Influence of contact-perimeter slip and heat transfer processes on oscillating hydrodynamic flows of immiscible liquids in capillary tubes

The hydrodynamic flows which arise in the presence of mechanical vibrations of a capillary tube filled with immiscible liquids are investigated. At the hermetically sealed ends of the tube there are air bubbles. It is assumed that the interfacial contact perimeters of the immiscible liquids can slip relative to the walls of the tube. The results of numerical calculations are given for a mercury electrocapillary transducer [1–4], which is a capillary tube filled with water and mercury. The calculated and experimental amplitude—frequency characteristics (the dependences of the amplitude of the electric potential difference on the vibration frequency) are compared.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 36–45, May–June, 1993.     

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.     

Influence of the Geometry of a Piezotransformer Transducer on Its Electric Potential During Electroelastic Vibrations of a Piezoceramic Disk

The resonant radial vibrations of a thin piezoceramic disk with solid electrodes and thickness polarization are considered as an example to study the influence of the geometry of piezotransformer transducers on their electric potentials and the mutual influence of neighboring transducers__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 75–80, February 2005.     

Methods of calculation and numerical analysis of conducting-gas flow in high-current electric arcs

The mechanism of conducting-gas acceleration in an electric arc by intrinsic magnetic field was first investigated in [1]. Further theoretical study of this question was associated with the numerical calculation of arcs [2–7]. A more general approach to the solution of the problem was realized in [4], where the finite-difference method was used. Integral calculational models were developed in [5–7]. The present work proposes a modified version of the difference method [4] and a series of integral methods for the calculation of the conducting-gas flow in a high-current electric arc. The development of integral methods is of interest in that they are usually associated with adequate accuracy in determining integral values and values averaged over the cross section by a relatively simple calculation, and also allow the solution of the problem to be obtained in a number of situations when the realization of a difference method is complicated. The results of different calculation methods are compared. The effect of conditions in the initial cross section of the calculation region of the arc on its characteristics is investigated and a numerical analysis of the heating and acceleration of conducting gas is carried out.Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 103–110, September–October, 1978.     

Angular vibrations of an ellipsoid of revolution in a confined viscous fluid

Vibrations of bodies in confined viscous fluids have been studied on a number of occasions, transverse vibrations of rods being the main subject of investigation [1–3]. The present authors [4] have considered the general problem of translational vibrations of an axisymmetric body in an axisymmetric region containing a low-viscosity fluid. The present paper follows the same approach and considers the problem of small angular vibrations of an ellipsoid of revolution in a circular cylinder with flat ends. In the general case, the hydrodynamic coefficients in the equation of motion of the ellipsoid are determined numerically for different values of the dimensionless geometrical parameters using Ritz's method. In the case of an unconfined fluid, analytic dependences in terms of elementary functions are obtained for the hydrodynamic coefficients. The theoretical results agree well with experimental investigations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 34–39, March–April, 1984.     

One-dimensional unsteady-state flow in a rotating grid

The article discusses the problem of determining the dynamic characteristics of rotating and fixed grids in turbine-type machines. The grid is regarded as a linear system with distributed parameters. In problems involved with determining the stability of complex systems and in control problems, the dynamic characteristics of the turbine-type machines must be known. Such characteristics have been studied, for example, in [1]. However, in [1] the discussion is limited to a system with lumped parameters, which is admissible only at small perturbation frequencies. Article [2] discusses the problem of the propagation of vibrations in a flow with a constant mean velocity. In what follows, this problem is solved with a variable velocity of the mean motion. In addition, it is assumed that, with vibrations, there is removal or supply of mechanical energy.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 77–83, September–October, 1971.     

