Plasma density and electeic field strength distributions at a boundary with an electrode

Close to the cathode in an arc discharge, or to the surface of a probe operating on the ionic branch of its characteristic, conditions are obtained under which the Langmuir layer freely passes ions coming from the plasma, while the reverse ion flow is virtually zero. The plasma density, ion distribution, and electric fieid-strength close to the electrode are found in the present paper. The extrapolated length is evaluated for the plasma density. The absolute value of the electric field strength increases logarithmically at the boundary with the electrode.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No, 2, pp. 4–6, March–April, 1970.     

Equation for thermionic emission in a plasma

The equation for thermionic emission from hot cathodes in the presence of a low-temperature plasma is discussed. The distribution function is obtained for the magnitude of the electric field intensity at the surface of the cathode, taking account of the effect of the individual fields of the various ions moving in the near-cathode layer. The thermionic flux density due to fluctuations of the field is found to be significantly higher than that calculated by Richardson's formula with Schottky's correction.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 40–45, May–June, 1972.     

Particle collisions in a turbulent flow

An equation for the two-point probability density function of the two-particle the coordinate and velocity distribution is obtained. A closed system of equations for the first and second two-point moments of the velocity fluctuations of a pair of particles with allowance for the turbulent flow inhomogeneity is given. Boundary conditions for the equations of the particle concentration and the intensity of the relative random velocity during particle collision are obtained. A unified formula describing the interparticle collision process as a result of turbulent motion and the average relative particle velocity slip is obtained for the kernel of the coagulation equation. The effect of the average velocity slip of the particles and the carrier phase on the parameters of motion of the dispersed admixture and its coagulation is investigated on the basis of a two-point two-time velocity fluctuation autocorrelation function with two time and space scales representing the energy-bearing and small-scale motion of the fluid phase.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 104–116, March–April, 1996.     

Convective instability of a horizontal layer of fluid between permeable membranes

The equilibrium stability is investigated of a system consisting of two semi-infinite isothermal masses of fluid divided by a horizontal layer of finite thickness of the same fluid with a vertical temperature gradient directed downwards. The transition layer is separated by thin permeable membranes. Neutral stability curves are constructed for different membrane resistances. In the case of high permeability, the equilibrium is absolutely unstable with respect to monotonic-type longwave perturbations. For low permeability membranes, instability with respect to monotonic finite-wavelength perturbations is characteristic.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 171–173, July–August, 1985.     

Determination of particle charge and size from the propagation of ultrasound in suspensions

The propagation of small perturbations in raulticomponent disperse media consisting of an uncharged dispersion fluid, positive and negative ions and charged particles or droplets of another fluid is investigated. When weak waves pass through emulsions and suspensions, because of the difference in the velocities of the ions and charged particles a non-uniform distribution of electric potential develops in the medium [1–3]. Expressions relating the amplitude of the electric potential and the amplitude of the fluid velocity in the wave, the particle charge and the parameters characterizing the medium are derived. Relations are obtained for the phase shift between the values of the electric potential and the fluid velocity. It is proposed to use the expressions obtained, which describe the propagation of ultrasound, for the experimental determination of the particle charge and other parameters of the disperse medium, in particular, the particle size.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–128, January–February, 1988.     

Stationary simple waves in a plasma with anisotropic pressure

Stationary simple waves in a plasma with anisotropic pressure are investigated on the basis of the hydrodynamic equations of Chew, Goldberger, and Low. In Sec. 1, for the case where the vectors of the average flow velocity and the magnetic field intensity are parallel, the system of equations is reduced to two quasilinear equations for the velocity components. In Sec. 2 the equations for the characteristics are obtained, the system being assumed to be hyperbolic. For the special case of irrotational flow the character of simple waves in flows adjacent to various contours is studied. Section 3 contains a qualitative investigation of changes in the flow parameters in simple waves. In Sec. 4 the possibility of a transition to an unstable state of the plasma is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 12–19, March–April, 1971.The author thanks V. B. Baranov for the formulation of the problem and for his advice and constant attention to the work and also A. G. Kulikovskii for discussion of the results.     

