Asymmetry and direction reversal in fluctuation-induced biased Brownian motion

The biased movement of a Brownian particle in a periodic potential fluctuating between a flat and a kinked ratchet state, as first studied by Chauwin, Ajdari, and Prost, is examined. The purpose is to study the physical origin of the frequency-dependent direction reversal of the biased Brownian motion in this system. We show that the existence of the directional reversal depends not only on the lengths of the projections of the two ratchet arms on the potential axis (the arm-projection asymmetry), but also the overall spatial geometry of the potential in a period. In particular, we show that the direction reversal can be obtained in this kinked ratchet model even when the two arm projections are equal. Since this two-state model is the simplest to generate direction reversal and particles can be separated more efficiently in a fluctuating potential if direction reversal exists, the results obtained in this study should be useful for future application in particle separation.