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Electro-osmotic flow through a nanopore

Published online by Cambridge University Press:  14 May 2014

M. Mao ,
J. D. Sherwood  and
S. Ghosal
M. Mao
Affiliation:
Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA
J. D. Sherwood
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
S. Ghosal*
Affiliation:
Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Drops and Bubbles: Electrohydrodynamic effects Micro-/Nano-fluid dynamics: Microfluidics Micro-/Nano-fluid dynamics: MEMS/NEMS
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 167 - 183
Copyright
© 2014 Cambridge University Press 

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