In this paper, the instability of two layers of insulating and conducting immiscible liquids separated by a deformable interface and subjected to unipolar injection is examined. Taking into account the slight deformation of the interface between the two liquids, a system of equations and boundary conditions is derived at marginal state. Non zero numerical solutions for both layers exist only for eigenvalues of the instability parameter T, which depends on the following parameters: injection level C, Bond number Bo, a new non-dimensional parameter P proportional to interfacial tension and the ratio of the layers’ thickness and of liquids viscosity. The variations in the instability criterion Tc, corresponding to the smallest eigenvalue, are examined in detail as a function of the main characteristic parameters C, P and the Bond number. We find that for some values of P, two instability mechanisms convective and interfacial ones can take place. When the strength of interfacial tension or the liquid thickness ratio is very low, the critical number tends to a value corresponding to interfacial instability. The influence of injection-induced convection in the insulating layer and the effect of interfacial deformation on interfacial instability are also discussed.

In this article the hydrodynamic instability of a horizontal two-layer system consisting of insulating and conducting immiscible liquids layers comprised between two rigid electrodes and subjected to a unipolar injection is examined. A theoretical model taking into account the slight deformation of the interface between the two liquids is developed and the system of equations and boundary conditions at marginal state (for which the smallest eigenvalue leads to the critical conditions for instability) is derived. The general numerical solution of the two systems of equations relative to the two layers is constructed for specified values of: the instability parameter T, measure of the injection level C, Bond number Bo, a new non-dimensional number P, proportional to the surface tension and the wave number k. In this work, we present a detailed study of the effect of the deformation of the interface between the two layers accounted by Bond number and by parameter P. The results show that, with surface deformation, the instability criterion strongly depends on P number. For some values of P two instability mechanisms (in the bulk and at the interface) can take place. When strongly decreasing the strength of surface tension or the liquid thickness ratio, the critical number tends to a value such that the system is very close to interfacial instability.

This paper deals with the extraction from a meniscus of water droplets of small size into an immiscible insulating liquid by the use of a multistage voltage pulse. A previous study on a particular oil established that this EHD Drop-on-demand technique allows producing droplets of size smaller or much smaller than the needle diameter. The case of a dielectric liquid characterized by a rather high value of the water/oil interfacial tension is considered here. It is shown that by adequately modifying the shape and level of the multistage voltage pulse, droplets are produced with a diameter ranging over a large interval. It was expected that the short enough pulse duration would give electrically neutral droplets; in practice it is found that the droplets carry minute but nonzero charges. An explanation is given for the charging mechanism and other changes of the pulse shape allow to further minimize the droplets charge. Finally having in mind the possibility to investigate experimentally the electrocoalescence of two close drops, results are presented concerning the injection of two successive droplets.

Results are presented concerning the influence of an applied electric field on the coalescence of a water droplet with a much bigger water drop, both drops being immersed in a crude oil. This original study of electrocoalescence in crude oil was performed through high-speed optical observations, using a near-infrared camera, of a droplet falling onto a bottom drop, a bipolar square voltage being applied. For low electrical field strength, the electrostatic pressure at the water/oil interface of the merging droplet partly counteracts the capillary forces, which slows down the drop coalescence process. Above threshold field strength, the electric forces drastically affect the dynamics of drop deformation and merging. At a working temperature T = 60 °C, partial coalescence was observed, leaving a daughter drop of size increasing with the applied field. At T = 40 °C, there was an abrupt transition from coalescence to non-coalescence, the top droplet inducing an upward directed nearly conical deformation of the bottom drop. This is attributed to charge exchange between the colliding water drops at each polarity reversal of the applied voltage, thus generating a bouncing-like behaviour at a frequency twice the voltage frequency. The charge exchange occurs through a very thin filament interconnecting the drops during a short time and presumably generated by interface instability. Under strong enough applied field, there was also formation of a very fine mist around the zone of drop quasi contact; this mist is ascribed to the break-up of the transitory very thin ligament bridging the drops. Some explanations and considerations are proposed for the various observations; in particular, it is proposed that the contrast between the transitions to partial coalescence (at 60 °C) and to non-coalescence (at 40 °C) arises from geometrical differences in the temporary small bridge interconnecting the drops.

The paper presents recent improvements and results on the on-demand injection of small electrically neutral water drops in oil by high electric field pulses. The technique consists in applying a voltage pulse promoting the deformation of a water meniscus at the end of a capillary tube through the action of electric forces. For pulses of calibrated energy, the transient deformation can lead to the inertia-based ejection of a small uncharged droplet. Application of in-house developed multi-stage electric pulses offers, in contrast to usual single pulses, wider ranges of droplet size, improved reproducibility and stable ejection trajectories. Influence of the main parameters on the extracted droplet diameter is presented: it is shown that, by using capillary tubes of outer tip diameter close to 0.5 mm, it is possible to obtain, in a reproducible way, drops of diameter ranging from less than 15 μm up to more than 250 μm.

