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 rho and constant viscosity mu 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 combined volume V of the two drops is less than (4/3) pi R-3 Pressure and axial excitations are found to have identical responses but axial and radial excitations are shown to excite different modes These modes are compared to those exhibited by single pendant (sessile) drop systems In particular, while a single pendant (sessile) drop has one additional oscillation mode compared to a free drop, a DDS is found to exhibit roughly twice as many oscillation modes as a pendant (sessile) drop The effects of dimensionless volume V/R-3, dimensionless plate thickness d/R, and Ohnesorge number Oh = mu/root rho R sigma, where sigma is the surface tension of the DDS-gas interface, on the resonance frequencies are also investigated (C) 2010 American Institute of Physics [doi 10.1063/1.3514197]