Can a cylindrical geometry describe reaction-driven diffusion in   nanometric porous media?
  We present a theoretical model describing the current transient behavior observed during electrodeposition in an opal modified electrode. As a basic unit we consider a cylindrical vessel with a porous and corrugated surface, whose radius changes periodically with z, the vertical axis of the 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 outfluxes 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. DAjello, M. L. Sartorelli, M. C. Ribeiro, L. Lauck
physics.chem-ph