Entropic transport without external force in confined channel with oscillatory boundary

The dynamics of point-like Brownian particles in a periodic confined channel with oscillating boundaries has been studied. Directional transport (DT) behavior, characterized by net displacement along the horizontal direction, is observed even without external force which is necessary for the conventional DT where the boundaries are static. For typical parameter values, the average velocity Vt of DT reaches a maximum with the variation of the noise intensity D, being alike to the phenomenon of stochastic resonance. Interestingly, we find that Vt shows nontrivial dependences on the particle gravity G depending on the noise level. When the noise is large, Vt increases monotonically with G indicating that heavier particle moves faster, while for small noise, Vt shows a bell-shape dependence on G, suggesting that a particle with an intermediate weight may move the fastest. Such results were not observed for DT in a channel with static boundaries. To understand these findings, we have adopted an effective one-dimensional coarsening description, which facilitates us to introduce an effective entropic force along the horizontal direction. The average force is apparently nonzero due to the oscillatory boundary, hence leading to the net transport, and it shows similar dependences as Vt on the noise intensity D and particle gravity G. The dependences of the DT behavior on other parameters describing the oscillatory channel have also been investigated, showing that DT is more pronounced for larger oscillation amplitude and frequency, and asymmetric geometry within a channel period and phase difference between neighboring periods are both necessary for the occurrence of DT.