Small vibrations of a sphere in a spherical volume of viscous fluid

Problems of the vibration of bodies in confined viscous fluids have been solved to determine the added masses and damping coefficients of rods [1–3] and floats [4–5]. The solutions of these problems, based on the use of simplifications of the boundary-layer method [4–6], are obtained analytically in general form and are in good agreement with the experimental data. However, in each specific case the possibility of using such solutions for given values of the fluid viscosity and vibration frequency must be justified either experimentally [2, 4, 5] or theoretically as, for example, in [1], where an analytic solution was obtained for concentric cylinders. The present paper offers a general solution of the problem of the small vibrations of a sphere in a spherical volume of fluid valid over a broad range of variation of the dimensionless kinematic viscosity. The limiting cases of this solution for both high and low viscosity are considered. The asymptotic expressions obtained are compared with calculations based on the analytic solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 29–34, March–April, 1986.     

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.     

Nonlinear evolution of waves in forced decaying capillary jets

The investigation of nonlinear waves in decaying capillary jets is of great interest both from the point of view of nonlinear wave processes in media and for practical applications associated with the generation and propagation of flows of monodisperse droplets [1–4]. The formation and dynamics of satellite droplets are particularly important in the study of the decay of thin capillary jets [5–8]. Investigation of the conditions of formation of satellites open up important prospects for the preparation of monodisperse microscopic granules with diameters appreciably less than the diameter of the original jet. This is of great importance in modern technologies based on the use of materials in disperse form [9–13]. The present paper is devoted to the investigation of nonlinear waves in decaying capillary jets.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 54–60, May–June, 1993.     

Electroconvective stability of a weakly conducting liquid

In inhomogeneous electric fields, at sufficiently high field strengths, a weakly conducting liquid becomes unstable and is set in motion [1–4]. The cause of the loss of stability and the motion is the Coulomb force acting on the space charge formed by virtue of the inhomogeneity of the electrical conductivity of the liquid [4–13]. This inhomogeneity may be due to external heating [4–6], a local raising of the temperature by Joule heating [2, 7, 8], and nonlinearity of Ohm's law [9–13]. In the present paper, in the absence of a temperature gradient produced by an external source, a condition is found whose fulfillment ensures that the influence of Joule heating on the stability can be ignored. Under the assumption that this condition is satisfied, a criterion for stability of a weakly conducting liquid between spherical electrodes is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–142, July–August, 1979.     

Nonmonodisperse breakup of capillary jets in a variable electric field

The electrical charging of capillary jets has a strong influence on their stability [1–10]. Well-known theoretical studies have been devoted to the linear [1–6], weakly linear [7], or finite-amplitude [10] stability of such jets in a constant electric field. In the present paper, an investigation is made in the framework of the full nonlinear equations. The main attention is devoted to effects associated with allowance for a time-variable electric field. It is shown that a sharp decrease of the surface charge may lead to an appreciable decrease in the size of the satellite droplets; allowance for the long-wavelength background also leads to a decrease in the size of the satellite droplets. In contrast, a sharp increase of the surface charge increases the relative contribution of the satellite droplets. At the same time, introduction of small-scale background perturbations can lead to a decrease in the contribution of the fine satellite droplets and to a weakening of their reaction to a rapidly increasing electric field. It is shown that the degree of monodisperseness can be increased by a relatively slowly varying electric field. An averaged effect of an electric field that varies rapidly in time is found. Appreciable increase of the initial perturbation amplitude in the case of a periodically varying electric field can lead to an appreciable increase in the degree of monodisperseness. The introduction of short-wavelength perturbations in a periodic electric field with large amplitude of the pulsations can lead to disappearance of the satellite droplets.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 55–62, March–April, 1991.     

Superposition of low-amplitude shear vibrations on steady shear flow of an elastic fluid

The previously proposed theory of viscoelastic behavior of polymer fluids is compared with experiments on the superposition of low-amplitude shear vibrations on a steady flow. It is shown that the theory agrees satisfactorily with experiments on a single polymer solution. The superposition of a steady shear flow and low-amplitude vibrations can be used to investigate some nonlinear effects characteristic of elastic fluids by relatively simple methods. The literature devoted to this question is fairly extensive; we cite only investigations in which the main results have been obtained [1–3]. The most common experimental scheme is one-dimensional (parallel superposition), although there is also a two-dimensional scheme of orthogonal superposition of shear vibrations on steady flows. Since almost all the effects in the second scheme are qualitatively similar to the first [3], but are not so clearly manifested, we give the theoretical and experimental results relating to the parallel scheme in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–7, January–February, 1976.We are grateful to É. Kh. Lipkina for help in the calculations.     

