Simple,coupled algorithms for solving creeping flows and their application to electro‐osmotic flows

In this study we developed simple, coupled algorithms for solving low‐Reynolds‐number flows applicable to micro‐scale flows such as electro‐osmotic flows. The most popular scheme, i.e. the projection method, is not suitable for such flows because of its undesirable slip effect on boundaries at low‐Reynolds‐numbers. In our method, the velocity and pressure are strongly coupled, and the momentum and pressure equations are solved iteratively by using the successive over relaxation (SOR) method while exchanging the unknown variables as soon as they have been updated. The developed methods are applied to a model flow for evaluating their performance. It was found that the coupled schemes are indeed superior to a projection method, i.e. the fractional‐step method, in both numerical accuracy and CPU time. The code is then applied to a dc electro‐osmotic flow within a cavity driven by electrical force acting on the ions spread in the fluid. In this application, the system of equations for the fluid flow and that for the ion transport are solved in a decoupled way, but each system is solved by using fully implicit schemes. From the simulations and by introducing the concept of vorticity source, we can identify two roles of the body force, one contributing to build‐up of the osmotic pressure and the other to the fluid flow. The interesting reverse flow occurring after the external potentials applied on the electrodes have been shut off is also investigated in terms of the vorticity source. Copyright © 2010 John Wiley & Sons, Ltd.