Analytical solution of electro-osmotic flow in rectangular Nano-channels by combined Sine transform and MHPM

The aim of this manuscript is to study the electro-osmotic flow through 2D Nano-channels analytically. In this work, the electro-osmotic flow is considered in a rectangular channel. A mixture of water or other neutral solvent and a salt compound such as sodium chloride and other buffers in which the ionic species are entirely dissociated, is considered as the operative fluid in the present study. The governing equations are derived from Navier–Stokes, Boltzmann distributions and Poisson–Nernst–Planck theory. Based on the assumption that the channel height and width are greater than the electric double layer (EDL), the Debye–Huckel approximation is applied solving equations. The Debye–Huckel approximation is used to convert the three coupled differential equations to one partial differential equation and this equation is solved using a new hybrid method based on combining the method of Sine transform and modified homotopy perturbation method. The validity of results is verified by comparing the present method with FDM. All results are presented for velocity profiles, electrical potential distributions, mole fraction cation and anion distributions and other physical properties. Results reveal that very large pressure drops are required to drive flows in small channels. However, useful volume flow rates can be obtained at a very low driving voltage. In this manuscript, we specifically focus on the new analytical solution with combining the Sine transform and MHPM. Results show very good agreement and high accuracy in comparison with FDM.