Flow of a viscous fluid in a closed cavity in the presence of slip effects

Slip at the wall is observed in the flow of non-Newtonian fluids [1–4] and rarefied gases [5]. The most complete information on the phenomenon is obtained in capillary viscosimetry. For small radii of the capillaries and in porous media the slip effect is manifested even for Newtonian fluids (water, kerosene, for example) [6]. Experiments [2, 4] show that the influence of the entrance section can be ignored if the length of the capillary exceeds its radius by about 100 times. For the measurement of the rheological characteristics of high-viscosity fluids the use of long capillaries is difficult, and it is necessary to calculate the two-dimensional flow at the entrance section with allowance for slip. The need for such calculations also arises, for example, when one is choosing the optimal parameters of the screw devices employed in the processing of polymers [7]. Two-dimensional flows of a viscous incompressible fluid are frequently calculated with the flow function and vorticity =– used as variables [8–14]. The expressions for the vorticity on the boundary are usually obtained from the viscous no-slip condition [8, 9]. In the present paper, expressions are obtained for the vorticity on a wall in the presence of slip. The obtained expressions are used to solve a test problem on the flow of a viscous incompressible fluid in a cavity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 10–16, January–February, 1980.     

Determination of the constants of electrochemical reactions and the ion mobility coefficients in weakly conducting liquids from an analysis of the current—voltage characteristics

The problem is considered of the passage of a direct current through a solution of a weak electrolyte in a two-dimensional cell. Allowance is made for the electrochemical reactions of dissociation and reconbination which take place in the electrolyte when the rate of dissociation of the molecules is regarded as dependent on the electric field intensity [1–3]. For electrolytes whose recombination coefficient is of the order of magnitude of the Langevin coefficient, theoretical current—voltage characteristics are given for the limiting cases of large and small values of the characteristic times for the ion concentrations to be changed by electrochemical reactions and the transport of ions by the electric field. A method of determining the dissociation rate, the recombination coefficient, and the ion mobility coefficients is proposed on the basis of comparison of the theoretical and experimental current—voltage characteristics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 113–120, November–December, 1984.     

Hydroelastic vibrations of a beam floating on the surface of an incompressible liquid

The article considers the problem of determining the forms and the frequencies of the free vibrations of a floating beam of elliptical cross section, on the basis of simultaneous solution of the equations of mechanical bending vibrations and the equations of hydrodynamics. The difference between the forms of the vibrations of a beam in a liquid and in a void is evaluated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 128–132, January–February, 1973.     

On nonisothermal electroconvection

The flow from the tip of a needle electrode is caused by the Coulomb force acting on the space charge [1–3]. This charge is formed because of the dependence of the conductivity on the temperature, nonuniformity of which is due to Joule heating [1] and the electric field intensity [2] or processes near the electrode [3–5]. The present paper considers the stability of a dielectric liquid between spherical electrodes in order to elucidate the possibility of a thermoelectrohydrodynainic flow due to Joule heating. In the presence of external heating, the possibility of such a flow has been demonstrated both experimentally and theoretically [6–8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 133–137, March–April, 1980.     

Aspects of self-similar diffraction gas flows and their numerical simulation

A large number of papers has been devoted to the investigation of the interaction of a plane shock wave with bodies of various geometric shapes, and they have been generalized and classified for a stationary body in [1, 2]. Separate results of experimental and theoretical investigations of the interaction of a shock wave with a wedge, cone, sphere, and cylinder moving with supersonic velocities are contained in [3–9]. Analysis of the available results shows that the features of the unsteady gas flows formed in this case largely depend on the nature of the boundary-value problem that arises for the system of differential gas dynamic equations. The question of the wave structure of the unsteady gas flow and the accuracy of the obtained solution is central to the numerical investigation of the present class of problems. The most characteristic types of unsteady self-similar gas flows that arise on the interaction of a plane shock wave with bodies of a wedge or convex corner type are calculated on the basis of an explicit numerical continuous calculation method of the second order of accuracy. The accuracy of the numerical solutions is discussed on the basis of a comparison with the experimental data. The case of the interaction of a shock wave with the rarefaction wave that arises in a supersonic flow past a convex corner is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 146–152, July–August, 1986.     

