Asymmetric Brownian transport in a family of corrugated two-dimensional channels

Brownian dynamics simulations of passive particles along two-dimensional channels with curved midline and varying width are considered in this work. By considering finite-length channels formed by sinusoidal unit cells, it was found that axial asymmetry (e.g., non-zero midline) can induce asymmetric particle transport in the sense that the particle current is dependent on the transport direction (either left-to-right or right-to-left). Geometrically, this is caused by a combination of transient transport mechanism and non-uniform variation of the channel width, which produces the effect of a conical, diverging or converging, tube. Numerical results and theoretical predictions show that sinusoidal channels with curved midline and varying width can exhibit important levels of current asymmetry. In this way, this class of channels can be used as mass transport rectifiers where Brownian particles move preferentially in one direction than in the opposite direction. It is also shown that the transport asymmetry vanishes as the particle trajectories approach equilibrium conditions for sufficiently large channels.