Oscillation Frequencies of Droplets Held Pendant on a Nozzle

Small-amplitude oscillations of liquid droplets held pendant on a nozzle and surrounded by either air or another liquid were investigated experimentally. The oscillations were induced by mechanical means, and the natural frequencies of oscillations were visually determined. Results are compared to existing related theories of Miller and Scriven and of Strani and Sabetta. As may be expected, the presence of the solid support causes measured oscillation frequencies for the lowest oscillation mode to deviate greatly from the Miller and Scriven low viscosity approximation (n = 2) for free spherical drops. Experiments are in qualitative agreement with the first (n = 1) mode predicted by Strani and Sabetta, with the best correspondence occurring under circumstances where the ratio of nozzle to drop radii is small. The difference between the experimental results and the theory of Strani and Sabetta can be attributed to the restrictive boundary conditions of their analytic model. Thus, better theoretical characterization of pendant droplet oscillations will require numerical computations.