Estimate of the amplitudes of the fields created by an unsteady gamma source

It is known [1–4] that an unsteady gamma source gives rise to an electromagnetic field in the surrounding space. Most of the studies of the characteristics of such fields have been performed in the approximation which is linear in the field [1–3]. An exception is [4] in which the slowing down of Compton electrons by the electric field is taken into account. It follows from [1, 2] that the characteristic scale of the fields created close to the source is of the order of 3 · 10⁴ V/m. Although this value is appreciably lower than the value of breakdown fields in air, electric discharges are observed [5] in the vicinity of a gamma source, indicating the presence of substantially larger fields. One effect not taken into account in the latter approximation which could lead to an increase in the field is the increase in electron termperature due to the electric field [6]. On the one hand, this decreases the electron mobility and consequently also the conductivity of the system, On the other hand, it is known that the electron attachment coefficient for electronegative molecules strongly affects the characteristics of electric fields and depends on the electron energy. Therefore, the electron balance equation must take account of the dependence of on the electric field through the electron energy, and this leads to a further change in conductivity. We take account of these effects on the shaping of electric fields in air in the vicinity of the source. It is assumed that electron lifetimes are determined solely by their attachment to molecules. This is a good approximation for air pressures near normal [1–3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 163–170, July–August, 1976.     

Blowing into a supersonic stream through a permeable surface

Distributed blowing of gas into a supersonic stream from flat surfaces using an inviscid flow model was studied in [1–9]. A characteristic feature of flows of this type is the influence of the conditions specified on the trailing edge of the body on the complete upstream flow field [3–5]. This occurs because the pressure gradient that arises on the flat surface is induced by a blowing layer whose thickness in turn depends on the pressure distribution on the surface. The assumption of a thin blowing layer makes it possible to ignore the transverse pressure gradient in the layer and describe the flow of the blown gas by the approximate thin-layer equations [1–5]. In addition, at moderate Mach numbers of the exterior stream the flow in the blowing layer can be assumed to be incompressible [3]. In [7, 8] a solution was found to the problem of strong blowing of gas into a supersonic stream from the surface of a flat plate when the blowing velocity is constant along the length of the plate. In the present paper, a different blowing law is considered, in accordance with which the flow rate of the blown gas depends on the difference between the pressures on the surface over which the flow occurs and in the reservoir from which the gas is supplied. As in [8, 9], the solution is obtained analytically in the form of universal formulas applicable for any pressure specified on the trailing edge of the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 108–114, September–October, 1980.I thank V. A. Levin for suggesting the problem and assistance in the work.     

Model of a fracture as an emitter of elastic vibrations

During the past two decades a new method has begun to be intensively developed for the investigation of fracture processes which is based on recording the mechanical vibrations generated by the defects of a medium [1]. The new method's problems include: extraction of a useful signal from the extraneous noises, identification of the type of defect, determination of its characteristic dimensions, and an estimate of the danger of the situation which has developed. The solution of the problems indicated has great meaning in such practical applications as nondestructive quality control and the engineering diagnostics of materials and manufactured goods. Therefore, the investigation of the spectrum of the signals produced by the formation of macroscopic fractures, such as the terminal and, consequently, most dangerous phase of fracture, is of great interest. The kinematical characteristics of a fracture as an emitter of elastic vibrations are formulated in this paper. The spatial and time spectra of the dynamical motions caused by the appearance of a growing fracture in a thin plate are discussed. Relationships are derived between the spectral characteristics of propagating disturbances and the parameters of the fracture.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 160–166, March–April, 1976.The author thanks L. I. Slepyan for valuable discussion and attention to this research.