Pedro A. Vázquez

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

The time evolution of the problem of electrohydrodynamic convection in a liquid between two plates is analysed numerically. The equations are non-dimensionalized using the ion drift velocity and the viscous time scales. Following the non-dimensionalization 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.

Characterization of injection instabilities in electrohydrodynamics by numerical modelling: comparison of particle in cell and flux corrected transport methods for electroconvection between two plates

Numerical simulations are carried out for the characterization of injection instabilities in electrohydrodynamics and, in particular, the development of electroconvection between two parallel plates. The particle-in-cell and the finite element-flux corrected transport methods are used for the simulation of the test case, as they have proved very powerful and accurate in the solution of complex transport problems. Results are presented for unipolar injection (both strong and weak injections) between two plane electrodes immersed in a dielectric liquid, and the good agreement obtained by the two methods demonstrates not only their theoretical validity but also their practical ability to deal with transport problems in the presence of steep gradients. Some differences appear mainly in the prediction of small oscillations of the velocity and consequently of the electric current. These differences are highlighted and an explanation of their source is given.

Thermal and electrohydrodynamic plumes. A comparative study

In this paper we deal 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 nonconducting 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.

Dynamics of electrohydrodynamic laminar plumes: Scaling analysis and integral model

In this paper electrohydrodynamic plumes are examined in the region far from the injecting electrode and the collector plate, for both two-dimensional and axisymmetric geometries. The relative importance of the conduction mechanisms (convection, drift and diffusion of electric charge) is analyzed. Diffusion turns out to be negligible compared to convection and drift for the experimental conditions. But the transverse drift (Coulomb repulsion) is of the same order of magnitude than convection. We find a set of three differential equations giving the evolution of the velocity at the center of the plume and the widths of the plume and the charged core inside.

Dynamics and linear stability of charged jets in dielectric liquids

The physical system to be considered is a blade-plane configuration in a dielectric liquid. For high electric fields, injection from the blade takes place with ions of the same polarity. The Coulomb force acting upon the injected charges originates an electrohydrodynamic (EHD) flow, referred in what follows as the charged jet. A laminar solution of this EHD jet is obtained using similarity analysis. If transport of charge is dominated by convection, i.e., neglecting molecular diffusion and ion drift, and the electric field is assumed constant, the problem is mathematically equivalent to the bidimensional thermal plume in the limit of large Prandtl numbers. The authors examine the stability of this EHD jet using linear theory and parallel-flow approximations. Neutral stability curves are computed numerically in terms of a nondimensional parameter which is the electrical analogous to the Grashof number. Finally, some experimental observations are presented, followed by a short discussion. The role played by the viscosity correlates reasonable well with the theoretical analysis. >

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 charge 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 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 is provided to help understand the bifurcation behavior.

Stability analysis of the 3D electroconvective charged flow between parallel plates using the Particle-In-Cell method

The 3D Electrohydrodynamic convection between parallel plates immersed in a dielectric liquid is studied numerically in a cylindrical cell. The distribution of charge is computed with Particl-In-Cell, the electric field with finite elements and the velocity field with an imposed roll. Critical values of the stability parameter are obtained for different mobilities and are compared with the value from the linear stability analysis.

Numerical modeling of EHD flows due to injectors of finite size

The two-dimensional flow, electric field and distribution of charge is numerically calculated in a box, with an applied voltage and injection of charge occurring at the bottom. The aim of this paper is to study the evolution of the charge density and the flow as the injecting region is decreased.

Numerical simulation of two-dimensional EHD plumes mixing finite element and particle methods

We have simulated numerically a two-dimensional electrohydrodynamic (EHD) plume. We have used a technique mixing finite elements and particle methods. A quasiregular mesh, following the lines of the electric field, has been built to better describe the density of charge at the nodes. The influence of the electric field on the injection of charge has been taken into account. We show the results of several simulations for different values of the applied tension.

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 73 of the harmonic part of the electric potential, sometimes with a range of multiplicity in between.