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— The study of a nonlinear resonance between the capillary waves on the surface of a moving charged jet relative to the material medium at a multimode initial deformation is considered. In analytical asymptotic calculations of the second order of smallness according to dimensionless amplitude of oscillations, it is shown that realization of internal nonlinear resonant interaction of capillary waves of arbitrary symmetry takes place on the jet surface both of degenerate and secondary combinational. The resonances positions depend on the system’s physical parameters: the values of surface tension coefficients and the radial electric field intensity near the jet surface, the velocity of its motion with respect to the material medium, the values of the waves and azimuthal numbers of the interacting waves, spectrum of the waves that define the initial deformation.

AbstractA purely theoretical approach has been proposed for constructing the classification of the observed modes of liquid electrodispersion from the edge of a capillary, through which the liquid is supplied into a discharge system, in contrast to the phenomenological classifications suggested previously. The classification is proposed to be realized in accordance with the physicochemical properties of liquids, as well as the degree of symmetry of azimuthal surface waves of a jet ejected from a meniscus and the regularities of droplet detachment directly from the meniscus. It has been shown that, when a low-viscosity and rather high-conductivity liquid is dispersed, the meniscus emits strongly charged droplets, which are unstable with respect to their own charges and disintegrate into smaller droplets. Low-conductivity liquids emit either weakly charged droplets stable with respect to their own charges or charged liquid jets, which disintegrate into stable droplets.

AbstractAnalytical derivations of the second order of smallness with respect to dimensionless amplitude \\( \\) of oscillations of an uncharged electroconducting droplet in an external electric field have yielded an analytical expression for the intensity of its dipole electromagnetic radiation related to the oscillations, with this expression enabling one to study the radiation intensity as depending on the physical parameters of the problem. This problem is of interest in connection with radio-locating probing meteorological objects, such as clouds, fogs, and tornados. The time evolution of the electromagnetic radiation intensity and its components, i.e., the magnitude of the induced charge and dipole moment, of the droplet has been studied. The dipole radiation intensity has been determined in the second order of smallness with respect to the squared ratio between the characteristic linear size of the droplet and the wavelength of the emitted radiation. The intensity has appeared to be higher by a value of \\( 1pt \\) than the intensity obtained by the calculations linear with respect to \\( \\). However, a correction (quadratic with respect to \\( \\)) to the radiation of the droplet is realized in another frequency range, thereby affecting the spectrum of the electromagnetic radiation.

AbstractTheoretical analysis has been employed to study the effects of electrical conductivity and viscosity of a liquid on its electrodispersion from the edge of a capillary, through which the liquid is supplied to a discharge system. It has been shown that, when a high-conductivity and low-viscosity liquid is dispersed, it emits strongly charged small droplets, which are primordially unstable with respect to their own charges and disintegrate into several hundred still smaller droplets, which are also strongly charged and unstable. A corona discharge is ignited around each droplet and a glow arises, which is referred to as the “fan” glow. When a low-conductivity or a high-viscosity liquid is dispersed, it emits small charged droplets, which are stable with respect to their own charge (in the first case) or strongly charged droplets, which disintegrate into two or three droplets stable with respect to their own charge (in the second case).

Abstract—The higher-order azimuthal modes of a charged jet of ideal incompressible conducting liquid that moves relative to the surrounding dielectric medium are first investigated. It is shown that there are thresholds of the surface electric charge density above which electrostatic instability of the parent jet surface is implemented. The instability manifests itself in ejection of daughter jets, which are thinner by approximately two orders of magnitude and thereafter disintegrate into droplets. As the mode number increases and the jet velocity relative to the medium decreases, the threshold heights increase. A similar phenomenon is recorded in reference to the velocity of the relative motion of jet and medium. In this case the instability is called aerodynamic but it is implemented at fairly high speeds.

