Equilibrium configurations of the conducting liquid surface in a nonuniform electric field

Possible equilibrium configurations of the free surface of a conducting liquid deformed by a nonuniform external electric field are investigated. The liquid rests on an electrode that has the shape of a dihedral angle formed by two intersecting equipotential half-planes (conducting wedge). It is assumed that the problem has plane symmetry: the surface is invariant under shift along the edge of the dihedral angle. A one-parametric family of exact solutions for the shape of the surface is found in which the opening angle of the region above the wedge serves as a parameter. The solutions are valid when the pressure difference between the inside and outside of the liquid is zero. For an arbitrary pressure difference, approximate solutions to the problem are constructed and it is demonstrated the approximation error is small. It is found that, when the potential difference exceeds a certain threshold value, equilibrium solutions are absent. In this case, the region occupied by the liquid disintegrates, the disintegration scenario depending on the opening angle.     

Formation of root singularities on the free surface of a conducting fluid in an electric field

The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation. This enables us to show that for almost arbitrary initial conditions the surface curvature becomes infinite in a finite time.     

Air ionization in a near-critical electric field

A set of experimental dependences of the air ionization effective rate on the electric field strength is presented. The concept of the critical breakdown field is discussed. It is indicated that experimental data are quantitatively inconsistent with analytical results based on this concept. This inconsistency is eliminated if the ionization balance takes into account not only dissociative adhesion of electrons to oxygen molecules but also their detachment from the molecules that gained a charge during the charge exchange process. Based on the results obtained, a new physical interpretation of the critical field is suggested. A formula for the effective rate of air ionization in near-critical fields is derived.     

Dynamics and applications of a microscale liquid surface interacting with an electric field

We analyze the dynamics of a microscale liquid surface interacting with a time-dependent electrostatic field. The analysis is based on Hamilton’s theory, which can deal with electrodynamics as well as mechanics. The analysis predicts that the mass of a liquid interacting with an electrostatic field is reduced as a result of its motion. The mass reduction occurs through the formation of a high-aspect liquid meniscus, which is eventually transformed to a molecular flow of the liquid. The high-aspect liquid meniscus is used to erect a CNT on the glass surface, and the molecular flow is used to initiate a plasma-induced reaction that produces a hydrogen-storing polymer.     

Two-parametric family of exact solutions for the profile of the surface of a conducting liquid in a nonuniform electric field

Possible equilibrium configurations of the free surface of a conducting liquid in an external nonuniform electric field are investigated. The liquid is at the tip of a wedge-shaped electrode, and the counter-elecrode is a thin straight conducting filament parallel to the edge of the wedge. The conformal mapping method is used to obtain a two-parametric family of exact solutions for the shape of the surface. The solutions describe the deformation of the surface right to separation of a drop from the electrode.     

Equilibrium configurations of uncharged conducting liquid jets in a transverse electric field

Solutions for the problem on the equilibrium configurations of uncharged conducting liquid jets in a transverse electric field are obtained. These solutions correspond to finite-amplitude non-axisymmetric azimuthal deformations of the surface of a round jet: the jet is stretched along the field in its cross-section. The range of electric fields is determined for which solutions of the problem exist. If the electric field strength is over some critical value, the electrostatic equations have no solution, and the jet splits. The obtained solutions are qualitatively examined for stability under small azimuthal perturbations.     

Effect of the electric field on the shape of a bubble in a conducting liquid

Technical Physics - It is found that a bubble in a conducting liquid is stretched in the direction of the electric field. Expressions are derived for the extension coefficient of the bubble as a...     

Interaction of strongly nonlinear waves on the free surface of a dielectric liquid in a horizontal electric field

The nonlinear dynamics of the free surface of an ideal dielectric liquid with a large relative permittivity in a strong horizontal electric field has been considered. It has been demonstrated that the interaction between oppositely propagating solitary waves in arbitrary geometry is elastic: they conserve their energy and momentum. The interaction between waves has been numerically simulated with the use of conformal variables. It has been shown that the interaction deforms the waves; this effect is weak for waves with a relatively small amplitude: deformation for oppositely propagating waves with the identical shape is determined by the fourth power of their amplitude. At multiple collisions of strongly nonlinear waves, a tendency to the formation of singularities, i.e., points with a high energy density of the field, is observed.     

Ionization of an air-methane mixture in a near-critical electric field

The process of effective ionization at the early stages of development of an electric discharge in methane-air mixtures at moderate and high pressures is analyzed. The ionization in an external electric field with consideration given to background electrons, electron attachment to and detachment from atoms and oxygen molecule, recharging, and anion-neutral electron exchange is considered. The dependences of the rates of ion-molecular processes on the temperature and electric field strength are examined.     

Formation of electric discharges above the free surface of a current-carrying liquid

The study is devoted to analysis of the formation of high-current electric discharges developing above the free surface of a liquid metal, deformed as a result of the interaction of the electric current passing through the liquid metal with the intrinsic magnetic field. We report on the electric characteristics of discharges and parameters of their initiation, consider the patterns of deformation of the free surface and the formation of electric discharges, describe the processes occurring in the system, and discuss the mechanism of cyclic formation of discharges above the liquid metal surface.     

