arXiv:1405.3583v1 [physics.flu-dyn] 14 May 2014 Under consideration for publication in J. Fluid Mech. 1 Electroosmotic flow through a nanopore M. Mao 1 J. D. Sherwood 3 and S. Ghosal 1,2 †, 1 Department of Mechanical Engineering and 2 Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA 3 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK (Received ?; revised ?; accepted ?. - To be entered by editorial office) Electroosmotic pumping of fluid through a nanopore that traverses an insulating mem- brane 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. Key words: 1. Introduction A nanopore is simply a hole of small size in an impermeable membrane separating two regions containing an electrolytic buffer. A size range of 1–100 nm is fairly typ- ical. Living cells and intracellular organelles are usually bounded by lipid membranes containing nanopores constructed of membrane-bound proteins. The transport of small molecules and polymers across such nanopores is a very common feature in living cells and is essential to their normal function (Alberts et al. 1994; Pfanner & Neupert 1990; Matouschek et al. 2000; Martin et al. 1991; K¨ unkele et al. 1998). Synthetic nanopores (Li et al. 2003; Storm et al. 2005a,b ; Smeets et al. 2006; Hall et al. 2010; Garaj et al. 2010; Schneider et al. 2010) have been the focus of much interest in recent years follow- ing the demonstration of their use as effective single molecule sensors (Kasianowicz et al. 1996). The main distinguishing feature of nanopore systems responsible for many of the novel effects is that their geometric dimensions are small enough so that electrokinetic effects are important. Such effects have been invoked to explain a range of observations re- lating to experiments involving free as well as hindered translocation of DNA across synthetic nanopores (Keyser et al. 2006; Ghosal 2006, 2007a ,b ; van Dorp et al. 2009; Laohakunakorn et al. 2013b). Nanopores also exhibit other unusual properties, some of which could be potentially exploited to build novel microfluidic devices. For example, † Email address for correspondence: s-ghosal@u.northwestern.edu