Liquid-bridge mediated droplet switch: A tristable capillary system

Abstract

The double-droplet switch is the simplest example of a system of capillary surfaces (liquid/gas interfaces at small scales) that demonstrates bistability. A liquid bridge placed between the droplets allows the nonlinear response to be mediated by a pressure po maintained outside the bridge. Response diagrams that give droplet volumes versus po are constructed through computations. The combination of the nonlinear pV responses of the bridge and the droplet switch reveals regions with markedly different behaviors depending on the control parameters. The response diagrams show regions with high sensitivity to po, behavior dominated by the double-droplet response, and also regions with low sensitivity to po, where the bridge response dominates. Stability is determined following the Poincaré approach with illustration using nonequilibrium energy contours (“landscapes”). The computations predict regions of hysteresis with three stable equilibria. When imperfections arising from contact-circle movement at the boundaries are included, five simultaneously stable equilibria and double hysteresis loops are predicted.