(19j) Macrotransport Theory and the Fick-Jacobs Approximation

The Fick-Jacobs equation is an approximate method for projecting the transport of particles in a channel with a slowly varying cross-sectional area to a one-dimensional, effective transport equation. For periodic systems, we also have an asymptotically exact methodology embodied in Brenner’s macrotransport theory. Macrotransport theory thus serves as an excellent method to test the approximations in the Fick-Jacobs equation. In this presentation, I will discuss two results, obtained in collaboration with Ehud Yariv: (i) the failure of the Fick-Jacobs approximations for purely diffusive transport in symmetric channels and (ii) the success of macrotransport theory to describe force-driven transport in periodic entropy barriers. Both examples highlight the utility and rigor of Brenner’s macrotransport theory.