In 1965, Rice and Whitehead published the seminal contribution to the theory of the transport of electrolyte solutions in long (ideally infinite) nanometer-diameter capillaries. 
Briefly, the potential, ϕ, at a radial distance, r, is given by the Poisson-Boltzmann equation,
where κ is the inverse Debye length,
determined by the ion number density, n, the dielectric constant, ε,  the Boltzmann constant, k, and the temperature, T.  Knowing the potential, φ(r), the charge density can then be recovered from the Poisson equation, whose solution may be expressed as a modified Bessel function of the first kind, I, and scaled to the capillary radius, a. An equation of motion under combined pressure and electrically-driven flow can then be written,
where η is the viscosity, dp/dz is the pressure gradient, and F is the body force driven by the action of the applied electric field, E, on the net charge density in the double layer.
When there is no applied pressure, the radial distribution of the velocity is given by,
From the equation above, it follows that fluid flow in nanocapillaries is governed by the κa product, that is, the relative sizes of the Debye length and the pore radius. 
By adjusting these two parameters and the surface charge density of the nanopores, fluid flow can be manipulated as desired.