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.