Finite element modelling of electro‐osmotic flows on unstructured meshes

Abstract

Purpose

This paper seeks to numerically model electro‐osmotic flow (EOF) through microchannels using a finite element‐based unstructured mesh solution methodology.

Design/methodology/approach

The finite element method (FEM) combined with the characteristic‐based split (CBS) algorithm is used to solve the coupled Navier‐Stokes equations in order to simulate EOFs. The Laplace and Poisson‐Boltzmann equations are solved explicitly a priori to the solution of the fluid dynamic equations. The external electric field and internal potential values are then used to construct the source terms of the fluid dynamics equations.

Findings

Proposed methodology works excellently on unstructured meshes for both two‐ and three‐dimensional flow problems. The results obtained for benchmark channel flow problems show an excellent agreement with analytical and experimental data.

Originality/value

The idea of using the FEM and the CBS algorithm to solve the governing equations of EOFs is proposed. This particular method of solving these equations is unprecedented. In addition to benchmark examples, a problem of practical importance is also solved in this paper.

Citation

Arnold, A.K., Nithiarasu, P. and Tucker, P.G. (2008), "Finite element modelling of electro‐osmotic flows on unstructured meshes", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 18 No. 1, pp. 67-82. https://doi.org/10.1108/09615530810839750