Electron conductivity of a thermally ionized gas in an electric field

It is well known that the current carriers in a thermally ionized gas vary in composition, but that electrons [1] make the fundamental contribution to the conductivity of the gas, since their mobility is incomparably larger than that of other current-carrying particles. We shall thus be concerned only with electron conductivity. If the gas is under a high pressure in a weak electric field, then in estimating its electrical conductivity by classical means the same concepts are usually employed as those which Drude applied in the theory of metallic conduction. The Drude-Lorentz formula for electrical conductivity was subsequently perfected by Cowling and Chapman who introduced a coefficient to take into account the rate at which the particle interaction forces decrease with distance [2], For electron Coulomb interaction this coefficient takes the value 0.532 instead of 0.500 as compared with the Drude-Lorentz formula.For high pressures and low electric field strengths the electron drift velocity in the field is vanishingly small compared with the mean velocity of random motion, and so it is logical to suppose that the electron free time is independent of the drift velocity, and this supposition leads in the end to the conclusion that Ohm's law is applicable to gases at high pressure in very weak fields.However, we must not overlook the fact that even under the conditions mentioned the conclusion concerning the validity of Ohm's law is only an approximation which becomes less accurate, the lower the gas pressure and the greater the field strength.In what follows the conductivity of the gas is also determined by Drude's method, but with the refinement that in determining the electron free time the drift velocity of these particles in the field is considered.     

Dielectric liquid drop in a harmonic electric field

The problem of the shape of a liquid drop and flows inside and outside the drop in a harmonic electric field is theoretically considered using the small-parameter expansion method. Taking the second-order terms into account makes it possible to consider charge transport over the drop surface.     

Investigation of the electrode potential drop at a molybdenum electrode in a flow of argon seeded with potassium

The results of an experimental investigation of the operation of an electrode in argon containing 0.15% of potassium at temperatures from 1400 to 1800 °C and a pressure of 1 atmosphere when the gas and the electrode are in thermal equilibrium are presented. The current-voltage characteristics obtained are compared with the theory of electrode processes developed previously [1, 2]. Good agreement is obtained between the theoretical and experimental data.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 132–136, July–August, 1970.     

Instability of a conducting drop in a variable electric field

In solving the problem of the stability of the capillary waves in a drop placed in a variable electric field a drop with an infinite set of capillary waves is treated in accordance with the Rayleigh approach as an oscillatory system with an infinite number of generalized coordinates, in particular the amplitudes of the different modes. In the problem formulation stage the general model used in [7, 8] is employed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 50–55, January–February, 1989.     

Electrical parameters of a channel with finite electrodes with allowance for the electrode potential drop

Spatial problems involving the electric field in an MHD channel were formulated in [1] with allowance for the electrode potential drop. It was assumed that the electrode layer had a small thickness, so that relationships on the boundary of the layer could be applied to the surface of the electrode. It was assumed that the electrode potential drop ° could be represented as a function of the current density jn at the electrode in the form of a known function ° =f (j_n) determined experimentally or deduced from the appropriate electrode-layer theory. An approximate method was then put forward for solving such problems by reducing them to the determination of the electric field from a known distribution of the magnetic field and the gas-dynamic parameters. It was shown that when =°/ E is small (E is the characteristic induced or applied potential difference), the solution can be sought in the form of series in powers of . In the zero-order approximation, the electric field is determined without taking into account the electrode processes. The first approximation gives a correction of the order of . The quantity °, which is present in the boundary conditions on the electrode in the first-order approximation, is determined from the current density calculated in the zero-order approximation.One of the problems discussed in [1] was concerned with the electric current in a channel with one pair of symmetric electrodes. Its solution was found in the first approximation in the form of the integral Keldysh-Sedov formula. In this paper we report an analysis of the solution for ° taken in the form of a step function.     

Interaction of a shock wave with a magnetic field in a medium with finite conductivity

We consider the process of the interaction of aplanar shock wave with a magnetic field (impact on a magnetic wall) in a medium having finite conductivity.The problem cannot be solved analytically in the general form. Numerical methods are used to study the problem. A computer is used to calculate the complete system of one-dimensional nonsteady equations of MHD with finite conductivity which depends on temperature in a nonlinear fashion. Results are also presented of particular analytic solutions obtained under simplifying assumptions.We discuss the dependence of the process dynamics on the magnitude of the magnetic field intensity and the law of variation of the medium conductivity with temperature.In the numerical calculations we note the formation of a T-layer, a phenomenon which occurs under definite conditions in unsteady MHD problems [1].In conclusion the authors wish to thank N. G. Basov, A. A. Samarskli, and O. N. Krokhin for posing the problem and for fruitful discussions, and also D. A. Gol'din and A. A. Ivanov for carrying out the numerical calculations.     

Effect of finite conductivity in a medium on shock-wave interaction with a magnetic field

We consider the problem of shock-wave incidence on a magnetic wall, which has been studied in [1]. It is shown that the dynamics of the processes which take place in this case depend significantly on the behavior of the conductivity-temperature dependence (T) of the medium and also on the magnitude of the magnetic-field intensity H₀.An exact solution of the problem is constructed for a special form of the law (T). For an arbitrary law (T) the problem is studied numerically by means of digital computer computations; the results are compared with the exact results.Analysis of these solutions shows that the dissipative properties of the medium (electrical conductivity, viscosity), which determine the structure of the refracted wave front, affect the nature of the entire flow as a whole.The formulated problem also makes it possible to clarify the characteristic features of the decay of a discontinuity in a conducting medium.The authors wish to thank A. A. Samarskii, L. A. Zaklyaz'minskii, L. M. Degtyarev, and A. P. Favorskii for discussions of the study, D. A. Gol'dina and A. A. Ivanov for carrying out the numerical calculations, and also G. A. Lyubimov for several helpful comments.     

