Axisymmetric oscillation modes of a double droplet system

A double droplet system (DDS) consists of a sessile and a pendant drop that are coupled through a liquid filled cylindrical hole in a plate of thickness d. For a small hole radius R, equilibrium shapes of both drops are sections of spheres. While DDSs have a number of applications in microfluidics, a DDS oscillating about its equilibrium state can be used as a fast focusing liquid lens. Here, a DDS consisting of an isothermal, incompressible Newtonian fluid of constant density ρ and constant viscosity μ that is surrounded by a gas is excited by oscillating in time (a) the pressure in the gas surrounding either drop (pressure excitation), (b) the plate perpendicular to its plane (axial excitation), and (c) the hole radius (radial excitation). In contrast with previous works that assumed transient drop shapes are spherical, they are determined here by simulation and used to identify the natural modes of axisymmetric oscillations from resonances observed during frequency sweeps with DDSs for which the combin...