Analytical prediction of electrowetting-induced jumping motion for droplets on textured hydrophobic substrates: Effects of the wetting states

In electrowetting, an applied electric voltage can induce spreading, sliding, or even jumping of an individual droplet by changing the intrinsic balance of the three-phase interfacial tensions. This technique has been widely used for manipulating droplets in microfluidics and by lab-on-a-chip devices in recent decades. In the present paper, we present an analytical prediction of the jumping velocity for droplets undergoing electrowetting on textured hydrophobic surfaces with different wetting states. In particular, we consider wetting a liquid droplet on a textured hydrophobic substrate with a voltage applied between the droplet and the substrate. Once the voltage is turned off, the energy stored in the droplet during electrowetting is released and could even result in the detachment of the droplet. The effects of the initial and electrowetting states, i.e., the Cassie-Baxter state and the Wenzel state, on the jumping velocity of droplets are systematically discussed. Based on energy conservation, the energy conversion between the surface energy, the elastic energy of the contact line, and the kinetic energy of droplets due to internal viscous dissipation in different wetting states is analyzed. Closed-form formulas for the jumping velocity of different droplet wetting states are systematically derived. Finally, a unified form for predicting the electrowetting-induced jumping velocity of droplets on both flat and textured substrates with different wetting states is obtained. It can describe the jumping motion under various wetting conditions, which is validated by some experimental results. This work provides theoretical insights into the accurate control of the electrowetting-induced jumping motion of droplets on textured hydrophobic surfaces.