The electroosmotic droplet switch: Countering capillarity with electrokinetics

Abstract

Electroosmosis, originating in the double-layer of a small liquidfilled 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 R 2 ͞ ͦ ͦVB is small enough. Here is surface tension of the droplet liquid͞gas interface, is the liquid dielectric constant, and is the zeta potential of the solid͞liquid pair. As droplet size diminishes, the voltage required to pump eletroosmotically scales as V ϳ R 2 ͞B. Accordingly, the voltage needed to pump against smaller higherpressure 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.bistability ͉ controlled adhesion ͉ electroosmotic pump ͉ palm beetle ͉ electro-capillary transducer T he natural tendencies of surface tension alone can move liquid between two small droplets. Droplets initially of different curvatures and connected by a liquid-filled conduit come to rest in one of two stable configurations owing to capillarity (recognized for connected bubbles, by ref. 1). The pumping action of electroosmosis can move liquid against this capillary force. A voltage signal applied to an electroosmotic pump positioned between the two droplets precisely controls toggling between the two configurations. This action characterizes the ''electroosmotic droplet switch'' (EODS), whose behavior and potential applications are the subject of this work.This work begins with a description of the system, including a discussion of the bistable nature of the two-droplet system and the model of flow in the EODS. Next, we provide validating data for the model based on time-dependent operation of the device. Model predictions include the parameter limits for successful switching and the time needed to switch the system between stable states. Scaling laws, indicating favorable operation of the EODS down to micrometer-size droplets, are then discussed. Finally, two examples of applications are suggested through demonstrations of unit operations of the...

Capillarity-based switchable adhesion

“…Note that S does not depend on N due to the parallel action of pressure across all holes in the top plate. In the absence of a substrate and for N ¼ 2, the predictive capability of S has been demonstrated in (14).…”

“…1A, typical value is α ≈ 0.2), L the porous layer thickness, μ the liquid viscosity, and ψ the pump porosity. In the absence of a substrate and for N ¼ 2, the basic scaling of τ with the inverse of V when S ≫ 1 has been demonstrated in (14). Fig.…”

“…Configurations like that in Fig. 2B (ii) are unstable over long times due to volume scavenging (14,19). However, scavenging can be suppressed by designing a high interdroplet flow resistance; for example, by choosing a small pore size for the pump material.…”

“…1A. The EO pump moves liquid efficiently against the resisting capillary pressure of the gas/liquid surfaces, using the same principle as the electroosmotic droplet switch (14).…”

“…In releasing, liquid is pumped back into the device until the bridge becomes unstable and breaks. The spacer is crucial to the release because it fixes the bridge length, enabling the bridge to neck in until it pinches off and breaks (14,15). This is akin to separating two glass slides with a drop between; easily done with spacers present but difficult if the slides can make contact.…”