An analytical study on electroosmotic flow within a microchannel disregarding the Debye–Huckel approximation

Abstract

The present work investigates analytically an electroosmotic flow (EOF) of a Newtonian liquid in a microchannel between two parallel plates. Homotopy perturbation method (HPM) is used to solve the constitutive governing equations. The Poisson-Boltzmann equation for electrical potential distribution is considered. Present work disregards the Debye–Huckel approximation to minimize exactness of present results. Consequently, using the electric potential profile obtained, a modified Navier–Stokes equation is solved for velocity distribution. The energy equation is also altered based on scale analysis to find temperature distribution. Finally, based on the temperature profile Nusselt number is determined. The proposed results are shown in comparison with a numerical and an established result which considers the Debye–Huckel approximation. It is seen that the present results agree well with the numerical predictions for a varied range of zeta potential. But, the established conventional method differs from the numerical result for higher range of zeta potential. Nusselt number is evaluated and shown as function of the electrokinetic length for different zeta potentials. The work finally concludes that the proposed model can be applied for predicting EOF in microchannels for wider range of zeta potential.