Electro-osmotic flow through a nanopore

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.

Electro-kinetic phenomena in porous PET films filled with liquid crystals

“…The presented before, Equations (4) and (5) were obtained for a capillary of an infinite length. The results of numerical solution of the problem for a finite ratio h/R [10] are in a good agreement with these analytic expressions for the porous films used in our experiments (h=R ) 200).…”

“…[5][6][7] In particular, such phenomena can be considered as promising challenge for elaboration of portable diagnostic chips and nanofluidic molecular sensors. However, despite a long history of experimental and theoretical investigations devoted to the electrically induced flows in channels and porous materials, [8][9][10][11] a number of problems are not solved up to now. [12,13] For example, there is a lack of information about specific features of such flows arising in non-Newtonian liquids with some degree of an orientational order, like liquid crystals (LCs), showing complicated electro-rheological behaviour.…”

Electrically generated eddies at an eightfold stagnation point within a nanopore

“…The potential difference applied to generate the flow was φ = 1 mV, so that e φ/kT ≈ 0.04: fluid velocities are everywhere proportional to ( φ) 2 as long as e φ/kT is sufficiently small for the linearized Poisson-Boltzmann equation to be valid, in which case the streamlines are independent of φ. Further details of the computational scheme are given by Mao et al 8 The difference in electrical potential between the two ends of the pore, at the wall of the cylindrical pore, is φ c (34) when h a and this analytic prediction is shown in Figure 4 as a function of h/a. We see that the analytic result is in good agreement with computed results φ c, 0 ( s = 0) for h/a < 0.4.…”

“…If h/a is sufficiently small, the resistance of the pore changes only slightly 9 from that predicted for the electric field (5b) when h = 0. We therefore expect the current along the centreline of the pore, well away from the edges, to be little changed, and the electric field along the centreline is still (to a first approximation) −ẑ φ/(aπ ) (8). The potential difference between the ends (z = ±h/2) of the pore along the centreline should therefore be…”

“…A cylindrical hole of radius a passes through an uncharged thin dielectric plate of thickness h: the hole represents a nanopore in a membrane, and we are interested in the induced charge electroosmotic flow generated by an electric potential difference applied between the two sides of the membrane. [7][8][9] We set up cylindrical polar coordinates, with z axis along the axis of symmetry and with the plane surfaces of the membrane at r > a, z = ±h/2.…”