Experimental and numerical observations on vortical structures in 3D AC electro-osmotic flows

This paper presents an experimental and 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 micro-Particle-Tracking Velocimetry (astigmatism µ-PTV). The experimental obtained velocities are used to validate an ACEO model extended with a standard Gouy-Chapman-Stern (GCS) model accounting for the surface conduction effect. The surface conduction becomes significant in ACEO due to excess charges accumulating in the electric double layer at a high applied voltage or at a low frequency. It reduces the tangential gradient of the electric field and lowers the predicted slip velocity. A qualitative agreement between the simulations and experiments is found for the velocity field when changing AC voltage (1V and 2V ) and the frequency (from 50Hz to 3000Hz). However, the predicted magnitude of the velocity profiles are much higher than the experimentally obtained ones, except in some cases at very low frequency. For frequency higher than 200Hz, a correction factor of 0.36 is introduced to make the numerical results quantitatively comparable to these experimental ones. In addition, the primary circulation, given in terms of the spanwise component of vorticity (¿y = ¿ux/¿z - ¿uz/¿x), is numerically and experimentally analyzed as function of frequency and amplitude of the AC voltage. The outline of the vortex boundary is determined via the eigenvalues of the strain-rate tensor estimated from the velocity field. It reveals that the experimental circulation is frequency dependent, tending to zero at both low and high frequency and the maximum around 600Hz for 1V and 200Hz for 2V. The variation of the predicted vortex circulation, after correction, as function of frequency and voltage is in good correspondence with the experiments after using a velocity-field correction factor. 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