Plane model of fluid interface rupture in an electric field

Abstract

Modeling of an air-fluid interface in an electric field is presented. Specifically, equilibrium of the interface under the dominant forces-electric stress, surface tension, and pressure-is investigated. Since interface shape and equilibrium are related, the shape of an electrified interface is also addressed. To determine the electric stress, an analytical expression for the electric field in the vicinity of the interface is determined. The operating point of the interface is shown to exist in a three-dimensional parameter space that is divided by a critical surface into equilibrium, quasiequilibrium, and nonequilibrium subdomains. The three parameters are applied voltage, electrode separation, and pressure difference. Interface size, counterelectrode size, and fluid properties are also considered. The subdomain in which the operating point resides defines the important characteristics of the interface. The operating point moves within, and transfers between, equilibrium subdomains, and points on the critical surface represent "rupture points" of the interface. The final shape of the interface is solved iteratively using this equilibrium model. Interfaces emitting an electrospray can have a range of apex angles, and it is shown that the magnitude of this angle impacts equilibrium. It is revealed that the excess pressure difference term is critical in determining the interface shape ͑specifically the cone generatrix͒ and that minimization of the potential energy of all forces can be used to predict the magnitude of the apex angle and pressure immediately after interface rupture. The equilibrium model is important from an operational and optimization perspective, as it is useful to predict the conditions required to break equilibrium and transfer to a quasiequilibrium state ͑i.e., an electrospray͒, and the conditions necessary to maintain quasiequilibrium once it is formed.

Electromigration occurences and its effects on metallic surfaces submitted to high electromagnetic field: A novel approach to breakdown in accelerators

“…Conducting liquids subjected to fields tend to form coneshaped structures (Taylor cones), stabilized by the balance of electrostatic and surface tensions forces [64,67,68]. If the field is increased the cone becomes unstable and the emission of micro-droplets starts [46,47,[69][70][71], together with ions or electrons depending on the polarity [72]. In the case of molten metal the Taylor cones can be frozen by quickly switching off the voltage (see § 4.2.3).…”

Application of an Equilibrium Model for an Electrified Fluid Interface—Electrospray Using a PDMS Microfluidic Device

“…For a full description on the development of the equilibrium model, the reader should consult Gubarenko et al [10]. The model defines the 'critical function':…”

“…In a recent study, Gubarenko et al [10] developed a model of an electrified fluid interface that examined the impact of operational parameters on interface equilibrium. The model predicted the conditions that cause the interface to rupture and form an electrospray and the conditions necessary to maintain an electrospray once it is formed.…”

“…The equilibrium model [10] addressed limitations found in previous models of an electrified interface. Using the concept of an operational domain, the model identified the conditions necessary to cause an interface to rupture and form an electrospray and the conditions necessary to maintain an electrospray.…”

An ion gating strategy for a miniaturized planar Ion Mobility Spectrometer

“…Details on the design and operation of the electrospray emitter chip have been previously reported [12][13]. …”