Electrowetting dynamics of sessile droplets in a viscous medium

Electrowetting is a technique that reversibly or irreversibly alters the wetting properties of a droplet on a hydrophobic substrate by applying an electrical field. In this paper, we studied electrowetting dynamics of sessile droplets on a hydrophobic substrate surrounded by viscous liquids. Through this study, we answered the following unanswered questions: the drop's transient response immediately after the actuation, the drop's retraction and resultant dynamics, and the effect of multiple wave actuation on the droplet transition. An overall energy balance approach is extended for analyzing the transient wetting dynamics of droplets from the initial position to the new equilibrium position in viscous media with appropriate governing parameters. The governing nondimensional parameters are the electrowetting number ($\eta$), the Roshko number ($\mathrm{Ro}$), the Ohnesorge number ($\mathrm{Oh}$), and the viscosity ratio (${\mu }_r$) between the droplet and the surrounding medium. This theoretical study, in corroboration with the experimental study, describes the transient evolution of the drop motion from the initial position to the new equilibrium position and predicts the shift from in-phase to out-of-phase drop response for the applied waves.

Figure 1

(a), (b) Schematic illustrations of (a) electrowetting of the aqueous droplet in a liquid medium when it is subjected to the ac electric field and (b) truncated spheroid shape of the droplet. (c) Initial transient response (immediately after the voltage is applied) of the aqueous droplet of $(V=3\mu \mathrm{L},{\mu }_d=0.91\mathrm{mPa}\mathrm{s})$ in a silicone oil (${\mu }_m=100.60\mathrm{mPa}\mathrm{s}$) medium subjected to a sine wave of $U_{\mathrm{ac}}=350\mathrm{V}$ at a frequency $f=10\mathrm{Hz}$ from experiment. Theoretical results for the corresponding droplet are illustrated as (d) height and the rate of change of height with respect to time and (e) comparison of all the different energies considered in the theoretical model.

Figure 2

(a) Transient variation of the droplet height for different electrowetting numbers. The additional terms are fixed to $\mathrm{Oh}=0.009, \mathrm{Ro}=4.45$, and ${\mu }_r=110.55$. (b) Transient variation of the droplet height for different Roshko numbers. The additional terms are fixed to $\mathrm{Oh}=0.009, {\mu }_r=110.55$, and $\eta =0.89$. The experimental results are represented by symbols and the results obtained from the proposed model are represented by the solid lines. (c) Effect of Roshko number on drop spreading dynamics. Minimum height achieved by a drop ($\mathrm{Oh}=0.009$ and ${\mu }_r=110.55$) by a single electrowetting wave as a function of Roshko number, for different electrowetting numbers. The experimental results are represented by open symbols, and the lines represent the theoretical results. (d) Three different regimes proposed to study the transient response of drop spreading, which can be categorized into in-phase, out-of-phase, and nonresponsive behavior.

Figure 3

(a) Minimum height achieved by a drop ($\mathrm{Oh}=0.009$ and ${\mu }_r=110.55$) by a sequence of sine waves ($\eta =0.65$) for different Roshko numbers. The initial height, when the number of waves is zero, is represented at 0.1 instead, because of the logarithmic nature of the plot. The maximum error obtained was $E_{h_{\min }^{*}}=\pm 0.013$. The experimental results are represented by symbols and the results obtained from the proposed model are represented by solid lines. (b) Effect of viscosity ratio on drop spreading dynamics. Transient variation of the droplet height with additional terms fixed to $\mathrm{Oh}=0.009, \mathrm{Ro}=4.45$, and $\eta =0.89$. (c) Minimum height achieved by a drop ($\mathrm{Oh}=0.009$ and $\mathrm{Ro}=4.45$) by a sequence of sine waves ($\eta =0.65$) for different viscosity ratios. The maximum error obtained was $E_{h_{\min }^{*}}=\pm 0.037$.