Induced pressure gradients due to entrance and exit effects in electroosmotically driven flows through nanopores within the continuum regime

Abstract

In this paper, a theoretical model is devised for analysing the effects of induced pressure gradients on electroosmotically driven nanopore flows within the continuum regime, without presuming the validity of the Boltzmann distribution of ionic charges. The charge density distributions are obtained from the conservation considerations of the individual ionic species and are subsequently employed to obtain the potential distribution. This is utilized in conjunction with the Navier–Stokes equation, to obtain a closed form expression of the fully developed steady-state velocity profiles within the nanochannel. From the theoretical analysis, it is revealed that channels with more severe electric double layer overlap effects are characterized with more significant impacts of the adverse pressure gradients induced on account of entrance and exit effects. These effects are found to be significantly more prominent for relatively shorter channels, in which case the induced pressure effects are found to be capable of resulting in a reduction in the flow rate even of the order of 10%. Such findings can be of potential importance for an accurate design of electrokinetically actuated nanofluidic systems in which the entrance and exit pressure losses cannot be trivially overruled.