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.     

Effective ionization of air in a near-critical electric field at high temperatures

The effective ionization at the early stages of the development of an electric discharge in air at moderate and high temperatures and pressures was analyzed. Ionization in an external electric field were studied with consideration given to background electrons, the attachment and detachment of electrons from atoms and molecules, and recharging and conversion of anions. The rates of ion-molecular reactions, in particular, detachment, depend not only on the external field strength but also on the temperature. The ionization thresholds were demonstrated to decrease with increasing temperature.     

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is established that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time. Zh. éksp. Teor. Fiz. 114, 2043–2054 (December 1998)     

On the instability of conical protrusions of liquid surface in electric field

Electric field is analyzed at the tip of the conical protrusion of a conductive liquid surface that forms as the field strength approaches certain threshold values. When the field exceeds the threshold, the cone tip generally becomes unstable and emits a slender jet. The field strength at the sharp tip of a conducting liquid cone tends to infinity. Even though the field has a singularity, the cone tip becomes unstable only if the semi-cone angle decreases below the Taylor angle, which is the same for all conducting liquids. It is shown that similar conical protrusions can form if the liquid is a dielectric and its permittivity is sufficiently high. In this case, the equilibrium cone angle depends on the permittivity. When the permittivity is lower than approximately 17.60, cones cannot form, and the ensuing phenomena do not occur.     

Dynamics of domain-wall motion in ferroelectric liquid crystals in an electric field

The director reorientation in smectic liquid crystals with ferroelectric properties has been considered in the case where the interaction of liquid-crystal molecules with the surface leads to a partial unwinding of the helical structure of the liquid crystal and the reorientation occurs as a result of the domain-wall motion. The dependences of the velocity of domain-wall motion on the electric field strength, electric field variation frequency, boundary conditions, spontaneous polarization, and viscosity of the liquid crystal have been determined. It has been demonstrated that an increase in the electric field variation frequency or the polar part of the anchoring energy and the spontaneous polarization of the liquid crystal at a constant field frequency results in an increase of the velocity of domain-wall motion. As a consequence, the time of the electro-optic response of the liquid crystal in weak electric fields (from 0.4 to 2.0 V/μm) decreases by a factor of more than three.     

Acoustic field imaging by light reflection at the free surface of a liquid

In this paper we present a novel technique for acoustic field imaging. This technique is based on reflection of a collimated laser beam at the free surface of a liquid. The reflected beam becomes phase modulated by the acoustic wave as in acoustical holographic systems. We do not use a reference acoustical beam for holographic reconstruction but we observe this phase modulation using dark-field techniques. It gives a measurement of the acoustic field power as a function of the position. The authors have built an optical imaging system and carried out experiments with piezocomposite transducers. The technique presented in this work is able to give fast quantitative information about the performance of individual ceramic rods of the piezocomposite.     

Electroconvection of a poorly conducting fluid in a steady electric field

The emergence of electroconvection and nonlinear flows of a nonisothermal poorly conducting fluid in a steady electric field of a horizontal capacitor is investigated. The main mechanism of charge formation in the fluids under investigation is electric conduction due to the temperature dependence of the charge mobility. The Galerkin method is used for obtaining a system of nonlinear differential equations for the amplitudes of spatial modes; on the basis of this system, steady-state, periodic, and random nonlinear regimes of the fluid flow are investigated. The scenarios of transition to chaotic flows (via intermittence and a subharmonic cascade) are discovered. The interrelation between the electroconductive and thermogravitational mechanisms of convection is analyzed, and hysteretic transitions between monotonic and oscillatory regimes are studied. Qualitative comparison with the experiment is carried out.     

Exact solutions to the problem on the shape of an uncharged conducting liquid jet in a transverse electric field

Exact solutions are obtained for the problem of an equilibrium configuration of an uncharged cylindrical jet of a conducting liquid in a transverse electric field. The transverse cross section of the jet moving between two planar electrodes is deformed under the action of electrostatic forces (capillary forces play a stabilizing role). According to the solutions obtained, the initially circular cross section of the jet may be significantly (formally, unboundedly) stretched along the lines of forces of the field, and the boundaries of the jet asymptotically approach the electrodes.     

Nonuniform quasistatic electric field in a weakly conducting anisotropic medium

The intensity distribution of a nonuniform electric field in a quadrupole electrooptic deflector, the properties of the medium in which are described simultaneously by permittivity and conductivity tensors which are not proportional to each other, is calculated as a function of the phase of the ac control voltage. It is shown that the space charge arising in this case is phase-shifted relative to the control voltage. The computational results are compared with experimental data. Zh. Tekh. Fiz. 67, 51–54 (October 1997)     

Formation of conic cusps at the surface of liquid metal in electric field

The formation dynamics is studied for a singular profile of a surface of an ideal conducting fluid in an electric field. Self-similar solutions of electrohydrodynamic equations describing the fundamental process of formation of surface conic cusps with angles close to the Taylor cone angle 98.6° are obtained. The behavior of physical quantities (field strength, fluid velocity, surface curvature) near the singularity is established.