Electro-osmotic flow through a nanopore

• Published in: Journal of fluid mechanics Vol. 749; pp. 167 - 183
• Main Authors: Mao, M., Sherwood, J. D., Ghosal, S.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.06.2014
• Subjects: Applied fluid mechanics; Applied sciences; Computational fluid dynamics; Electronics; Exact sciences and technology; Flow rate; Flow rates; Fluid dynamics; Fluid flow; Fluid mechanics; Fluidics; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical models; Mechanical engineering; Membranes; Micro- and nanoelectromechanical devices (mems/nems); Nanostructure; Physics; Reciprocal theorems; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; microfluidics; MEMS/NEMS; electrohydrodynamic effects; Fluid mechanics; Electroosmosis; Nanoelectromechanical device; Numerical simulation; Nanostructure; Microstructure; Modeling; Microelectromechanical device; Microfluidics; Nanoporosity
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2014.214

Electro-osmotic pumping of fluid through a nanopore that traverses an insulating membrane is considered. The density of surface charge on the membrane is assumed to be 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.