The electroosmotic droplet switch: Countering capillarity with electrokinetics

doi:10.1073/pnas.0505324102

The electroosmotic droplet switch: Countering capillarity with electrokinetics

^†School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853; and ^‡Institute for Nuclear and Energy Technologies, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany

Communicated by Ronald F. Probstein, Massachusetts Institute of Technology, Cambridge, MA, July 6, 2005 (received for review April 29, 2005)

Abstract

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 σR ²/ε|ζ|VB is small enough. Here σ is surface tension of the droplet liquid/gas interface, ε is the liquid dielectric constant, and ζ is the zeta potential of the solid/liquid pair. As droplet size diminishes, the voltage required to pump eletroosmotically scales as V ∼ 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.

Footnotes

↵ § To whom correspondence should be addressed at: 120 Olin Hall, School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853. E-mail: phs7{at}cornell.edu.
Author contributions: M.J.V., P.E., and P.H.S. designed research; M.J.V., P.E., and P.H.S. performed research; M.J.V. and P.H.S. analyzed data; and M.J.V. and P.H.S. wrote the paper.
Abbreviation: EODS, electroosmotic droplet switch.
↵ ¶ The voltage applied to the electrodes V _app results in a smaller effective voltage across the glass disk V _eff because of a decomposition potential [electrochemistry at the electrodes (7)] and a voltage drop across the gaps on either side of the disk in the pump chamber (Fig. 2 A). The decomposition potential is measured at V = 2.5 V. The voltages are linearly related as V _eff = 0.49(V _app – 2.5). All voltages reported in this work are V _eff, from which V _app can be readily obtained by this equation, which depends only on chamber geometry, electrode, and liquid materials (measurement details to be reported elsewhere).
↵ ∥ Consider switching from A′A to AA′ as a 1D dynamical system: dΘ₂/dt ∝ v _net = c ₁+c _2· Δp(Θ₂), with c ₁ and c ₂ positive. It can be shown (graphically or by linear stability analysis) that the first fixed point (v _eo = v _ca) is stable, because at that point dΔp/dΘ₂ ∝–dΔp/d(Θ₁ – Θ₂) < 0 (compare Fig. 1C).