RESEARCH PAPER Application of astigmatism l-PTV to analyze the vortex structure of AC electroosmotic flows Zhipeng Liu • Michel F. M. Speetjens • Arjan J. H. Frijns • Anton A. van Steenhoven Received: 29 April 2013 / Accepted: 13 August 2013 / Published online: 28 August 2013 Ó Springer-Verlag Berlin Heidelberg 2013 Abstract The three-dimensional (3D) flow due to AC electroosmotic (ACEO) forcing on an array of interdigita- ted symmetric electrodes in micro-channels is experimen- tally analyzed using astigmatism micro-particle tracking velocimetry (astigmatism l-PTV). Upon application of the AC electric field with a frequency of 1,000 Hz and a voltage of 2 Volts peak–peak, the obtained 3D particle trajectories exhibit a vortical structure of ACEO flow above the electrodes. Two alternating time delays (0.03 and 0.37 s) were used to measure the flow field with a wide range of velocities, including error analysis. Presence and properties of the vortical flow were quantified. The steady nature and the quasi-2D character of the vortices can combine the results from a series of measurements into one dense data set. This facilitates accurate evaluation of the velocity field by data-processing methods. The primary circulation of the vortices due to ACEO forcing is given in terms of the spanwise component of vorticity. The outline of the vortex boundary is determined via the eigenvalues of the strain-rate tensor. Overall, astigmatism l-PTV is pro- ven to be a reliable tool for quantitative analysis of ACEO flow. Keywords AC electroosmosis  3D velocity measurement  Vortical flow  Microfluidics 1 Introduction AC electroosmosis (ACEO) is increasingly utilized in micro/nano-fluidic applications due to its ability to gener- ate a flow using a low-voltage AC electric field (Ramos et al. 1999). The low voltages admitted by ACEO offer essential advantages over the conventional DC electroos- mosis systems relying on high voltages. Namely, undesir- able side effects, e.g., bubble formation due to electrolysis and electrolyte contamination due to Faradaic reactions, are significantly weaker or absent altogether in ACEO. ACEO as a flow-forcing technique has a great potential for the actuation and manipulation of micro-flows and has found successful applications in micro-pumping (Brown et al. 2000; Studer et al. 2004; Bazant and Ben 2006), micromixing (Sasaki et al. 2006; Huang et al. 2007), and manipulation of polarizable particles (Gagnon and Chang 2005; Wu et al. 2005; Park and Beskok 2008). In order to obtain a complete understanding of ACEO- induced flow, flow visualization is the main approach employed. By tracing individual seeding particles, Ramos et al. (1998) first reported a local flow field parallel with the electrode surfaces using a low amplitude AC signal in aqueous electrolyte, which exhibited the fundamental description of the ACEO flow. Later, based on the path- lines of tracer particles, Green et al. (2002) qualitatively demonstrated the vortical structure of an ACEO flow above a pair of symmetric electrodes. So far, AC electroosmotic flow has been observed experimentally on various elec- trode surfaces (Bazant and Ben 2006; Huang et al. 2007; Garacia-Sanchez et al. 2006; Kim et al. 2009; Green et al. 2000; Motosuke et al. 2013). However, the experimental descriptions of the ACEO flow are mainly restricted to a two-dimensional (2D) flow field, even though the ACEO flow shows a three-dimensional flow structure. Therefore, Z. Liu (&)  M. F. M. Speetjens  A. J. H. Frijns  A. A. van Steenhoven Mechanical Engineering Department, Eindhoven University of Technology, P.O.Box 513, 5600 MB Eindhoven, The Netherlands e-mail: zh.liu@tue.nl 123 Microfluid Nanofluid (2014) 16:553–569 DOI 10.1007/s10404-013-1253-2