Stability limit of droplets in combined fields*

The condition for stability of a droplet subject to an external field arises in many practical and theoretical circumstances. Here we present the experimental results for a droplet’s stability limit under combined electrostatic and gravitational fields – a nonlinear system in which the droplet takes various non-elementary shapes at different combined field strengths. The system is characterized in terms of three dimensionless groups prescribing the drop geometry and the relative magnitudes of electrostatic, gravitational and capillary pressures. The stability limit is well represented by a plane in the coordinate system spanning these dimensionless groups, a result valid across several orders of magnitude of experimental data. We rationalize this result on the basis of the scaling for the energy differentials of the unstable mode. Our methodology may be more broadly applied in deducing the stability limits of systems subject to combined fields.