European Journal of Mechanics B/Fluids 27 (2008) 297–308 Double layer overlap in ac electroosmosis Siddharth Talapatra, Suman Chakraborty ∗ Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur-721302, India Received 2 November 2006; received in revised form 24 May 2007; accepted 12 June 2007 Available online 21 July 2007 Abstract The frequency-dependent ﬂow of electrolytes between pairs of parallel plate micro-electrodes is analyzed in this paper, for the cases in which electric double layers formed in vicinity of the solid boundaries may strongly interact with each other. Closed form expressions for the potential distributions are ﬁrst developed under certain simplifying assumptions, depicting the interactions between the oscillating electric ﬁeld and charge density distribution within the double layer. It is revealed that the impact of double layer overlap on ac electroosmotic ﬂows turns out to be more predominant at frequencies of the order of relaxation frequency of the electrode–electrolyte system. At higher frequencies, potential drop across the double layer tends to zero, due to polarization of the electrode-solution interface, and virtually no electroosmotic ﬂows can be obtained in such cases.  2007 Elsevier Masson SAS. All rights reserved. Keywords: Ac electroosmosis; Double layer overlap; Microﬂuidics 1. Introduction Under the inﬂuence of an alternating electric ﬁeld, electrolytes kept in between parallel plate micro-electrodes may be subjected to body forces on account of charge density distribution and the induced potential gradients. This, in turn, gives rise to a ﬂuid ﬂow, which can be attributed to the interaction of the tangential component of a non-uniform electric ﬁeld with the induced charge in the electric double layer (EDL). Termed as ac-electroosmosis, such ﬂows have been observed experimentally [1], and have been found to be immensely useful for electrokinetic manipulation of particles in biotechnological research. Typical applications have encompassed the characterization and separation of latex spheres [2], viruses [3], DNA and proteins [4] over submicron length scales. Mathematical models have also been postulated in recent times [5] to analyze the interactions between the oscillating electric ﬁeld and the charge at the diffuse double layer on the electrodes, under a thin double layer approximation. However, in many cases, the solid–liquid interfaces (inner surfaces of the parallel plates constituting the microﬂuidic channel) may be sufﬁciently close to each other, so that their EDLs overlap and interact with each other. This may have signiﬁcant consequences in terms of causing a reduction in electroosmotic velocity and inducing a peak dispersion due to a transition in nature of the velocity proﬁles [6]. These effects cannot be mathematically captured by employing the classical Poisson– Boltzmann equation under thin double layer approximations, since such a treatment implicitly involves incorrect * Corresponding author. E-mail address: suman@mech.iitkgp.ernet.in (S. Chakraborty). 0997-7546/$ – see front matter  2007 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.euromechﬂu.2007.06.005