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

Abstract

SUMMARYIn 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.

Enhancement of mixing within a micro cavity by use of transient induced-charge electro-osmotic flow around micro electrodes

“…The potential on the bottom electrode is grounded, and the potential on the top electrode is given with 0 0 ψ > for the time interval 0 c t t ≤ ≤ (to be called the switch-on or charging process) and zero for c t t > (the switch-off or de-charging process), where c t corresponds to a turn-over time. During the charging process, the spatially averaged velocity ( ) V t shows a single peak at low 0 ψ and double peaks at high 0 ψ and then a slowly decaying pattern [5]. During the de-charging process, ( ) V t shows a single peak and relatively fast decaying pattern [5].…”

“…During the charging process, the spatially averaged velocity ( ) V t shows a single peak at low 0 ψ and double peaks at high 0 ψ and then a slowly decaying pattern [5]. During the de-charging process, ( ) V t shows a single peak and relatively fast decaying pattern [5]. Computation is stopped at t T = (period), during the switch-off stage, when ( ) V t becomes 5% of the maximum value measured during the switch-on stage.…”

“…(1)-(5) are solved numerically by using a finite-volume method as described in Suh and Kang [5]. In this study, the mixing performance of the given model flow is investigated quantitatively by using the Lyapunov exponent and qualitatively by using the pattern of particle scattering.…”

“…1. In this study, we set induced-charge electro-osmotic flows created within the cavity by the application of the external potential difference between the electrodes are governed by the following nondimensional equations [5,6]:…”

“…In their studies, the double layer was assumed to be in a steady state and very thin and the slip velocity was calculated by use of the Smoluchowski formula. Recently Suh and Kang [5] performed numerical simulations of transient induced-charge electro-osmotic flows within a micro cavity in the case of overlapped double layer and this suggested the possible manifestation of the mixing enhancement in view of the asymmetric streamline patterns exhibited between the time period when the external potential is on and the time period when it is off.…”