵陷阱是通过分别连接到一维链的每个位点的死角或凹穴来建模的。这种几何形状与周期性交替的外部驱动相结合，会产生棘轮效应，该效应对颗粒尺寸非常敏感，因此可以进行颗粒分选。当我们更改大小粒子的密度时，典型的行为是反转当前方向。在最佳情况下，两种类型的粒子朝相反的方向移动，颗粒分离原则上是完美的。我们表明，在最简单的情况下，只有一种类型的粒子，该模型是完全可溶的。在一般情况下，我们使用增强的平均场近似以及直接数值模拟。