O. V. Zubareva

Exact solutions for equilibrium configurations of charged conducting liquid jets.

A wide class of exact solutions is obtained for the problem of finding the equilibrium configurations of charged jets of a conducting liquid; these configurations correspond to the finite-amplitude azimuthal deformations of the surface of a round jet. A critical value of the linear electric charge density is determined, for which the jet surface becomes self-intersecting, and the jet splits into two. It exceeds the density value required for the excitation of the linear azimuthal instability of the round jet. Hence, there exists a range of linear charge-density values, where our solutions may be stable with respect to small azimuthal perturbations.

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

An exact particular solution for an equilibrium uncharged conducting jet configuration in a transverse electric field

The problem concerning the equilibrium configurations of the surface of an uncharged conducting jet in a transverse electric field has been considered. It is established that this electrostatic problem is analogous to the problem of the potential streamlining of a two-dimensional gas bubble by the ideal liquid, for which effective analytical solution methods are available. Using this analogy, an exact solution for the jet shape has been constructed and studied with respect to stability in the particular case in which the difference of pressures inside and outside the jet is zero. This solution is characterized by a significant degree of deformation, whereby the aspect ratio of the jet cross section amounts to 23/4.

Exact solutions for shapes of two-dimensional bubbles in a corner flow

A one-parameter family of exact solutions for the deformations of two-dimensional bubbles in a corner flow of an ideal liquid is obtained. The solutions correspond to the special case where the pressure inside the bubble equals the stagnation pressure. The parameter of the model is the corner angle. The solution family includes classical McLeod’s solution which corresponds to the corner of angle π. For the particular case of a right-angled corner, the solution describes the straining flow past a bubble. In view of the known analogy between the distributions of a planar electric field and the velocity field for a two-dimensional potential flow, our solutions give equilibrium configurations of the surface of a conducting liquid in an external electric field.

Nonlinear dispersion relation for electrocapillary waves on the surface of a dielectric liquid

It is shown that the problem of determining the profile of an electrocapillary wave on the surface of the ideal dielectric liquid in a tangential electric field admits exact solution in the limiting case of a large permittivity of the liquid. An exact expression for the nonlinear dispersion relation between the frequency, wavenumber, and amplitude of the wave is obtained and analyzed.

The dynamics of large-scale spatial structures in current-carrying fluids and the electric explosion of conductors

Abstract Experiments investigating an electric explosion of conductors and shock waves generated by that in air are discussed. A model of a non-equilibrium phase transition, resulting in electric current interruption (the formation of a heterogeneous low-conducting state), is suggested. This phase transition is shown to be brought about by hydrodynamic and current vortex structures arisen because of a convective instability of current-carrying fluids. The steady-state solutions of the model proposed are found and their stability is explored. The dynamics of the large-scale spatial (hydrodynamic and current) structures in a nonlinear element from the electric circuit is considered. Here, the model suggested and the Lorenz model are viewed as models of the nonlinear element. The proposed model parameters are identified by the experimental results of an electric explosion of conductors.

Space charge influence on the angle of conical spikes developing on a liquid-metal anode.

The influence of the space charge of ions emitted from the surface of a conical spike on its shape has been studied. The problem of the calculation of the spatial distributions of the electric field, ion velocity field, and the space charge density near the cone tip has been reduced to the analysis of a system of ordinary differential equations. As a result of numerical solution of these equations, the criterion for the balance of the capillary and electrostatic forces on the conic surface of a liquid-metal anode has been determined. It has allowed us to relate the electrical current flowing through the system, the applied potential difference, and the cone angle. We have compared the results of our calculations with available experimental data concerning emission from the surface of pure liquid gallium, indium, tin, and some liquid alloys, such as Au+Si , Co+Ge , and Au+Ge . On the basis of the proposed model, explanations have been given for a number of specific features of the emissive behavior of different systems.

Nondispersive propagation of waves with finite amplitudes on the surface of a dielectric liquid in a tangential electric field

The evolution of waves with finite amplitudes on the free surface of the ideal dielectric liquid in a strong tangential electric field is considered. It is shown that, in the case of a large permittivity of the liquid, nonlinear waves of arbitrary configuration can propagate in this system without distortions.

An analysis of the equilibrium configurations of charged cylindrical jets of a conducting liquid

A region of physical parameters is found where the equilibrium configurations of charged cylindrical jets of a conducting liquid can exist; these configurations correspond to the azimuthal mode n=2 of the surface deformations of a round jet. A critical value of the jet linear charge is determined for which the jet splits into two. It is shown that such instability is excited in a soft regime.

Repeated interruption and restoration of current in liquid metals as a nonlinear phenomenon

Abstract The evolution of large-scale convective instabilities in a plasma-like medium in the field of its own electric current is considered in the framework of the magneto-hydrodynamics of incompressible viscous resistive liquids. The simplest low-mode model of the nonlinear interaction of perturbations is proposed and analytically investigated. According to this model, if the amplitude of the current exceeds its critical value, the effective resistance of the medium can break into oscillations. The model has enabled us to estimate with reasonable exactness the threshold commutation current and the frequency of current oscillation for experiments on repeated interruption and restoration of electric current through the InGa eutectic.