A Finite Difference Approach To Solve the Nonlinear Model of Electro-Osmotic Flow in Nano-Channels

Abstract

This article considers a system of coupled equations constructed by the nonlinear model of electro-osmotic flow through a one-dimensional nano-channel. Functions that belong to this system include distributions of mole fraction of cation and anion, electrical potential, and velocity. We try to find an accurate closed-form solution. To this end, some mathematical approaches are concurrently used to convert the equations to a nonlinear differential equation in terms of the mole fraction of anion. The latter nonlinear differential equation is transformed into a nonlinear algebraic system by the finite difference method, and the system's solution is obtained using Newton's iterative algorithm. Furthermore, equations for the mole fraction of cation, electrical potential, and velocity in terms of the mole fraction of anion are obtained. We calculate errors by substituting the proposed solution into the equations to validate the results. Comparing the results with some other numerical research works demonstrates an acceptable accuracy.