Coulomb-driven flow of a dielectric liquid subject to charge injection by a sharp electrode

Injection of charge by a sharp electrode into a surrounding dielectric liquid leads to Coulomb forces that set the liquid into motion. An analysis is presented of this motion in a small region around the edge of the electrode, which determines the injected current as a function of the far electric potential seen by this region. By using an injection law appropriate for nonpolar liquids, the analysis predicts an electric current that increases first exponentially and then as the power 7 3 of the harmonic part of the electric potential, sometimes with a range of multiplicity in betweenMinisterio de Ciencia e Innovación PB95-0008

Numerical simulation of EHD flows using Discontinuous Galerkin Finite Element methods

The aim of this paper is to explore the capability of Discontinuous Galerkin Finite Element methods to solve numerically the charge transport equation in EHD convective flows, in both strong and weak injection regimes. These methods are especially suited to treat purely hyperbolic problems, as it is the charge transport equation in most EHD problems. We consider the 2D electroconvective flow between two parallel plates. We compare our com- putations with the analytical results in the hydrostatic regime, the linear and non-linear stability analysis, computing both the electric and velocity fields. The stability of the finite amplitude electroconvection is also anal- ysed. Comparisons are made with computations in the literature obtained with other numerical techniques. The results show that DG-FEM are a very good alternative to simulate numerically EHD convective flows

Self-consistent modeling of laminar electrohydrodynamic plumes from ultrasharp needles in cyclohexane

This paper presents a self-consistent model of electrohydrodynamic (EHD) laminar plumes produced by electron injection from ultra-sharp needle tips in cyclohexane. Since the density of electrons injected into the liquid is well described by the Fowler-Nordheim field emission theory, the injection law is not assumed. Furthermore, the generation of electrons in cyclohexane and their conversion into negative ions is included in the analysis. Detailed steady-state characteristics of EHD plumes under weak injection and space-charge limited injection are studied. It is found that the plume characteristics far from both electrodes and under weak injection can be accurately described with an asymptotic simplified solution proposed by Vazquez et al. Physics of Fluids 12, 2809 (2000) when the correct longitudinal electric field distribution and liquid velocity radial profile are used as input. However, this asymptotic solution deviates from the self-consistently calculated plume parameters under space-charge limited injection since it neglects the radial variations of the electric field produced by a highdensity charged core. In addition, no significant differences in the model estimates of the plume are found when the simulations are obtained either with the Finite Element Method or with a diffusion-free particle method. It is shown that the model also enables the calculation of the current-voltage (IV) characteristic of EHD laminar plumes produced by electron field emission, with good agreement with measured values reported in the literature.Ministerio de Economía y Competitividad FIS2014-54539-P

Study of the transition from conduction to injection in an electrohydrodynamic flow in blade-plane geometry

A dielectric fluid can be set into motion with the help of electric forces, mainly Coulomb force. This phenomenon, called electroconvection, can be induced by electrohydrodynamic conduction, injection, and induction. Conduction is based on the dissociation/recombination phenomenon, generates heterocharge layers, and occurs for low electric field values. Injection produces homocharge layers in the electrode vicinity and requires stronger electric fields to be initiated. This study is an experimental observation of the transition from conduction to injection of a dielectric liquid in blade-plane geometry using Particle Image Velocimetry. In addition, the electric current is measured to completely understand the flow behavior

Numerical analysis of the stability of the Electrohydrodynamic (EHD) electroconvection between two plates

The time evolution of the problem of Electrohydrodynamic (EHD) convection in a liquid between two plates is analysed numerically. The equations are nondimensionalized using the ion drift velocity and the viscous time scales. Following the non-dimensionalisation of the respective model, two different techniques have been used to describe the charge evolution, namely the Finite-Element Flux-Corrected Transport Method and the Particle-In-Cell technique. The results obtained with the two schemes, apart from showing good agreement, have revealed the appearance of a two-roll structure not described in previous works. This is investigated in detail for both strong and weak injection.Ministerio de ciencia y tecnología FQM-42

Thermal and electrohydrodynamic plumes: a compartive study

This paper deals with self similar thermal and electrohydrodynamic (EHD) plumes. The former arises from hot lines or points, whereas the latter arises when sharp metallic contours submerged in non conducting liquids support high electrostatic potential, resulting in charge injection. Although the motive force is buoyancy in one case and Coulomb force in the other, it is shown that the solution for EHD plumes is the same as for thermal plumes in the limit of large Prandtl numbers. We present the analysis of axisymmetric plumes for large values of Prandtl number, and this analysis is subsequently applied to EHD plumes. The validity of the approximations for EHD plumes is discussed in the light of experimental data.Ministerio de ciencia y tecnología PB93-118

