Formation of electrohydrodynamic flows in strongly nonuniform electric fields for two charge-formation modes

The main features of the formation of electrohydrodynamic (EHD) flows are analyzed for two basic regimes of electrization of weakly conducting liquids: injection from the electrode surface and dissociation in the bulk. Analysis is carried out on the basis of the results of computer simulation of EHD flows in a strongly nonuniform electric field in the needle-plane electrode system. This system creates favorable conditions for the injection as well as dissociation mechanisms of charge formation. Typical features are revealed for each model of charge formation. The current-time characteristics of the transient process of stabilization of EHD flows are calculated.     

Computer simulation of EHD flows in a needle-plane electrode system

Complex investigation of the structure of electrohydrodynamic (EHD) flows in a needle-plane electrode system is carried out on the basis of analysis of experimental data and the results of computer simulation. An algorithm of iterative simulation of the volume charge distribution in a fluid is developed. Simulation is carried out using the ANSYS system. The fields of velocities and pressures, as well as electric characteristics of EHD flows, are calculated. Analysis of the results reveals a number of features of EHD flows in the electrode system under investigation. Peculiarities of the band structure are determined, and the characteristic size of the low-pressure zone near the active electrode, as well as the sizes of the acceleration and deceleration zones of the fluid in the electrode gap, is determined.     

Electric convection of low-conductivity liquid in a horizontal capacitor in the presence of unipolar charge injection

Electric convection of low-conductivity liquid in a horizontal plane capacitor is analyzed with allowance for unipolar charge injection. Dynamics of charge transfer through stationary isothermal liquid in the presence of modulated electric field is studied. Effect of modulation amplitude and frequency on the spatiotemporal distribution of charge density and electric potential is considered. Nonlinear electric convection of nonisothermal low-conductivity liquid is studied in the presence of static electric field in a 2D system. Hysteresis transitions between two different (with respect to intensity) regimes of electric convection are analyzed.     

Charging of a conducting sphere moving in a weakly ionized gas under an arbitrarily oriented external uniform electric field

A charging conducting sphere moving in a weakly ionized gas is investigated. An external uniform electric field is applied with arbitrary orientation relative to the gas flow. The ion current is obtained analytically and investigated numerically in ballistic assumption. It is shown that charging regimes depend not only on the net charge of the sphere but also on the gas flow type, and the parameter ξ_± – the ratio of ion drift velocity far from the sphere to the gas velocity. The cases |ξ_±|<1 and |ξ_±|>1 yield two different charging regimes for Stokes and potential flows. For the potential flow, the ion current has been found analytically in continuous ξ_±-parameter space. The stationary charge of an isolated sphere is also calculated numerically as a function of α. It achieves maximum magnitudes in direct (α=0) and back (α=π) flows respectively.     

Nonlinear periodic waves on the charged surface of a viscous finite-conductivity fluid

The profile of a periodic capillary-gravitational wave propagating over the surface of a viscous finite-conductivity fluid is found in a second-order approximation in initial deformation amplitude. When the finiteness of the rate with which the potential of the fluid smoothes out as capillary-gravitational waves travel over its free surface is taken into account, the intensity of nonlinear interaction between the waves changes. This intensity is found to depend on the electric charge surface density, conductivity of the fluid, and wavenumbers. The finiteness of the potential smoothing rate influences the nonlinear interaction between the waves nonmonotonically.     

Experimental manifestation of vortices and Rossby wave blocking at the MHD excitation of quasi-two-dimensional flows in a rotating cylindrical vessel

Experiments on the excitation of counterpropagating zonal flows by the magnetohydrodynamic (MHD) method in a rotating cylindrical vessel with a conic bottom have been performed. Flows appear in a conducting fluid layer in the field of ring magnets under the action of a radial electric field. The velocity fields have been reconstructed by the particle image velocimetry (PIV) method. In the fast rotation regimes with a thin fluid layer, where the Rossby-Obukhov scale does not exceed the characteristic sizes of the vessel, the system of perturbations appears with almost immobile blocked anticyclones in the outer part of the flow and rapidly moving cyclones in the main stream. The diagram of regimes is plotted in the variables of the relative angular velocities of the averaged zonal flow and transfer of vortices about the system rotation axis. Attention is focused on the results for the regions of the diagram with slow motion of vortices with respect to the rotating coordinate system near the parameters for stationary Rossby waves (blocking of circulation). The results are compared to the results previously obtained in similar experiments using the source-sink method.     

Nonlinear analysis of interaction between finite-amplitude capillary waves in a layered inhomogeneous liquid

The nonlinear capillary wave motion in a two-layer liquid with a free surface is analytically investigated accurate to the second order of smallness in ratio of the wave amplitude to the layer thickness. The layers differ in physicochemical properties. A capillary analogue to the “dead water” effect is observed in the system in both linear and quadratic approximations. In the absence of an electric charge at the interfaces, internal nonlinear resonance interaction between capillary waves is also absent regardless of the place of their origination. When there is a charge at the interlayer boundary, capillary waves resonantly interact with each other.     

