### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 167-183 |

Number of pages | 17 |

Journal | Journal of fluid Mechanics |

Volume | 749 |

DOIs | |

State | Published - Jun 2014 |

### Keywords

- MEMS/NEMS
- electrohydrodynamic effects
- microfluidics

### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

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## Cite this

*Journal of fluid Mechanics*,

*749*, 167-183. https://doi.org/10.1017/jfm.2014.214