AbstractAnalytical asymptotic methods are used to study the critical conditions for realization of electrostatic instability of various azimuthal modes of electrically conducting liquids with respect to external electrostatic fields, in which a liquid jet surface acquires induced charges. A uniform electrostatic fields, which is directed perpendicularly to the symmetry axis of an unperturbed liquid jet and impart an elliptical shape to the jet cross section, and a radial axially symmetric field have been selected as such external fields. An analytical expression has been derived for an arbitrary azimuthal mode of capillary waves on the surface of an elliptical jet. It has turned out that the critical conditions for the realization of the electrostatic instability of azimuthal modes are independent of the initial amplitudes of the waves (despite the existence of an intermode interaction), but rather are determined by the jet radius, the surface tension coefficient of the liquid, the strength of the external electrostatic field, and the presence of a stationary deformation of the equilibrium jet shape relative to a jet with a circular cross section. For an elliptical jet, the time dependences of the amplitudes of unstable azimuthal waves have been plotted under different initial conditions.

AbstractThe intensity of acoustic radiation of droplets and the width of the frequency range for which this radiation is accounted are evaluated in asymptotic calculations of the first order of smallness with respect to the dimensionless oscillation amplitude and equilibrium deformation of natural weakly charged droplets. The calculations are carried out using the ideal incompressible conducting fluid model. It is shown that acoustic radiation of fluid-droplet aerosol of natural origin, namely, clouds and fogs, is accounted for the ultrasonic frequency range, while acoustic radiation of rain occurs over the sonic range and such radiation can be hearable. The boundary between the ultrasonic and sonic acoustic radiations with respect to the droplet radius depends on the physical characteristics of the medium and the droplet and can be displaced both to one or another side.

AbstractAsymptotic calculations of the second order of smallness for a small dimensionless amplitude of the oscillation of droplets of natural origin in a material environment in an intracloud or ground-level electric field are used to show that, among other modes, the zero and the first mode of droplet oscillations are excited, which do not occur in calculations made in the first order of smallness. The intensity of acoustic radiation in such modes is calculated using the model of an ideal noncompressible electrically conductive fluid. The monopole acoustic radiation of a droplet is shown to be six orders of magnitude more intense than the dipole radiation. In an approximation quadratic in terms of the dimensionless oscillation amplitude, the monopole radiation intensity does not depend on the droplet radius and the strength of the external electric field, while the dipole-radiation intensity greatly depends on the droplet radius. The dependence of the strength of the electric field only appears in the third order of smallness. Oscillating rain droplets emit acoustic radiation in the audible frequency range, while cloud and fog droplets, in the ultrasonic range. The time dependence of acoustic radiation of a droplet of both monopole and dipole type under the initial excitation of a finite segment of the continuous spectrum of modes has the form of beats.

— The peculiarities of a liquid viscosity effect on the liquid electrodispersion from the end of capillary through which the liquid is supplied to the discharged system or during the disintegration of a strongly charged drop were studied in an analytical way. It was shown that, upon the electrodispersion of the electroconducting liquid with a low-viscosity, the latter emitted highly charged droplets, initially unstable with respect to their own charge, breaking up into hundreds of even smaller and strongly charged ones, with a corona discharge being ignited around them. As a result, a fan-shaped glow appeared at the top of the liquid meniscus at the end of the capillary or at the top of the decaying charged drop. For the viscous electroconducting liquid, the series of successive disintegrations of the charged daughter droplets were immediately interrupted owing to viscosity damping effect of self-charge-resistant droplets, and no corona discharge glow was formed.

— Peculiarities of the electrostatic instability realization of a fluid’s charged surface on the charged and uncharged drops’ vertices in an external electrostatic field in a cylindrical jet and a flat surface are studied. It was shown that the critical values of the electric charge surface density under the above conditions on the threshold instability realization are different in magnitude regardless of the phenomenological similarity. The reason presumably consists in the spatial change distinction (of the situations under consideration) of the electric field intensity in proximity of the growing emission projection during instability realization of the fluid’s charged surface. Equilibrium and nonequilibrium drops, jets, plane shapes, and their symmetry were discussed.