Numerical simulation of the dynamics of a liquid conducting surface in a strong electric field

Two-dimensional numerical simulation is performed on the instability of a liquid conducting surface with axial symmetry in a strong electric field. The method of splitting with respect to physical factors with transformation of the calculation region to the canonical form [1] is used to investigate the flow of liquid with a free surface. This approach enables one to study the time dependence of the basic physical quantities in the nonlinear mode when the emitting point is formed. It is demonstrated that this dependence exhibits a collapse behavior: a critical time t _c exists, in the vicinity of which a physical quantity either diverges or goes to zero as ∼(t _c -t)^γ. The values of the critical exponent γ are found for the electric field, curvature radius, and the axial velocity at the point tip, and the correlation between them demonstrated.     

Nonlinear dynamics of the free surface of a conducting liquid in an electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in an external electric field is investigated. It is found that in the absence of gravity and surface tension the equations of the two-dimensional motion of the medium can be solved in the approximation of small angles of inclination of the surface. It is shown that singularities of the square-root type, for which the curvature is infinite but the surface itself remains smooth, can form on the surface of a conducting liquid over a finite time. Pis’ma Zh. Tekh. Fiz. 24, 25–29 (June 26, 1998)     

Equilibrium surface configurations of a conducting liquid in external spatially periodic electric field

The problem of possible equilibrium configurations of the free surface of a conducting liquid in an external spatially periodic electric field is considered. It is shown that, under identical conditions, the problem admits solutions with different wavelengths, including the wavelength corresponding to the field period and the half shorter wavelength corresponding to the period of the electrostatic pressure oscillations. In the former case, an exact partial solution is found that describes a surface profile with allowance for the capillary forces.     

Large-scale magnetohydrodynamic instability of a conducting liquid surface

The stability of a current-carrying rectangular liquid metal conductor with respect to small longitudinal surface perturbations was theoretically studied. It is shown that the instability increment tends to zero in both short-and longwave limits and, hence, passes through a maximum at a finite wavenumber. The characteristic times of instability development are estimated.     

Explosive growth of perturbations of the surface of a conducting liquid in an electric field

An analysis is made of the behavior of the free surface of a conducting liquid in an external electric field near the Tonks-Frenkel instability threshold assuming that the incipient wave is one-dimensional. It is shown that the surface dynamics is described by the nonlinear Klein-Gordon equation. This equation is used to formulate criteria for the explosive growth of perturbation amplitudes. Pis’ma Zh. Tekh. Fiz. 25, 65–69 (November 12, 1999)     

Agitation of a liquid in a strong external electric field

This article considers the condition for instability of the surface waves in a liquid system in a strong external electric field. As a result of the viscosity, such surface waves lead to vigorous volume agitation, accelerating chemical and physicochemical processes occurring in the system.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 6, pp. 981–988, December, 1969.     

Oscillatory instability of the interface between conducting liquids in a normal electric field

It is shown that a new type of oscillatory instability, unlike the Tonks-Frenkel instability, may occur at a charged interface between two electrically conducting liquids in a perpendicular electrostatic field. Pis’ma Zh. Tekh. Fiz. 23, 41–44 (August 26, 1997)     

Exact solutions for equilibrium surface configurations of a conducting liquid in the electric field of a charged straight filament

The problem of possible equilibrium configurations of the free surface of a conducting liquid in the electric field of a charged horizontal straight filament is considered. Using the method of conformal mapping, a one-parameter family of exact solutions of the problem is obtained, which take into account the effect of capillary forces. Conditions are found for which the region occupied by the liquid ceases to be simply connected and a charged drop is formed on the liquid surface     

Nonlinear electrohydrodynamic instability of two liquid layers

The nonlinear instability of two superposed dielectric fluids is studied under the influence of an oscillating external electric field. In addition, a small constant and normal electric field is superimposed on the system. With the use of the method of multiple scaling, a generalized derivation of the amplitude evolution is obtained in marginally unstable regions of parameter space. A Melnikov function is formulated for such an instability and it is shown that there exist transverse homoclinic orbits leading to chaotic motions.     

Electric action of a flame and a conducting liquid jet in an electric field

Expressions are obtained for the charge and potential of a spheroid-shaped burner with the flame on its top situated in an external field parallel to its rotation axis. Simple expressions for potentials of the burner are obtained in terms of the external field for the sphere, strongly oblate, and strongly stretched ellipsoids. In an analogous manner, electrification, of a spherical tank with the outflowing conducting liquid is considered, and the charges and potentials of the field strength gauge are determined.Notation E field strength - a, b, , and semiaxes of the ellipsoid - surface charge density - Q ₁ andQ ₂ charges of the tanks - g charge of the droplet - n _x shape coefficient - I current strength - C capacity - R resistance - r radius - relaxation time - u flow rate Moscow State Institute of Electronics and Mathematics (Technical University), Moscow, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal Vol. 68, No. 4, July–August 1995, pp. 589–593.     

Acceleration of the wall of a conducting cylinder undergoing thermal expansion in a strong magnetic field

Calculations are made of the abrupt acceleration of the wall of a cylinder undergoing heating in a strong magnetic field. It is shown that the expansion of a thin-walled liquid-metal cylinder resembles an “explosive instability”; in the model used, the velocity of the boundary and the azimuthal current increase without bound in a finite time. It is noted that this effect may also be observed for an elastic shell, and the influence of the electromagnetic retarding forces does not eliminate the singularity in the solution, but merely shifts the time when it appears. Pis’ma Zh. Tekh. Fiz. 23, 10–16 (June 12, 1997)     

Measurement of the electric field intensity by a spherical measuring transducer near a conducting surface

Translated from Izmeritel'naya Tekhnika, No. 2, pp. 45–46, February, 1988.     

Axisymmetric instabilities of conducting liquid cylinder in view of the effect of electric field

The axisymmetric electrocapillary instability of a conducting liquid cylinder is considered. Exact solutions of linearized Navier-Stokes equations are investigated in view of viscosity of liquid. The rates of rise of instabilities and the wavelength of the most unstable mode are found. Special attention is given to the effect of electric field.     

Stability of nonlinear waves on the ideal liquid surface in a tangential electric field

The propagation of waves with arbitrary amplitudes on the free surface of the ideal dielectric liquid in a strong tangential electric field is considered. A dispersion relation for the evolution of small perturbations of a stationary wave profile of the surface of a liquid with a large permittivity is obtained using conformal variables. It is established that, irrespective of the wave geometry, the amplitudes of small-scale perturbations do not increase with the time, which is evidence for the stability of wave solutions.     

On the possibility of oscillatory electrodynamic instability in nematic liquid crystal in a constant inhomogeneous electric field

It is shown that electrodynamic instability in a nematic liquid crystal in constant inhomogeneous electric field can exhibit an oscillatory character. A frequency has been found that is close to that of oscillations observed in experiments.

     

The effect of an oblique magnetic field on the surface instability of a finite conducting fluid layer

Summary The effect of an oblique magnetic field on the growth rate of Rayleigh-Taylor instability (RT) at the interface of a finite thickness layer of a viscous electrically conducting fluid in the presence of surface tension has been studied analytically. The effects of aligned and transverse magnetic fields on the coupled differential equations for the velocity and the magnetic field are discussed separately. The numerical results reveal that the nature and strength of the magnetic field and the layer thickness exacerbate or ameliorate the instability characteristic of such a layer.