Transport of finite size particles in confined narrow channels: diffusion, coherence, and particle separation

Transport of the finite size spherical Brownian particles is investigated in confined narrow channels with varying cross-section width. Applying the Fick-Jacobs approximation, we obtain the expressions of the particle current, the effective diffusion coefficient, and the coherence level of Brownian transport (the Péclet number). For the case of the biased constant force, the dependencies of the nonlinear mobility, the effective diffusion coefficient, and the Péclet number on the particle size exhibit striking behaviors. The Péclet number decreases with increasing the radius of the particle which shows that the big sizes of the particles reduce the coherence level of Brownian transport. There exists an optimized value of the radius at which the effective diffusion coefficient is maximal. For the case of the asymmetric unbiased force, due to the competition between the spatial asymmetry and the temporal asymmetry, the transport directions of the particles depend very sensitively on the size of the particle. Particles larger than a given threshold radius move to the left, whereas particles smaller than that move to the right. Therefore, one can separate particles of different radii and make them move towards opposite directions.