Driven Brownian transport through arrays of symmetric obstacles

TL;DR

This study numerically explores how overdamped Brownian particles move through a 2D array of obstacles under different driving directions, revealing complex transport phenomena like negative mobility and diffusion peaks.

Contribution

It introduces a detailed numerical analysis of Brownian transport in obstacle arrays, highlighting the effects of drive orientation and array geometry on mobility and diffusion behaviors.

Findings

Identification of negative differential mobility regions.

Observation of excess diffusion peaks.

Analysis of asymptotic transport behaviors.

Abstract

We numerically investigate the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius. Two limiting cases are considered in detail, namely, when the constant drive is parallel to the principal or the diagonal array axes. This corresponds to studying the Brownian transport in periodic channels with reflecting walls of different topologies. The mobility and diffusivity of the transported particles in such channels are determined as functions of the drive and the array geometric parameters. Prominent transport features, like negative differential mobilities, excess diffusion peaks, and unconventional asymptotic behaviors, are explained in terms of two distinct lengths, the size of single obstacles (trapping length) and the lattice constant of the array (local correlation length). Local correlation effects are further analyzed by continuously rotating the drive between the two limiting orientations.