Energy dissipation in electrosprays and the geometric scaling of the transition region of cone–jets

Abstract

The characterization of electrosprayed droplets by means of retarding potential and time-of-flight techniques yields relevant information on the physics of the cone–jet itself. The experimental data reveal that a significant fraction of the electric power injected in the cone–jet is degraded by ohmic and viscous dissipations, as well as converted into surface energy. The degradation of energy can be cast in the form of a measurable voltage deficit that depends on the fluid's viscosity, electrical conductivity and dielectric constant, but is independent of its flow rate. These experimental facts require an identical scaling rt for both the characteristic radial and axial lengths of the cone-to-jet transition, the region where conduction current is transformed into convected surface charge. This fundamental scale is the geometric mean of the electrical relaxation length and the distance from the Taylor cone apex where the dynamic and capillary pressures become comparable. These two lengths are of the same order in a wide range of operational conditions, which further confirms the importance of the role played by electrical relaxation phenomena in the physics of cone–jets. The validity of rt is further supported by the numerical results of Higuera (J. Fluid Mech., vol. 484, 2003, pp. 303–327), whose profiles of the transition region non-dimensionalized with rt remain unchanged when the flow rate is varied. Finally, the dissipation of energy significantly increases the temperature of fluids with high conductivities, and future models for the cone–jets of these liquids will need to account for thermal effects.