Small-scale turbulence in a closed-field-line geometry

Plasma turbulence due to small-scale entropy modes is studied with gyrokinetic simulations in a simple closed-field-line geometry, the Z pinch, in low-beta parameter regimes that are stable to ideal interchange modes. We find an enormous variation in the nonlinear dynamics and particle transport as a function of two main parameters, the density gradient and the plasma collisionality. This variation is explained in part by the damping and stability properties of spontaneously formed zonal flows in the system. As in toroidal systems, the zonal flows can lead to a strong nonlinear suppression of transport below a critical gradient that is determined by the stability of the zonal flows.     

Different types of nonlinear convective oscillations in a multilayer system under the joint action of buoyancy and thermocapillary effect

The nonlinear development of oscillatory instability under the joint action of buoyant and thermocapillary effects in a multilayer system, is investigated. The nonlinear convective regimes are studied by the finite difference method. Two different types of boundary conditions – periodic boundary conditions and rigid heat-insulated lateral walls, are considered. It is found that in the case of periodic boundary conditions, the competition of both mechanisms of instability may lead to the development of specific types of flow: buoyant-thermocapillary traveling wave and pulsating traveling wave. In the case of rigid heat-insulated boundaries, various types of nonlinear flows – symmetric and asymmetric oscillations, have been found.     

Induced soap-film flow by non-uniform alternating electric field

Fluid flows generated on soap films by non-uniform alternating electric fields are studied. Two parallel metal rods subjected to an AC voltage are placed perpendicular to the soap film, which is anchored in a dielectric frame. The fluid flow is generated by electrohydrodynamic induction. At very low signal frequencies there is induced surface charge, but there is no tangential electric field at the surface, so there is no force and no flow. Fluid flow is observed increasing the frequency, when there are both surface charge and tangential electric field. The flow velocity increases with decreasing thickness of the soap film.     

On nonlinear periodic capillary-fluctuation wave flow in a thin liquid film on a solid substrate

Analytical calculation of a nonlinear periodic wave flow on the free surface of a charged layer of an ideal incompressible conducting liquid resting on a solid substrate is carried out for the case when fluctuation-induced forces (the dispersion component of the wedging pressure) have a decisive effect on the system. It is shown that wave flows emerge in the liquid in calculations of the second order of smallness in the wave amplitude, which is assumed to be small compared with the thickness of the liquid layer. These flows result from nonlinear interaction as nonlinear corrections to the waves set at the zero time. The field of fluctuation-induced forces displaces these flows toward the periphery of the area of influence of these forces. This effect takes place both in the presence of an external electric field near the free surface and in its absence. The sign and value of the nonlinear corrections depend on whether an electric field is present near the free surface of the liquid. In the presence of an electric field, the curvature of the crest of the nonlinear waves increases; in its absence, the curvature decreases.     

Evidence of long-distance correlation of fluctuations during edge transitions to improved-confinement regimes in the TJ-II stellarator

Long-distance coupling between edge parameters' fluctuations has been investigated in the TJ-II stellarator. Results show long-range correlations in potential fluctuations, which are amplified by the development of radial electric fields during transitions to improved-confinement regimes, whereas there is no correlation between ion saturation current signals. These experimental findings suggest the importance of long-range correlations as a new fingerprint of the plasma behavior during the development of edge shear flows and the key role of electric fields to amplify them.     

Nonlinear properties of electron junctions in the presence of a space charge

The role of a space charge in the formation of nonlinear characteristics of an electron junction, into which is introduced an accelerated electron flow, is considered. To describe the reactive properties of a quasistationary space charge one uses the concept of differential capacitance. Analysis of the current regimes and of the nature of transitions between them made it possible to establish the regions of continuous and jumpwise variation of the differential capacitance as function of electric parameters, as well as to explain the regime of electron reflection, in which the value of the differential capacitance exceeds the value of the interelectrode capacity by several times. An equation is obtained for the reflection regime, which, independently of the electrode configuration, makes it possible to determine the variation in the junction capacitance from the value of the quasistationary space charge. Due to the practical significance of obtaining data on the nonlinear reactivity of an electron junction, its noise characteristics are considered. A specific HF current fluctuation is detected, occurring in the presence of noise minima for certain flight angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 51–69, September, 1986.     

