Electro-osmotic flow through a nanopore
arXiv:1405.3583 · doi:10.1017/jfm.2014.214
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.
16 pages, 6 figures
References in corpus (6)
Cited by in corpus (10)
- Osmosis, from molecular insights to large-scale applications
- Electroosmosis in a finite cylindrical pore: simple models of end effects
- Entrance Effects in Concentration-Gradient-Driven Flow Through an Ultrathin Porous Membrane
- Adaptive and Iterative Methods for Simulations of Nanopores with the PNP-Stokes Equations
- Wetting of nanopores probed with pressure
- Deformation and stability of a viscous electrolyte drop in a uniform electric field
- Solvo-osmotic flow in electrolytic mixtures
- Electro-osmotic diode based on colloidal nano-valves between double membranes
- Scaling laws for concentration-gradient-driven electrolyte transport through a 2D membrane
- Revisiting the access conductance of a nanopore in a charged membrane