(274d) Electrohydrostatics of Capillary Switches

Two liquid droplets, one sitting on the top and the other hanging from the bottom of a plate, that are connected via a cylindrical hole of radius R that is filled with the same liquid as the drops is referred to as a capillary switch (CS).  These coupled droplets could either maintain fixed contact lines or fixed contact angles with the plate.  In situations where the contact line of the droplets are pinned, the CS is known to exhibit two stable equilibrium states when the combined volume of the two droplets is greater than that of a sphere of radius R.  This fact is exploited in various applications, including optical lenses and adhesion, where the main challenge is to come up with ways to "toggle" the CS between its two stable states that are reliable, are energy efficient, and have fast response.  The use of an electric field to achieve these goals is explored theoretically in this work in which the axisymmetric shapes and stability of a CS where the liquid is a perfect conductor and the fluid surrounding the two droplets is a passive dielectric gas are determined as a function of the applied field strength.  The equilibrium shapes of the CS and the electric potential in the surrounding gas are governed by the augmented Young-Laplace equation and the Laplace equation, respectively, along with a volume constraint.  These equations are solved numerically by using the Galerkin finite element method.  Simulation results that give the variation of the dimensionless difference in volume between the two droplets as a function of the electrical Bond number (the ratio of electric to surface tension force) are used to infer whether an electric field represents an effective means of toggling a CS.  The analysis is then extended to situations where the droplets make fixed contact angles with the plate and the results are compared to those obtained where the contact lines are pinned.  When the contact angles are fixed, the electrohydrostatics of the CS is also amenable for study by domain perturbation analysis.  Aside from providing additional insights into the behavior of electrified CSs, the domain perturbation results also provide a convenient framework for benchmarking the simulation results.