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a b s t r a c tIn the present study we propose a charge-conservative scheme to solve two-phase electrohydrodynamic (EHD) problems using the volume-of-fluid (VOF) method. EHD problems are usually simplified by assuming that the fluids involved are purely dielectric (insulators) or purely conducting. Gases can be considered as perfect insulators but pure dielectric liquids do not exist in nature and insulating liquids have to be approximated using the ''TaylorMelcher leaky dielectric model'' [1,2] in which a leakage of charge through the liquid due to ohmic conduction is allowed. It is also a customary assumption to neglect the convection of charge against the ohmic conduction. The scheme proposed in this article can deal with any EHD problem since it does not rely on any of the above simplifications. An unrestricted EHD solver requires not only to incorporate electric forces in the NavierStokes equations, but also to consider the charge migration due to both conduction and convection in the electric charge conservation equation [3]. The conducting or insulating nature of the fluids arise on their own as a result of their electric and fluid mechanical properties. The EHD solver has been built as an extension to Gerris, a free software solver for the solution of incompressible fluid motion using an adaptive VOF method on octree meshes developed by Popinet [4,5].

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The disintegration of liquid drops with low electrical conductivity and subject to an electric field is investigated both theoretically and experimentally. This disintegration takes place through the development of a conical cusp that eventually ejects an ultrathin liquid ligament. A first tiny drop is emitted from the end of this ligament. Due to its exceptionally small size and large electric charge per unit volume, that drop has been the object of relevant recent studies. In this paper, universal scaling laws for the diameter and electric charge of the first issued droplet are proposed and validated both numerically and experimentally. Our analysis shows how charge relaxation is the mechanism that differentiates the onset of electrospray, including the first droplet ejection, from the classical steady cone-jet mode. In this way, our study identifies when and where charge relaxation and electrokinetic phenomena come into play in electrospray, a subject of live controversy in the field.

An ultra-fine liquid atomization procedure combining the advantages of electrospray and flow focusing is presented. Both techniques are known to produce strikingly small and steady liquid micro-jets issuing from menisci held by capillary forces. Such menisci take the form of a cusp-like drop attached to the feeding tube (flow focusing: FF) or a Taylor cone (electrospray: ES). The issuing micro-jets are forced or ‘sucked’ from the parent meniscus either by pressure or electrohydrodynamic forces. Subsequent capillary breakup of the jet leads to fine sprays of remarkable quality. Here we describe the joint effect of pressurization and electrification in a flow focusing device, and the subsequent coupling of both ES and FF phenomena. For any given liquid and flow rate, the combined procedure gives rise to significantly smaller droplet sizes than observed in any of the source techniques. The co-flowing gas stream removes space charges; in addition, the perforated plate facing the feed tube provides an electric barrier, shielding the jet-meniscus or ‘production’ area from the spray or ‘product’ area. As a result, space charges and electrified droplets are removed from the production area, thus avoiding the ambient electric saturation which becomes a limiting factor in ES-spraying: a significantly enhanced spraying stability ensues, with a much wider operation range than FF or ES. Other unexpected outcomes from the combination are also shown. A theoretical model is developed to predict the emitted droplet size: a first integral of the momentum equation yielding a generalized Bernoulli equation, and an explicit approximation for the jet diameter and droplet size, accurate within a broad parametrical band.