The electroosmotic droplet switch: countering capillarity with electrokinetics.

Electroosmosis, originating in the double-layer of a small liquid-filled pore (size R) and driven by a voltage V, is shown to be effective in pumping against the capillary pressure of a larger liquid droplet (size B) provided the dimensionless parameter sigmaR(2)/epsilon|zeta|VB is small enough. Here sigma is surface tension of the droplet liquid/gas interface, epsilon is the liquid dielectric constant, and zeta is the zeta potential of the solid/liquid pair. As droplet size diminishes, the voltage required to pump electroosmotically scales as V approximately R(2)/B. Accordingly, the voltage needed to pump against smaller higher-pressure droplets can actually decrease provided the pump poresize scales down with droplet size appropriately. The technological implication of this favorable scaling is that electromechanical transducers made of moving droplets, so-called "droplet transducers," become feasible. To illustrate, we demonstrate a switch whose bistable energy landscape derives from the surface energy of a droplet-droplet system and whose triggering derives from the electroosmosis effect. The switch is an electromechanical transducer characterized by individual addressability, fast switching time with low voltage, and no moving solid parts. We report experimental results for millimeter-scale droplets to verify key predictions of a mathematical model of the switch. With millimeter-size water droplets and micrometer-size pores, 5 V can yield switching times of 1 s. Switching time scales as B(3)/VR(2). Two possible "grab-and-release" applications of arrays of switches are described. One mimics the controlled adhesion of an insect, the palm beetle; the other uses wettability to move a particle along a trajectory.