R. Chicon

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.

Instability of an interface between air and a low conducting liquid subjected to charge injection

We study the linear stability of an interface between air and a low conducting liquid in the presence of unipolar injection of charge. As a consequence of charge injection, a volume charge density builds up in the air gap and a surface charge density on the interface. Above a certain voltage threshold the electrical stresses may destabilize the interface, giving rise to a characteristic cell pattern known as rose-window instability. Contrary to what occurs in the classical volume electrohydrodynamic instability in insulating liquids, the typical cell size is several times larger than the liquid depth. We analyze the linear stability through the usual procedure of decomposing an arbitrary perturbation into normal modes. The resulting homogeneous linear system of ordinary differential equations is solved using a commercial software package. Finally, an analytical method is developed that provides a solution valid in the limit of small wavenumbers.

CHAOTIC ELECTROCONVECTION IN A LAYER OF DIELECTRIC LIQUID SUBJECTED TO UNIPOLAR INJECTION: MAXIMAL LYAPUNOV EXPONENTS

This paper reviews the studies that have been carried out over the years to analyze the electroconvection of an insulating plane liquid layer subjected to unipolar charge injection from one of the electrodes. We consider in detail the motion near the onset of nonlinear instability that for brevity we call chaotic electroconvection. We also present some recent advances in the characterization of this chaotic motion. In particular, we have computed the maximal Lyapunov exponents for time series obtained from numerical simulation, for weak as well as strong injection regimes, and we discuss the relevance of these results for the characterization of this EHD chaos.

The stability of a horizontal interface between air and an insulating liquid subjected to charge injection

This paper presents the linear stability analysis of an interface between air and an insulating liquid subjected to a perpendicular electric field, in the presence of unipolar injection of charge. Depending on the characteristics of the liquid and the depth of the liquid layer two different instability thresholds may be found. One of them is characterized by a wavelength of the order of the liquid layer thickness and corresponds to the well-known volume instability of a liquid layer subjected to charge injection. The other one is characterized by a wavelength some ten times the liquid layer thickness and corresponds to the so-called rose-window instability, an instability associated to the balance of surface stresses.

Modelling the finite amplitude electroconvection in cylindrical geometry: characterization of chaos

The long-standing problem of finite amplitude electroconvection in insulating liquids subjected to unipolar injection is now addressed in cylindrical geometry. The geometrical pattern appearing first in experiments above the stability threshold corresponds to hexagonal convective cells. The cylindrical geometry is chosen as a mathematically tractable approximation to the hexagonal cells. An axially symmetric convection cell is considered, with free-slip conditions on the lateral walls of the cell. The velocity field is assumed to be self-similar, and axial symmetry allows to derive it from a stream function. Finite amplitude electroconvection is analyzed by using the particle type method previously developed. The linear and non-linear criteria for instability are computed. The velocity amplitude is always time-dependent and chaotic. We computed the Lyapunov exponent for the time series obtained from the simulation.

Lyapunov exponents of time series in finite amplitude electroconvection

We analyze the nonlinear time series obtained from numerical simulation of electroconvection induced by unipolar injection. These time series are non-steady and non-periodic and the dimension of the strange attractor seems to be very high. We focus our study in the computation of the maximal Lyapunov exponents, which are a measure of the divergence of two trajectories in the attractor. We have studied the evolution of the maximal Lyapunov exponent as the instability parameter varies. In all the series we found a positive maximal Lyapunov exponent, which is a strong evidence of chaos.

Influence of residual conductivity on the stability threshold of a dielectric liquid surface under electric field and charge injection

Two different Electrohydrodynamic (EHD) instabilities are found to coexist in experiments where an electric field, together with injection of charge, is applied perpendicularly onto an interface between air and a very low-conducting liquid. One is the classical EHD instability, while the other is the so-called Rose-window instability. A prelimary theoretical analysis is made of the effect upon the interface instability of a certain residual ohmic conductivity in the liquid. The rise of charge density in the liquid near the interface is enhanced by the presence of the residual conductivity, which could favour the generation of low wave-number instabilities.

Linear stability of an interface between a non-ohmic liquid and air subjected to an electric field and charge injection

The electrohydrodynamic (EHD) instability of an insulating liquid subjected to unipolar injection of ions has been the object of many different studies. It is due to the existence of a potentially unstable distribution of charge in the liquid bulk. Besides that classical instability, it has also been found experimentally that insulating liquids exhibit another kind of EHD instability when subjected to corona discharge from air. This instability, referred to as rose-window instability, is characterized by a pattern of large cells. Both instabilities arise above quite different voltage thresholds. In this paper we write down and numerically solve the linearized equations of motion of the liquid when the air above is considered. Our first aim is to discuss the effect of the air layer on the linear stability threshold for the classical EHD volume instability.

Interfacial EHD instability of a liquid of finite conductivity under unipolar charge injection

Low conducting liquids exhibit the so-called rose-window instability. This instability appears when charge is injected in an air-liquid interface. It seems to be associated to the destabilizing role of the electric pressure onto the surface. Depending on the liquid conductivity the charge on the interface is of the same sign (low conductivity) or opposite sign (high conductivity) to that of the injected charge. Both situations have different instability thresholds. In this paper we write down and solve numerically the linearized equations of motion of the liquid, assuming that it behaves as an ohmic conductor.

Electroconvection in small cylindrical cavities

The problem of electroconvection of an insulating liquid enclosed in a cylindrical cavity with an aspect ratio /spl Gamma/= R/d close to 1(2R is the cavity diameter and d the distance between the electrodes) is numerically approached by imposing no slip conditions on the lateral borders. This case, in which only one convective cell is present, is of great interest because for voltages just above the threshold of stability the power spectrum of experimentally measured current fluctuations is discrete. First, a fundamental frequency appears together with its harmonics and subharmonics, then biperiodic behavior and only for high enough values of the applied voltage the spectrum becomes continuous, and qualitatively similar to those measured in large aspect ratio systems. Stability and finite-amplitude electroconvection are investigated for different injection strengths by using a particle-type method, and considering a self-similar velocity field with cylindrical symmetry. The spectral features of the fluctuating component of the computed velocity amplitude are obtained and compared to the experimental ones.