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

Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis

We study the linear stability and nonlinear behavior of the electroconvection between two concentric halfcylinders with no-slip conditions on all boundaries. The no-slip condition makes impossible to apply the standard modal approach. Hence, we apply a finite element technique similar to the one we have used in a previous paper about the electroconvection in a rectangular enclosed domain. When compared to the classical problem of electroconvection between two full concentric cylinders, the linear criterion is higher, due to the viscous shear introduced by the lateral walls. As a consequence, the structure of the eigenmodes is very different. There is a repulsion between modeswith the same symmetry, forcing pairs of modes to cross each other repeatedly. For inner injection and small value of the ratio between the inner and outer radii the no-slip condition changes the nature of the bifurcation from subcritical to supercritical, while it is always subcritical for outer injection. To understand this behavior, we perform a modal analysis using the eigenfunctions obtained from the linear stability analysis as modal basis. We show that the supercritical branch is originated by the nonorthogonality of the modes when no-slip boundary conditions are imposed. These mechanism explains the previously unexplained appearance of the supercritical branch in the enclosed rectangular configuration.Ministerio de Economía y Competitividad FIS2014-54539-

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

Electrohydrodynamic linear stability analysis of dielectric liquids subjected to unipolar injection in a rectangular enclosure with rigid sidewalls

We investigate the linear stability threshold of a dielectric liquid subjected to unipolar injection in a 2D rectangular enclosure with rigid boundaries. A finite element formulation transforms the set of linear partial differential equations that governs the system into a set of algebraic equations. The resulting system poses an eigenvalue problem. We calculate the linear stability threshold, as well as the velocity field and charge density distribution, as a function of the aspect ratio of the domain. The stability parameter as a function of the aspect ratio describes paths of symmetry-breaking bifurcation. The symmetry properties of the different linear modes determine whether these paths cross each other or not. The resulting structure has important consequences in the non-linear behavior of the system after the bifurcation points.Ministerio de ciencia y tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458

Finite amplitude electroconvection induced by strong unipolar injection between two coaxial cylinders

We perform a theoretical and numerical study of the Coulomb-driven electroconvection flow of a dielectric liquid between two coaxial cylinders. The specific case where the inner to outer diameter ratio is 0.5 is analyzed. A strong unipolar injection of ions either from the inner or outer cylinder is considered to introduce free charger carriers into the system. A finite volume method is used to solve all governing equations including Navier-Stokes equations and a simplified set of Maxwell’s equations. The flow is characterized by a subcritical bifurcation in the finite amplitude regime. A linear stability criterion and a nonlinear one that correspond to the onset and stop of the flow motion, respectively, are linked with a hysteresis loop. In addition, we also explore the behavior of the system for higher values of the stability parameter. For inner injection, we observe a transition between the patterns made of 7 and 8 pairs of cells, before an oscillatory regime is attained. Such a transition leads to a second finite amplitude stability criterion. A simple modal analysis reveals that the competition of different modes is at the origin of this behavior. The charge density as well as velocity field distributions are provided to help understanding the bifurcation behavior.Ministerio de ciencia y tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458

Numerical Study of a Plane Poiseuille Channel Flow of a Dielectric Liquid Subjected to Unipolar Injection

In this paper, the interaction between a plane Poiseuille channel flow and an electroconvective movement induced by the electric field is numerically investigated. A flow is generated by an inlet parabolic profile in a rectangular duct. Space charges are injected in the flow through a metallic electrode placed on one of the channel walls and brought to a given potential. Transient numerical simulations have been carried out to investigate the structure of the flow. The entire set of the coupled Navier-Stokes and EHD equations is solved using an efficient finite volume technique. The behavior of the flow subjected to an applied voltage between the two electrodes is analyzed and time evolution of the charge density distributions is presented. The interaction between the convective movement induced by space charge injection and electric field and the mainstream flow, emphasizes the appearance of periodic transverse traveling waves convected in the channel. The dynamic of the flow through the variation of the ionic mobility parameter M is investigated. For a given Reynolds number and ionoc mobility parameter M it exists a threshold value Tc of the instability parameters T above which the transverse traveling rolls appear or not. When T is increased, different flow regimes have been highlighted starting from a complete steady state up to a fully unsteady electro-plumes flow configuration

Charge injection enhanced natural convection heat transfer in horizontal concentric annuli filled with a dielectric liquid

The natural convection heat transfer in a highly insulating liquid contained between two horizontal concentric cylinders is shown by two-dimensional numerical simulations to be noticeably enhanced by imposing a direct current electric field. This augmentation of heat transfer is due to the radial flow motion induced by unipolar injection of ions. It is found that there exists a threshold of the electric driving parameter T, above which the heat transfer enhancement due to the electric effect becomes significant. For relatively small T values, the mean Nusselt numbers are closely related to the flow pattern and Rayleigh number Ra. In addition, for sufficiently high T values, the flow is fully dominated by the Coulomb force, and thus the heat transfer rate no long depends on Ra.Ministerio de Ciencia y Tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458