N. M. Zubarev

Formation of the Taylor cone on the surface of liquid metal in the presence of an electric field

The hydrodynamic evolution of the surface of a liquid metal in the presence of an electric field is investigated using both analytical and numerical techniques. It is established that a free liquid surface with axial symmetry evolves with time into a cone-like shape, with the cone angle equal to Taylors static value of 98.6°. The mechanism behind such interesting flow behaviour is that the system of electrohydrodynamic (EHD) equations has a self-similar asymptotic solution that generalizes Taylors static result. The asymptotic solutions are found and the time-dependent behaviours of basic physical quantities (electric field strength, fluid velocity and surface curvature) near the singularity are established. The results and the analytical and numerical techniques used are thought to be useful in the development of time-dependent models of operating liquid metal ion sources and EHD sprayers.

Model of liquid-metal splashing in the cathode spot of a vacuum arc discharge

The formation of microjets is studied during the extrusion of a melted metal by the plasma pressure from craters formed on a cathode in a burning vacuum arc. An analytic model of liquid-metal splashing that includes two stages is proposed. At the first stage, the liquid motion has the axial symmetry and a liquid-metal wall surrounding the crater is formed. At the second stage, the axial symmetry is broken due to the development of the Plateau–Rayleigh instability in the upper part of the wall. The wall breakup process is shown to have a threshold. The minimal plasma pressure and the minimal electric current flowing through the crater required for obtaining the liquid-metal splashing regime are found. The basic spatial and temporal characteristics of the jet formation process are found using the analytic model.

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

Abstract 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.

Nonlinear waves on the surface of a dielectric liquid in a strong tangential electric field

Abstract The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope angles. It is established that the equation can be solved for liquids with sufficiently high values of the permittivity. This makes it possible to describe the interaction of the counter-propagating waves.

Criteria for hard excitation of electrohydrodynamic instability of the free surface of a conducting fluid

The nonlinear dynamics of the free surface of a liquid metal in a strong vertical electric field is considered. It is shown for the case of a horizontally bounded geometry that a fairly large-amplitude perturbation can remove the system from equilibrium, even if the initial surface is stable in the linear approximation. An analysis of possible equilibrium configurations of the charged equipotential surface enables us to estimate the threshold values of the surface perturbation amplitude and of the perturbed electric field strength required for the electrohydrodynamic instability to occur.

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.

Exact solution of the problem of the equilibrium configuration of the charged surface of a liquid metal

A broad class of exact solutions is obtained for the problem of the equilibrium configuration of the charged surface of a conducting liquid allowing for capillary forces. An analysis of the solutions showed that when the amplitudes of the perturbations reached certain critical values, the region occupied by the liquid ceases to be singly connected, which corresponds to the formation of liquid metal droplets. It is shown that a steady-state liquid metal profile may exist for which appreciable local amplification of the electric field can be achieved.

Charged-surface instability development in liquid helium: An exact solution

The nonlinear dynamics of charged-surface instability development is investigated for liquid helium far above the critical point. It is found that, if the surface charge completely screens the field above the surface, the equations of three-dimensional (3D) potential motion of a fluid are reduced to the well-known equations describing the 3D Laplace growth process. The integrability of these equations in 2D geometry allows the analytic description of the free-surface evolution up to the formation of cuspidal singularities at the surface.

Nonlinear Waves on the Surface of a Dielectric Liquid in a Horizontal Electric Field in 3D Geometry: Exact Solutions

It has been shown that waves of arbitrary configuration in 3D geometry may propagate without distortion along the surface of a dielectric liquid in the direction of a horizontal electric field. This situation occurs for the high-permittivity liquids in the case of a sufficiently high external field when the effect of electrostatic forces dominates. A general solution of the equations of motion that describes the interaction of counterpropagating waves of a small but finite amplitude has been obtained.

Exact solution for the steady-state surface profile of a liquid metal in an external electric field

An analysis is made of the equilibrium profile of the free surface of a liquid metal in an external electric field neglecting gravitational forces. It is shown that a conformal mapping method can be used to find a wide range of exact solutions corresponding to the case of planar symmetry.