Can a cylindrical geometry describe diffusion in a nanometric porous   media?
  In a recent paper [1] we developed a theoretical model to describe current transients arising during electrochemical deposition experiments performed at the bottom of sub-micrometric cylindrical vessels with permeable walls. In the present work we extended the model for describing the current transients observed during electrodeposition through porous networks produced by colloidal crystals. Instead of considering a cylindrically shaped membrane with a constant cross sectional radius, the membrane will have a corrugated surface, with a radius that changes periodically with z, the vertical axis of the cylindrically corrugated vessel. According to the model, the porous network is formed by the replication of those units, put side by side in close contact, and impregnated by an electrolytic solution. Through the lateral surface of those cylinders we allow for a selective flux of species. The inward or outward flux obeys a complex dynamics regulated by the competition between the diffusion kinetics and the chemical kinetics that answer for the reduction of species at a reactive surface located at the bottom of the cylindrical cavities. The analytical expression for the current transient is complemented by a random prescription for the influx or outflux of matter through the lateral surface plus a modulation in its intensity that follows the surface corrugation. The theoretical data are compared with the current transients obtained in nanosphere lithography experiments. 
P. C. T. D\'Ajello, M. L. Sartorelli, L. Lauck
physics.chem-ph cond-mat.soft