Theory of electrokinetic flow in a narrow parallel-plate channel

Abstract

We develop a theory of electrokinetic flow of a 1 : 1 aqueous electrolyte through a narrow channel, the two walls of which are charged, non-conducting, infinite parallel plates. The zeta (ζ) potential may have any value and double layer overlap is taken into account. Making use of the Poisson–Boltzmann equation for the double layer potential, previous work on this problem by Burgreen and Nakache is corrected and amplified. It is shown that the classical Smoluchowski expression for the electro-osmotic velocity, which applies at κh 1, is reduced by a factor which tends to zero with κh, where 1 /κ is the Debye–Hückel double layer thickness and 2h the channel width. The ratio of applied electric field (streaming potential) to the pressure gradient at zero electric current equals the ratio of volume flow to current at zero pressure gradient for all ζ and κh. But unless κh 1, this common ratio is much smaller than the Smoluchowski value (particularly at high ζ), tending to zero with κh. The apparent viscosity in the channel exceeds the viscosity of the bulk electrolyte (the electroviscous retardation effect). The ratio of these two viscosities has a maximum with respect to κh at fixed ζ and also a maximum with respect to ζ at fixed κh.