Stability limit of electrified droplets and bubbles

In many physical processes, including cloud electrification, electrospray and electrocoalescence, droplets and bubbles are exposed to electric fields and may either remain whole or burst in response to electrical stresses. Determining the stability limit of a droplet exposed to an external electric field has been a century-long mathematical challenge, and the only analytical treatment to date is an approximate calculation for a free-floating droplet. In this talk, we demonstrate, experimentally and theoretically, that the stability limit of a conducting droplet exposed to an external electric field is described by a power law with broad generality that applies to the cases in which the droplet is pinned or sliding on a conducting surface or free floating. The power law is simply derivable by the variational principle, provided the physical quantities defining the instability are selected to be independent of an arbitrary variation of the system. Practically, our finding provides a simple formula that captures the parameter range of bubbles and droplets that can be supported on electrified surfaces.