Ion distribution function at the boundary with an electrode

The ion distribution function is found in the case in which the Langmuir layer freely passes the ions incident from the plasma while the reverse ion flux is zero. These conditions are realized near the cathode in an arc discharge and at the surface of a probe operating on the ion branch of the characteristic. The electric field outside the Langmuir layer is assumed small. We obtain the connection between ion current and plasma density at the boundary with the electrode, the expressions for the ion mean kinetic energy and for the mean energy removed from the plasma by the ion, which differ markedly from the corresponding expressions in the Maxwellian distribution case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 47–54, May–June, 1969.     

Boundary layer stability on a wave-periodic surface

Stability under small perturbations is investigated for flows whose velocity depends periodically on the spatial coordinate in the direction of flow. Stability calculations are carried out for the case in which the velocity distribution is a solution of the boundary-layer equations.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 11–16, November–December, 1972.     

Effect of ion heat fluxes on the stability of an anisotropic collisionless plasma

Small perturbations of an unbounded volume of anisotropic collisionless plasma in a strong magnetic field are studied on the basis of MHD equations. It is assumed that there are present in the plasma ion heat fluxes connected with the third-order moments of the ion distribution function. The dispersion equation obtained, determining the velocity of five types of waves, is analyzed. In the space of the undisturbed plasma parameters the regions of values in which small perturbations are damped exponentially with time are found.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 153–157, March–April, 1993.     

A collisionless thermal wave in a plasma

Experiments are described on the collisionless propagation of heat in a plasma along the magnetic field. Thermal waves can be propagated in a medium whose thermal conductivity is a power function of the temperature. In a collisionless plasma, where the mean free path of particles is much greater than all typical lengths, in particular the length of the equipment, the heat must be propagated by a different method. Experiments to study this phenomenon showed that heat is propagated along the magnetic field with velocity exceeding that of ion-acoustic velocity (I. A. Velocity), and that the spatial width of the thermal disturbance is much less than the mean free path. Heat is propagated because hot electrons are replaced by cold [1]. Noise was observed experimentally in the vicinity of the ion plasma frequency and an estimate of its intensity was obtained. Theoretical discussion showed that the I. A. Velocity instability which develops at the wave front leads to collective friction of the cold electrons with the ions and makes it possible to find the effective collision frequency. It was also shown theoretically that, in accordance with experiment, noise is localized near _pi, and the level agrees with that obtained experimentally. The phenomenon can be pictured as follows: hot electrons expanding into the region occupied by cold electrons and ions create an electric field. Cold electrons, accelerating in this field, oscillate the I. A. Velocity. This instability leads to heating of the electrons and the appearance of collective friction which forms the heat front.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 51–59, January–February, 1971.     

Oscillating flows in capillaries filled with immiscible liquids

Hydrodynamic flows generated by mechanical vibrations of a capillary filled with immiscible liquids are investigated. Air bubbles are contained at the hermetically sealed ends of the capillary. Equations for the change in the volumes of the air bubbles as functions of time and velocity distribution in the liquids are obtained for the case when the radius of the capillary is much less than the lengths of the liquid columns. Results of numerical calculations are given for a capillary filled with two liquids: water and mercury. Amplitude-frequency dependences of the change in volumes of the air bubbles are constructed which have a resonance nature. Graphs of the dependence of the velocity of the water and the mercury on the radial coordinate at different times are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 13–18, September–October, 1987.     

Stationary flow of a conducting liquid in a rectangular channel with two nonconducting walls and two walls having an arbitrary conductivity parallel to an external magnetic field

The flow of a conducting liquid in a channel of rectangular cross section with two walls (parallel to the external magnetic field) having an arbitrary conductivity, the other two being insulators, is considered. The solution of the problem is presented in the form of infinite series. The relationships obtained are used for numerical calculations of the velocity distribution and the distribution of the induced magnetic field over the cross section for several modes of flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkostt i Gaza, No. 5, pp. 46–52, September–October, 1970.     

