Validated numerical analysis of vortical structures in 3D AC electro-osmotic flows

This paper presents an experimental validation of a numerical study on the vortical structures in AC electro-osmotic (ACEO) flows. First, the 3D velocity field of ACEO vortices above the symmetric electrodes is experimentally investigated using astigmatism microparticle tracking velocimetry. The experimental obtained velocities are used to validate an extended non-linear Gouy-Chapman-Stern (GCS) model accounting for the surface conduction effect. A qualitative agreement between the simulations and experiments is found for the velocity field when changing AC voltage (from 0.5 V to 2 V) and the frequency (from 50 Hz to 3,000 Hz). However, the predicted magnitude of the velocity profiles are much higher than the experimentally obtained ones, except in some cases at low frequency. For frequencies higher than 200 Hz, a correction factor was introduced to make the numerical results quantitatively comparable to the experimental ones. In addition, the primary circulation, given in terms of the spanwise component of vorticity, was numerically and experimentally analyzed as function of frequency and amplitude of the AC voltage. The outline of the vortex boundary was determined via the eigenvalues of the strain-rate tensor estimated from the velocity field. It revealed that the experimental circulation was frequency dependent, tending to zero at both low and high frequency and the maximum changing from around 600 Hz for 1 V to 300 Hz for 2 V. The variation of the predicted vortex circulation as function of frequency and voltage, after using the above correction factor, was in good correspondence with the experiments. These results yield first insights into the characteristics of 3D AC electro-osmotic flows and the ability of current numerical models to adequately describe them.