Minimal formulation of the linear spatial analysis of capillary jets: Validity of the two-mode approach

A rigorous and complete formulation of the linear evolution of harmonically stimulated capillary jets should include infinitely many spatial modes to account for arbitrary exit conditions [J. Guerrero et al., J. Fluid Mech. 702, 354 (2012)]. However, it is not rare to find works in which only the downstream capillary dominant mode, the sole unstable one, is retained, with amplitude determined by the jet deformation at the exit. This procedure constitutes an oversimplification, unable to handle a flow rate perturbation without jet deformation at the exit (the most usual conditions). In spite of its decaying behavior, the other capillary mode (subdominant) must be included in what can be called a “minimal linear formulation.” Deformation and mean axial velocity amplitudes at the jet exit are the two relevant parameters to simultaneously find the amplitudes of both capillary modes. Only once these amplitudes are found, the calculation of the breakup length may be eventually simplified by disregarding the subdominant mode. Simple recipes are provided for predicting the breakup length, which are checked against our own numerical simulations. The agreement is better than in previous attempts in the literature. Besides, the limits of validity of the linear formulation are explored in terms of the exit velocity amplitude, the wave number, the Weber number, and the Ohnesorge number. Including the subdominant mode extends the range of amplitudes for which the linear model gives accurate predictions, the criterion for keeping this mode being that the breakup time must be shorter than a given formula. It has been generally assumed that the shortest intact length happens for the stimulation frequency with the highest growth rate. However, we show that this correlation is not strict because the amplitude of the dominant mode has a role in the breakup process and it depends on the stimulation frequency.Ministerio de Economía, Industria y Competitividad, Spain, under Contract No. FIS2014-25161Junta de Andalucía under Contract No. P11-FQM-791

On two-dimensional finite amplitude electro-convection in a dielectric liquid induced by a strong unipolar injection

The hydrodynamic stability of a dielectric liquid subjected to strong unipolar injection is numerically investigated. We determined the linear criterion Tc (T being the electric Rayleigh number) and finite amplitude one Tf over a wide range of the mobility parameter M. A noticeable discrepancy is shown for Tf between our numerical prediction and the value predicted by stability analysis, which is due to the velocity field used in stability analysis. Recent studies revealed a transition of the flow structure from one cell to two with an increase in T. We demonstrate that this transition results in a new subcritical bifurcationMinisterio de Ciencia y Tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458

Complex flow patterns at the onset of annular electroconvection in a dielectric liquid subjected to an arbitrary unipolar injection

We numerically investigated the annular electroconvection that takes place in a dielectric liquid lying between two concentric cylinder electrodes. A uniform injection of arbitrary strengths either from the inner or outer cylinder introduces free charge carriers into the system, and the resulting Coulomb force induces electroconvection. The problem is characterized by a linear instability that corresponds to the onset of flow motion. The linear stability criteria were determined from direct numerical results and by linear stability analysis, and the results obtained with the two approaches show an excellent agreement. We focused on the fully developed flow pattern in the finite amplitude regime. We observed very different flow motions that were highly dependent on the injection strength.Ministerio de Ciencia y Tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458

Onset of convection in a finite two-dimensional container due to unipolar injection of ions

This work addresses the stability of a two-dimensional plane layer of a dielectric liquid enclosed in wall bounded cavities of different aspect ratios and subjected to unipolar injection of ions. Numerical simulations have been conducted to investigate the effect of lateralwalls, especially in the development of the electroconvective instability. It is found that an unexpected change of the bifurcation nature occurs for certain cavity aspect ratios. We showthat above the linear stability threshold for the rest state a supercritical bifurcation arises. This bifurcation takes place at a given value Tc1 of the parameter T (the electric Rayleigh number). Then, a second subcritical bifurcation occurs at a second threshold Tc2, featuring a typical hysteresis loop with an associated nonlinear criterion Tf , which is very characteristic of the Coulomb-driven convection. This behavior has been confirmed by different numerical codes based on different numerical methods. The physical mechanism which leads to this situation is analyzed and discussed. The evolution of the bifurcation diagrams with the aspect ratio of the cavity is also provided and analyzed.Ministerio de ciencia y tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458