Shape Oscillation of a Drop in ac Electrowetting

Abstract

A sessile drop oscillates when an ac voltage is applied in electrowetting. The oscillation results from the time-varying electrical force concentrated on the three-phase contact line. Little is known about the feature of drop oscillation in electrowetting. In the present work, the drop oscillations are observed systematically, and a theoretical model is developed to analyze the oscillation. It is revealed that resonance occurs at certain frequencies and the oscillation pattern is significantly dependent on the applied ac frequencies. The domain perturbation method is used to derive the shape-mode equations under the assumptions of a weak viscous effect and small drop deformation. The electrical force concentrated on the three-phase contact line is approximated as a delta function, which is decomposed and substituted into each shape-mode equation as a forcing term. The theoretical results for the shape and frequency responses are compared with experimental results, which shows qualitative agreement.

Bubble dynamics atop an oscillating substrate: Interplay of compressibility and contact angle hysteresis

“…13 for a drop and later modified for a bubble 14 neglects the coupling to the substrate and, therefore, involves no interaction of different "Rayleigh's" modes (associated with different Legendre polynomials). The interaction of these modes through the substrate is known to shift the eigenfrequencies from the values X n , see, e.g., Refs.…”

“…Second, the account of viscosity in the theoretical model applied in Ref. 13 can be improved. The contribution into dissipation of the viscous boundary layer developing near the substrate is known (see, e.g., Ref.…”

“…21) to prevail over the volume dissipation taken into account in this study. 13 For this reason, the decay rates should be estimated as being proportional to d ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffi ffi =xR 2 p rather than d 2 . An example of estimates for a hemispherical drop can be found in Ref.…”

“…Apart from the ability to manipulate sessile objects, these techniques also admit the possibility of mixing. 13,15,16 Although in many of these applications, the contact line (and=or contact angle) is not static, theoretical models often neglect this dynamic feature or treat it in a simplified way. Independent of how oscillations are induced, the behavior of a sessile droplet or a bubble is significantly determined and often is completely slaved by the dynamics of the triple line.…”

Smoothed particle hydrodynamics-based numerical investigation on sessile, oscillating droplets

“…The corresponding solution of an eigenvalue problem was limited to small shape deformations of the linearized Navier-Stokes equation. With the prospect of lab-on-a-chip applications, forced droplet oscillations by the electrowetting (EW) effect have been studied experimentally [5][6][7]. The droplets perform self-excited oscillations that were compared for small amplitudes with the aforementioned linearized models.…”