Dynamics of electroconvective nematic liquid crystal structures in a nonharmonic electric field

The emergence of electroconvection in a nematic liquid crystal under the action of a nonharmonic electric field is investigated. Analysis is carried out using a 2D model. We propose new forms of the varying electric field acting on the system, for which subharmonic oscillations exist: (a) electric field of a trapezoidal form and (b) external field varying in accordance with the law of “joined cosines.” The behavior of synchronous excitations in the insulating and conducting regimes, as well as subharmonic oscillations, is analyzed. The parametric instability domains are found, and the critical frequencies of transition between different response regimes are determined. The stability maps of the nematic liquid crystal are constructed on the frequency-voltage amplitude plane.     

Low-mode model of electroconvection of an ideal dielectric

A three-mode model of electroconvection of an ideal dielectric in the ac electric field of a horizontal capacitor is developed. With the help of this model, hysteretic transitions between different nonlinear regimes of electroconvection of the perfect liquid dielectric are found and investigated. The cases of zero-gravity and of heating from above in the gravitational field are considered. Frequency dependencies of the electroconvection oscillatory regimes are studied. Diagrams of the regimes are constructed. The following scenarios of transition to chaos are explored: through a subharmonic cascade, through quasi-periodicity, and from equilibrium. Behavior of the electroconvecton oscillations in the high-frequency limit is also studied.     

The onset of convection of a poorly conducting fluid in a modulated thermal field

The stability of a poorly conducting fluid in a constant electric field of a horizontal capacitor is investigated under a variable temperature gradient. It is assumed that free charge in the fluid is generated only due to the nonhomogeneous conductivity of the fluid. The Floquet theory is used to determine the convection thresholds. The instability boundaries and the characteristics of critical perturbations are determined. In addition to the synchronous and subharmonic responses to an external action, the instability can be attributed to quasiperiodic perturbations. The low-frequency limit of modulation is considered by an asymptotic method. The critical electric Rayleigh number is represented as a function of inverse frequency and heating level.     

Surface density of the polarization charge of a magnetic fluid jet in a uniform electric field

The behavior of magnetic fluid jets in electric and magnetic fields is investigated. A way of calculating the density of a charge forming on the jet’s surface is suggested, and a charge formation mechanism is put forward.     

The stability of stationary rotation of a regular vortex polygon

This paper is devoted to the Lord Kelvin's (1878) problem on stability of the stationary rotation of the system of n equal vortices located in the vertices of a regular n-gon. During the last decades this problem again became actual in connection with the investigation of point vortices in liquid helium and electron columns in plasma physics. This regime is described by the explicit solution of the Kirchhoff equations. The corresponding eigenvalue problem for the linearization matrix can be also decided explicitly. This was used in the works of Thomson (1883) and Havelock (1931) to obtain exhaustive results on the linear stability. Kurakin (1994) proved that for n/=8 it is unstable. We also present the general theory of stationary motions of a dynamical system with symmetry group. The definitions of stability and instability are necessary to modify in the specific case of stationary regimes. We do not assume that the system is conservative. Thus, the results can be applied not only to various stationary regimes of an ideal fluid flows but, for instance, also to motions of viscous fluids. (c) 2002 American Institute of Physics.     

Direct numerical simulation of electrohydrodynamic plumes generated by a hyperbolic blade electrode

This paper presents a numerical study of two-dimensional EHD flow occurring between a hyperbolic blade and a plate electrode. The whole set of coupled equations is solved: Navier–Stokes equations, Poisson equation and charge conservation equation. A finite volume approach designed for non-orthogonal structured grid is used to discretize all governing equations. An efficient numerical procedure based on total variation diminishing (TVD) scheme is implemented to compute the distribution of charge density. Two different injection laws are considered: a simple autonomous one and a non autonomous which relates the charge injected by the blade and the local electric field. The flow structure which results in an EHD plume analogous to a thermal plume, has also been successfully characterized numerically by the temporal evolution of the charge density distribution. Preliminary results indicate that the flow is characterized by two different regimes according the value of the applied voltage. The critical Reynolds number for which the transition between the steady and unsteady regimes occurs has been determined to be within the range Re = [1000, 1100].     

Steady Flow Regimes in the Problem of Intense Wind-Driven Circulation in a Thin Layer of Viscous Rotating Fluid

The problem of wind-driven circulation in a thin layer of homogeneous viscous rotating fluid is considered. In the limit of small Froude and Burger numbers it is described by two parameters—the Rossby number proportional to the forcing and the Ekman number. For small Ekman numbers and moderate Rossby numbers, the regimes of steady fluid circulation are investigated through numerical simulations of a Kármántype flow. Two different types of steady flows are shown to exist, and their physical interpretation based on a simple analytical model is proposed. A regime diagram on the plane of problem parameters is provided. The simultaneous existence of steady flows of two different types turns out to be possible in some domain of parameters, i.e., there is a dependence of the stationary solution to the problem on initial data. The asymptotic dependence of steady flow characteristics is investigated in the limit of small Ekman numbers.