Force-driven transport in entropy barriers

We consider theoretically the transport of a point-sized Brownian particle in a two-dimensional channel with a slowly varying, periodic cross-section. Such channels are associated with the concept of an ``entropy barrier," where the change in the number of available ``states" for the Brownian particle governs the transport process. Using generalized Taylor-Aris dispersion theory and long-wavelength asymptotics, we exactly compute the mean particle velocity and effective diffusivity (dispersivity) for two cases: electrophoretic transport in an insulating channel and motion under the influence of a constant force. At the same time, we arrive at rational definitions for the concept of an entropy barrier as a function of the driving force. The agreement between simulations and the exact calculation for a constant force is excellent and represents a significant advance over existing models of the transport process.