Analytical prediction of electrowetting-induced jumping motion for droplets on hydrophobic substrates

Abstract

Electric voltage applied in electrowetting can induce spreading of a liquid droplet on solid substrates and yield significant contact angle reduction, which has been widely used for manipulating individual droplets in microfluidics and lab-on-a-chip devices, and even for creating jumping motion of droplets. Here, we present a theoretical closed-form expression of lift-off velocity to predict electrowetting-induced jumping motion of a droplet on hydrophobic substrates. In particular, we consider a liquid droplet wetting on a hydrophobic surface with a voltage applied between the droplet and the substrate. By turning off the applied voltage, the energy stored in the droplet deformation by electrowetting releases and may be sufficient to overcome the energy barrier for detachment. Based on the energy conservation of the droplet-substrate system, we derive a closed-form formula to predict the droplet jumping velocity in terms of the Young contact angle, the Lippmann-Young contact angle, and the Ohnesorge number. The validity of the theoretical prediction is confirmed by comparing the predicted jumping velocities with both experimental observations and numerical simulations. The predictive formula indicates that the jumping motion can be enhanced by increasing the Young contact angle and decreasing the Lippmann-Young contact angle or the Ohnesorge number. Also, a phase diagram of droplet jumping motion is constructed based on this model, which provides insights on accurate control of the electrowetting-induced jumping motion of droplets on hydrophobic surfaces.