The electric field strength in orifice-like nanopores of ultrathin membranes

Here we show that the electric field inside an ultrathin membrane is weaker than conventional theory would predict, and that the reduced field is predictive of measured electroosmotic flow rates. Our theoretical analysis shows that the electric field inside a charged nanopore is affected by end effects and dependent on the Dukhin number Du when the pore length-to-diameter aspect ratio λ is less than 80 for Du ≪ 1 or 300 for Du ≫ 1. The electric field follows an unconventional scaling law; it no longer scales uniformly with the thickness of membrane, but with the local value of λ for each nanopore. (paper)