Model for a Brownian ratchet with improved characteristics for particle separation

Abstract

We introduce an extension of the simple on-off ratchet by including a second asymmetric sawtooth potential with half the periodicity and inverse asymmetry in the ratchet cycle. As a result of this additional potential, the Brownian particles exhibit reversal of the direction of their mean displacement when relevant parameters such as the on time of the potentials are varied. This direction reversal offers new opportunities for microfluidic particle separation in sieve devices. Based on the results of our extended ratchet model, we propose two designs. Compared to the classical microfluidic sieve, the proposed devices can be made of significantly smaller sizes without sacrificing the resolution of the separation process. In fact, one of our devices can be reduced to a single channel. We study our extended ratchet model by Brownian dynamics simulations and derive analytical and approximative expressions for the mean displacement using an extension of the method of discrete steps. We show that these expressions are valid in relevant regions of the parameter space and that they can be used to predict the occurrence of direction reversal.