Chapter 2 Physical Examination of Dielectrics Olivier Gallot-Lavallée, Olivier Gallot-LavalléeSearch for more papers by this author Olivier Gallot-Lavallée, Olivier Gallot-LavalléeSearch for more papers by this author Olivier Gallot-Lavallée, Olivier Gallot-LavalléeSearch for more papers by this author Book Author(s):Olivier Gallot-Lavallée, Olivier Gallot-LavalléeSearch for more papers by this author First published: 27 June 2013 https://doi.org/10.1002/9781118753491.ch2 AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onEmailFacebookTwitterLinkedInRedditWechat Summary In gaseous dielectrics, polarization is generally negligible ϵr≈1 and dielectric losses null. The mathematical properties of the field are thus the same as in a vacuum. The gas is only involved by way of phenomena of ionization, which it causes when the intensity of the field becomes sufficient. This chapter focuses on the study of these phenomena. This study is interesting because gases are used either as insulators in cables, or coupled with other dielectrics in the machines. In fact, they are the only insulators for which satisfactory theories on their ionization have so far been able to be put forward. The chapter talks about liquid and solid dielectrics and the breakdown of solid dielectrics. The problems posed by this breakdown are far more complex than those posed by gases. Dielectric Materials and Electrostatics RelatedInformation

In connection with the phenomenon of electrocoalescence of water droplets in oil, the electrically induced deformations of some water–oil interfaces are studied. Such problems involve the strong coupling of hydrodynamics and electrostatics as well as the accurate tracking/capturing of the evolving interfaces. The paper presents a Finite–Element Arbitrary Lagrangian–Eulerian (FE–ALE) approach in deforming meshes to investigate the time-dependent deformation of the interface between highly conductive water and an insulating immiscible fluid. The developed numerical scheme is first tested and then used to solve two 2D axisymmetric EHD problems. Computed results are compared with predictions from asymptotic developments and with experimental measurements.

An investigation is presented of the deformation and coalescence of two closely spaced drops of conducting liquid suspended in an insulating fluid under the action of an electric field. After a recap of previous work on two identical drops, the equation governing the droplets deformation is derived in the asymptotic case of very close drops subjected to a potential difference. The critical conditions for the existence of a stationary solution are determined for a pair of droplets anchored on coaxial rings and on capillary tubes. In particular, electrocoalescence is predicted to occur when the interfaces distortions are such that the initial drops spacing has decreased by nearly 50%. The case of drops subjected to a uniform field is also considered, and an approximate expression for the critical field is proposed based on a semiempirical relation estimating the potential difference between two close spheres as a function of the applied field, of the spheres radius, and of their spacing.

The paper focuses on two particular phenomena which contribute to the poor collection efficiency of fine particles (from similar to 0.1 mu m to similar to 2 mu m) by electrostatic precipitators (ESPs). Firstly, the influence of turbulence on collection rate is considered as well as the fact that the charged fine particles are expected to give the main contribution in the generation of small eddies in ESPs. Experiments on collection efficiency eta of cigarette smoke show that h decreases as the dust concentration is increased, due to the subsequent increase in eddy diffusivity. The second phenomenon observed in the study is the deagglomeration of agglomerates in the ESP. An agglomeration process occurs, which is more and more marked as the smoke concentration is raised. Once charged in the ESP, some of the agglomerates disintegrate under the Coulomb repulsion, which leads to an apparent collection efficiency strongly. depending on the particle size.

The possibility of using electrostatic precipitation to clean the gas above solar panels on the surface of planet Mars is investigated. Results are presented on corona discharge in carbon dioxide gas under reduced pressure ranging from 5 to 10 mbar with different electrode configurations. The corona discharge inception voltage and the threshold of bipolar discharge have been measured for the three configurations. The charging of suspended particles of micrometer size in the gas by unipolar ions is examined. In the considered reduced pressure, very likely diffusion charging dominates over field charging. The drift velocity of charged particles is then estimated and is found to be not drastically lower than in industrial precipitators for fine particles despite the much lower electric field which can be applied under reduced pressure. Finally the results of a laboratory experiment examining the dust deposit onto photovoltaic cells are presented. It appears that electrostatic precipitation reduces the rate of dust deposit and might be used in order to increase the lifetime of solar panels during Mars missions.

