Electro-osmotic flow through a nanopore

TL;DR

This paper investigates electro-osmotic flow through nanopores in insulating membranes, deriving analytical and numerical solutions to understand flow rates under different membrane thicknesses and validating results with existing theories.

Contribution

It provides analytical solutions for thin membranes and numerical solutions for arbitrary thickness, enhancing understanding of electro-osmotic flow in nanopores.

Findings

Analytical solution for zero-thickness membranes.

Numerical solutions for finite-thickness membranes.

Flow rate matches classical results for long cylindrical pores.

Abstract

Electroosmotic pumping of fluid through a nanopore that traverses an insulating membrane is considered. The density of surface charge on the membrane is assumed uniform, and sufficiently low for the Poisson-Boltzmann equation to be linearized. The reciprocal theorem gives the flow rate generated by an applied weak electric field, expressed as an integral over the fluid volume. For a circular hole in a membrane of zero thickness, an analytical result is possible up to quadrature. For a membrane of arbitrary thickness, the full Poisson--Nernst--Planck--Stokes system of equations is solved numerically using a finite volume method. The numerical solution agrees with the standard analytical result for electro-osmotic flux through a long cylindrical pore when the membrane thickness is large compared to the hole diameter. When the membrane thickness is small, the flow rate agrees with that calculated using the reciprocal theorem.