Investigation of a submerged air jet during high-intensity swirling

The characteristics have been determined experimentally for the jet flow originating in the vicinity of the shear section of a centrifugal atomizer (up to the sections corresponding to the termination of the reverse flow zone). The distribution has been obtained for the mean velocity, the additive concentration, and the intensities of the turbulent velocity pulsations for different initial swirling.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 6, pp. 148–154, November–December, 1971.The author wishes to thank G. B. Krayushkin for interpretation of the measurements and O. V. Yakovlevskii for taking part in discussion of results.     

Parameters of a closed arc stabilized by a longitudinal flow of argon

This article sets forth the results of an investigation of the temperature, velocity, dynamic head, and static pressure in high-current argon arcs used in plasma metallurgy. It is shown that the velocity and the amount of gas pumped through the column of the arc are determined by the current of the arc. A calculation is made and equations are presented which permit calculating this type of arc on the basis of a simplified equilibrium model. Experiment is compared with theory.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 66–74, January–February, 1973.     

Transport coefficients for a partially ionized two-temperature plasma with ions and neutral particles having different masses

The viscosity, heat-conduction, and diffusion coefficients are calculated for a two-temperature three-component plasma composed of ions, neutral particles and electrons when the masses of the ions m_i and neutral particles m_a are different. Similar transport coefficients for m_i=m_a were calculated in [1–3]. The numerical values obtained for the transport coefficients are compared with the values calculated from the formulas of [1–3]. Numerical calculations are carried out for helium with a cesium additive (m_i>m_a) and for krypton with a lithium additive (m_ia).Finally, the author is grateful to V. V. Gogosov, under whose direction this work was carried out.     

Two methods for calculating the load on the surface of a slender body executing axisymmetric vibrations in a sonic gas flow

Low-frequency axisymmetric vibrations of the surface of a slender body in a sonic flow are considered. The distribution of the stationary longitudinal velocity on the body is assumed to be linear. The linear equation with variable coefficients for the nonstationary part of the velocity potential is solved by two methods: by separation of the variables, as was done in [1] for a two-dimensional flow, and by the method of superposition of sources. Particular solutions with the required singularity are obtained.Translated from Izvestiya Akaderaii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 151–154, March–April, 1980.     

Concentration jump on the plane surface in a binary gas mixture

From the solution of linearized Boltzmann equations with the collision operators in the Gross and Krook form the authors have obtained an expression for the concentration jump of a vapor evaporating from a plane liquid surface into a stationary gas, for which the liquid surface is impermeable. Langmuir [1] was the first to point out that at the surface of an evaporating liquid the vapor pressure differs from saturated vapor pressure, i.e., a jump occurs in vapor concentration. An expression was obtained by Brock [2] for the concentration jump at the plane surface in the binary gas mixture with identical molecular masses of components by gas kinetic analysis. No solution has yet been obtained to the problem at different molecular masses of components.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 119–122, March–April, 1972.     

Diffusion and thermal slip of a binary gas mixture

Let us note that the phenomenon of diffusion slip at a constant gas-mixture temperature has been considered in [1], for example, and thermal slip for a single-component gas in [2]. The slip velocity of a binary gas mixture has been calculated in a field of the temperature gradient and of the partial pressure gradients. The kinetic equation is solved by an approximate method based on physical considerations. A formula has been obtained analytically for the slip velocity for arbitrary accommodation coefficients as well as for arbitrary gas concentrations and arbitrary molecule masses. The results agree to 1% accuracy with the numerical computations of other authors.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 51–55, July–August, 1970.     

Structure of turbulent viscosity in flow close to a rough surface

A formula for turbulent viscosity which allows a simple analytic expression to be obtained for the distribution of the averaged velocity of turbulent liquid flow at a rough surface is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 167–170, March–April, 1976.     

Interaction of high-speed microparticles with a system of polymer obstructions

The velocity and size distribution of high-speed glass microparticles in a flow under idenical conditions of acceleration is estimated with the use of the known statistical approach. The results are applied for the study of the interaction of microparticles with a system of polymer obstructions made of polyethylene and polyethelene terephthalate. The critical impact velocities corresponding to complete transition of the particle to the viscous-fluid state are determined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 115–118, March–April, 1971.