Multiphase electric curtains generate traveling waves which can lift and convey charged particles, whereas single-phase electric curtains create a standing wave. However, this paper confirms that, in certain conditions, such a standing-wave curtain can expel the deposited powder as well. Indeed, we present results of experiments performed in atmospheric air and in carbon dioxide with electrodes coated with an insulating material for different powders under various pressures down to that existing on Mars (p cong 7 mbar). Under high-enough pressure in air (p = 1 bar), a part of the powders is put into motion when raising the applied voltage below the ionization threshold. Above the discharge threshold, the deposited powder can be completely expelled from the stressed zone by the dielectric barrier discharges (DBDs) occurring in the gas just over the surface of the insulating layer. This proves that the charging of particles by collection of gaseous ions and electrons produced by the DBDs is involved in the lift and in the removal of powders. The powder removal becomes more difficult when p is lowered. For gas pressure around 7 mbar, a good powder removal requires a distance between axes of adjacent electrodes lower than 1 mm. The dust removal efficiency also depends on the size of the particles and on the contact between the particles and the substrate. With Mars analog dust being spread out with a brush, the removal of the so-produced agglomerated particles is often satisfactory. When injecting and dispersing the same powder into the vessel under reduced pressure, the layer resulting from particle sedimentation can be removed. However, when the injected tribocharged particles are driven directly onto the standing-wave curtain, the resulting dust layer remains unperturbed by the action of electric field and DBDs. Very likely, this is due to the intimate contact between the particles and the substrate. These observations are discussed in the light of the different forces acting on particles.

A numerical model for simulating precipitation of submicrometer particles in a singlewire electrostatic precipitator is discussed in this paper. It includes all important phenomena affecting the process: electric field, space charge density, gas flow, including the secondary electrohydrodynamic flow caused by the corona discharge and charged particles, and particle transport. A simplified corona model assumes just one ionic species and neglects the ionization zone. The fully coupled model for the secondary EHD flow, considering the ion convection, has been implemented. The dust particles are charged by ionic bombardment and diffusion. The gas flow pattern is significantly modified by the secondary EHD flow, which depends on the particle concentration. As for fine particles the drift velocity is small and particles practically follow the gas streamlines, the particle concentration has a very strong effect on the precipitation efficiency.

the electrohydrodynamic (EHD) flow in a relatively wide electrostatic precipitator (ESP) (width:height = 2) is 2-or 3-dimensional (3D). The previous our measurements of 3D time-averaged flow velocity fields suggested that the flow in the ESP duct centre is almost 2-dimensional. In this paper we present both the 3D instantaneous and time-averaged flow velocity fields in a relatively wide ESP (width:height = 2). The ESP used in this work was an acrylic parallelepiped with a negatively polarized wire discharge electrode and two plate collecting electrodes. The velocity field was measured using Particle Image Velocimetry in the observation midplane along the ESP.

We investigate the deformation and coalescence of two closely spaced drops of conducting liquid suspended in an insulating fluid under the action of an electric field. The equations governing droplets deformation are derived in the case of drops subjected to a potential difference. The critical conditions for existence of a stationary solution are determined for drops anchored on capillary tubes in the asymptotic case of very close drops. In particular, electrocoalescence is predicted to occur when the interfaces distortions are such that the initial drops spacing has decreased by nearly 50%. A numerical simulation gives the critical conditions for any spacing between the drops. Results compare favourably with the asymptotic approach in the common range of application.

On examine deux phénomènes qui peuvent jouer un rôle dans l’efficacité modeste de capture des fines particules (de 0,1 μm à ~2 μm) par les électrofiltres. Le premier concerne la turbulence qui tend à diminuer le taux de collecte; on rappelle une conjecture sur la génération de tourbillons qui est due principalement à la charge spatiale associée aux fi nes particules chargées. En travaillant avec de la fumée de cigare tt , les mesures montrent que l’efficacité de collecte par l’électrofiltre diminue avec la concentration de la fumée et ce fait est at tribué à l’augmentation du taux de turbulence. Le second phé nomène observé est la dispersion dans l’électrofiltre des agrégats de particules qui se forment par collisions entre les particules en suspension. L’éclatement des agrégats se produit so u l’effet de la répulsion coulombienne.

In this paper, results of particle image velocimetry (PIV) measurements of the electrohydrodynamic (EHD) flow velocity fields in an electrostatic precipitator (ESP) are presented. The measurements were carried out for various densities of submicron dust. The ESP was an acrylic parallelepiped with a wire discharge electrode, placed perpendicularly to the main flow, and two plate collecting electrodes. The positive DC voltage was applied to the wire electrode. The PIV measurements were carried out in an observation plane set perpendicularly to the wire electrode at its half-length. The obtained results show that the general shape of the flow patterns at different dust densities is similar in the bulk of the flow. However, the flow velocity and the level of its turbulence strongly depend on the dust density, in particular in the region around the wire electrode.