A Closed-Form Solution for Electro-Osmotic Flow in Nano-Channels

In this article‎, ‎a fluid dynamic code is implemented to investigate a non-linear model for electro-osmotic flow through a one-dimensional Nano-channel‎. ‎Certain mathematical techniques are simultaneously utilized to convert the coupled system of equations into a non-linear differential correlation‎. ‎This correlation is based on the mole fraction of anion‎. ‎By using a modified homotopy perturbation method‎, ‎the achieved non-linear differential equation is converted into a few linear differential equations‎. ‎The mole fraction of anion across the channel is found by solving the linear differential equations‎. ‎Finally‎, ‎the distribution of the mole fraction of cation‎, ‎electrical potential, and velocity are accurately derived based on the mole fraction of anion‎. ‎The present study confirms that by application of a modified homotopy perturbation method‎, ‎the results are in acceptable agreement with the previously validated data‎. ‎However, using the proposed method here‎, ‎a closed-form of the solution is achieved‎.

Keywords:

Electro-osmotic flow‎ , ‎Nano-channels‎ , ‎numerical solution‎ , ‎Poisson-Nernst-Planck‎