Mixing enhancement by degenerate modes in electrically actuated sessile droplets

Abstract

The dependence of oscillation dynamics of a sessile droplet on the actuation parameters (voltage and frequency) in AC electrowetting which leads to the manifestation of non-axisymmetric oscillation patterns were investigated through experiments and theoretical modeling. The symmetrical nature of the electrowetting force leads to a circular three phase contact line for low actuation voltages. At higher actuation voltages, despite of symmetrical actuation force the contact line showed a transition from axisymmetric to non-axisymmetric oscillations. We found a good match between the experimentally determined region in the actuation parameter space where non-axisymmetric modes are dominant and the theoretically modeled parametric instability region derived from the Mathieu equation. The results showed that these non-axisymmetric modes are degenerate sectoral modes defined by the spherical harmonic functions. In contrast to axisymmetric oscillations, for non-axisymmetric oscillations the variation of contact angle and base radius remained in-phase between successive resonant modes. Finally, mixing by these parametric oscillations was investigated and the best mixing time was approximately 2% of the diffusive mixing time.