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

Document Type : Research Paper

Authors

1 1. Department of Mathematics, Izmir Institute of Technology, Izmir, Türkiye. 2. Department of Mathematics, Azerbaijan Shahid Madani University, Tabriz, Iran.

2 Department of Aerospace Science and Technology, Politecnico di Milano, Milan, Italy.

3 Department of Physics, Sari Branch, Islamic Azad University, Sari, Iran.

4 Department of Applied Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.

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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 30 September 2024

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History

  • Receive Date: 04 July 2024
  • Revise Date: 27 September 2024
  • Accept Date: 28 September 2024

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