Direct contact heat transfer to a drop translating in a transverse electric field

An experimental study has been performed on heat transfer to a single drop translating in an immiscible liquid on which a steady uniform electric field is imposed perpendicular to the drop path. Particular attention has been paid to the effect of field-induced circulations inside and outside the drop. Three different combinations of liquids were tested: one for which the drop-to-medium permittivity ratio ?^* multiplied by the drop-tomedium resistivity ratio χ^* is large compared to unity and two for which ?^* χ^* ? 1. In the former a remarkable enhancement of heat transfer was obtained which could be ascribed to the induced circulations. However, a less remarkable enhancement obtained in the latter two could not be explained by the circulations which are predicted to be vanishingly weak.     

A mathematical model for an alloy solidification problem in the presence of an electric field

A one-dimensional mathematical model for a process of solidification of a binary alloy in the presence of an electric field is studied. A situation in which the thermal properties of each phase are different and the latent heat is non-zero is considered. A quasi-static approximation for the thermal and electric fields is used. Local existence and uniqueness of a classical solution to the resulting free boundary problem are proved for two kinds of boundary conditions. Moreover, under particular hypotheses, the monotonicity of the free boundary and the global existence of the solution is proved.

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Sommario Si studia un modello matematico unidimensionale per un processo di solidificazione di una lega binaria in presenza di un campo elettrico. Si considera una situazione in cui le proprietà termiche di ogni fase sono differenti e il calore latente è non nullo. Si usa una approssimazione quasi-statica per i campi elettrico e termico. Si dimostra l'esistenza locale e l'unicità di una soluzione classica per il problema di frontiera libera risultante con due tipi di condizioni di bordo. Inoltre si dimostra, sotto particolari ipotesi, la monotonia della frontiera libera e l'esistenza di soluzione globale.

     

Effect of surface and volume ionization on the electrode potential drop

We consider the change in the potential of the electric field in the free fall layer at the electrodes as a function of the characteristics of the surface and the volume ionization. Systematic calculations are made of the electrode potential drop for a tungsten cathode and anode in a lithium and cesium plasma. The potential of the electric field is obtained as a function of the plasma pressure, the degree of volume ionization, the electron temperature, the electrode temperature, and the current density.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 137–139, July–August, 1970.     

Eshelby tensor for a crack in an orthotropic elastic medium

In the present Note, we provide new analytical expressions of the components of Hill tensor $\mathbb{P}$ (or equivalently the Eshelby tensor $\mathbb{S}$) associated to an arbitrarily oriented crack in orthotropic elastic medium. The crack is modelled as an infinite cylinder along a symmetry axis of the matrix, with low aspect ratio. The three dimensional results obtained show explicitly the interaction between the primary (structural) anisotropy and the crack-induced anisotropy. They are validated by comparison with existing results in the case where the crack is in a symmetry plane. To cite this article: C. Gruescu et al., C. R. Mecanique 333 (2005).     

On diffraction of acoustic and electric waves in piezoelectric medium by an absorbent half-plane electrode

Diffraction of incident acoustic and incident electric waves in a transversally isotropic piezoelectric medium at the boundary of a half-plane absorbent electrode is systematically investigated using the quasi-hyperbolic approximation. The electrode is assumed to be very thin so that its thickness and stiffness can be neglected. By exact inversion, the explicit expressions for the scattering waves are obtained. A closed form solution is obtained by applying Laplace transformations and the Wiener–Hopf technique. By means of the Cagniard–de Hoop method a detailed investigation of the structure of the electro-acoustic wave is conducted. The mode conversion between electric and acoustic waves, the effect of electro-acoustic head wave, the Bleustein–Gulyaev surface wave and the structure of the wave in terms of the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in detail. It is shown that in piezoelectric materials, absorbent electrodes are neither completely opaque nor completely transparent to electric and acoustic waves. The dynamic field intensity factors at the tip of the electrode are functions of the angle of incidence and time; they are derived explicitly and discussed through a detailed numerical analysis.     

Transfer of energy from an evaporating drop in a vapor medium

The article considers the temperature distribution around an evaporating drop in a vapor medium. The transfer of energy is effected by molecular thermal conductivity, convection, and radiation. The mean length of the free flight path of the radiation considerably exceeds the characteristic distance at which the temperature changes. The times required for relaxation of the temperature to a steady-state value are determined, as well as the characteristic distances at which the temperature distribution changes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 74–78, January–February, 1972.The authors thank V. G. Levich for his evaluation of the results obtained.     

Equilibrium shapes of a drop pendant in an electrostatic field

The stationary shapes of a conducting fluid drop in the gap between the plates of a plane capacitor are studied. The drop is held on the upper plate by the surface tension forces. The self-consistent problem of the determination of the drop shape and the charge distribution over its surface is solved. Estimates are obtained for the maximum volume of the stationary drop at the given fluid parameters and electric field strength.     

Asymptotic of the electromagnetic field above a layerlike anisotropic medium of high conductivity

The model of an anisotropic, layerlike medium is often employed in problems of electromagnetic probing, and many papers have been written on the propagation of an electromagnetic field in such media. A systematic exposition of such problems was set out by Tikhonov, Sku-garevskaya, and Dmitriev [1–6]. In this paper we shall construct an asymptotic for the electromagnetic field of a point source lying above a layerlike medium of finite anisotropy having a fairly high longitudinal and transverse conductivity, or in which the source lies at a considerable height above the medium. The principles here laid down for the construction of the asymptotic indicate quite clearly under what circumstances the asymptotic is feasible, and if necessary allow the next approximations to be taken into account.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 175–188, March–April, 1966.