Current of interacting particles inside a channel of exponential cavities: Application of a modified Fick-Jacobs equation

Abstract

Recently a nonlinear Fick-Jacobs equation has been proposed for the description of transport and diffusion of particles interacting through a hard-core potential in tubes or channels of varying cross section [Suárez, Phys. Rev. E 91, 012135 (2015)]PLEEE81539-375510.1103/PhysRevE.91.012135. Here we focus on the analysis of the current and mobility when the channel is composed by a chain of asymmetric cavities and a force is applied in one or the opposite direction, for both interacting and noninteracting particles, and compare analytical and Monte Carlo simulation results. We consider a cavity with a shape given by exponential functions; the linear Fick-Jacobs equation for noninteracting particles can be exactly solved in this case. The results of the current difference (when a force is applied in opposite directions) are more accurate for the modified Fick-Jacobs equation for particles with hard-core interaction than for noninteracting ones.