Self-similar behavior of successive Coulombic fissions of evaporating charged water droplets

Abstract

Charged droplets suspended in an electrodynamic balance experience a form of instability known as Coulombic fission when electric forces (resulting from the electrical charges on the droplet surface) surpass surface tension forces. For a pure-fluid droplet with a given diameter, a charge limit (known as Rayleigh limit, qR) exists at which Coulombic Fission occurs. In an evaporating droplet with a certain initial amount of charge (q), the Rayleigh limit is reached when the droplet decreases to a certain smaller diameter due to evaporation. During Coulombic fission, the droplet releases some of the charges and returns to a stable state. Further evaporation will lead to the next Rayleigh limit. As a result, several successive Coulombic fissions may occur during the evaporative lifetime of a droplet. In this study, charged, sub-millimeter droplets of deionized water were suspended using an electrodynamic balance and left to evaporate into their surroundings. As many as 15 Coulombic fissions were observed during the evaporation of a single droplet. The time of evaporation and droplet diameter at Coulombic fissions were recorded using high-speed imagery and digital image processing. The amount of charge at the time of each fission was calculated based on droplet size and Rayleigh limit. It was found that during each fission, the droplet releases about 14 % of its charge. Results indicated that droplets with similar initial relative charge (q/qR) sustained Coulombic fissions at similar normalized diameters independently of initial droplet size and evaporation rate. As a consequence of this, and in accordance with the d2-law of pure-fluid droplet evaporation, the times at which Coulombic fissions occur during the droplet's lifetime can be predicted for a given initial droplet size and evaporation rate.