The process of charging aerosol particles in an electric field,with allowance for diffusion of the ions

A study is made of the charging of highly conducting particles in disperse media. To this end, in the case of a small volume concentration of particles, there is a study, within the framework of electrohydrodynamics [1, 2], of the charging of an ideally conducting spherical particle in a unipolar charged gas. It is assumed that the particle is at rest relative to the gas, and its size and ion concentration are fairly small, so that the electric self-field of the ions may be neglected. A computer was used to calculate the dependences of the charging current on the charge of the particle for various values of the external electric field intensity. A comparison is made with the experimental data on the charging of particles [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 177–180, January–February, 1986.The author wishes to express his gratitude to L. T. Chernyi for formulating the problem, and to V. V. Gogosov for a useful discussion of the results.     

Inductive acceleration of an electrically conductive particle in a viscous liquid

The characteristics of the motion of a particle in an electrically conducting liquid with constant crossed electric and magnetic fields present have been investigated in connection with the problem of MHD-separation in many papers (for example, see the bibliography in [1]). The separation of electrically conducting particles contained in a dielectric liquid, which can be accomplished with the help of a variable magnetic field [2], is also of practical interest. The ponderomotive force acting on a spherical conducting particle near a straight conductor through which the discharge current of a capacitor bank is flowing is found in this paper, and the motion of a particle in a viscous liquid under the action of this force is investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 31–34, November–December, 1984.     

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.     

Charging of perfectly conducting and nonconducting particles in a suspension by collisions with walls

The change in the electric charge of perfectly conducting and nonconducting particles of a suspension as a result of their collision with walls in a flow of the suspension is found. Criteria for the applicability of the obtained expressions to real particles are given. For the density of the electric current in rarefied suspensions consisting of a nonconducting gas and charged particles a condition is obtained that is satisfied for flow of a suspension at impermeable walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 80–87, July–August, 1980.I thank L. I. Sedov and V. V. Gogosov for a helpful discussion of the work.     

Internal rotation in the hydrodynamics of weakly conducting dielectric suspensions

Hydrodynamic phenomena in weakly conducting single-phase media due to interphase electric stresses are reviewed in [1]. In the present paper, a model is constructed of a dielectric suspension with body couples due to the field acting on free charges distributed on the surface of the particles of the suspension. Averaging of the microscopic fields yields macroscopic equations for the field and the polarization of the dielectric suspension with allowance for the finite relaxation time of the distribution of the free charge on the phase interface. The developed model is used to consider the occurrence of spontaneous rotation of a dielectric cylinder in a weakly conducting suspension in the presence of an electric field; compared with the case of single-phase media [2], this is characterized by a significant reduction in the threshold intensity of the electric field with increasing concentration of the particles [3]. In the present model of a dielectric suspension, the destabilization of the cylinder is due to the occurrence of rotations of the particles of the suspension due to the interaction between the polarization and the motion of the medium. The relaxation equation for the polarization for the given model is analogous to the corresponding equation for media which can be magnetized [4–6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 86–93, March–April, 1980.     

Propagation of shock and detonation waves in dust-laden gases

This article examines the flows of a two-phase mixture of a gas with solid particles arising as a result of the propagation of shock waves or detonation waves through a homogeneous medium at rest. It is assumed that the basic assumptions of the mechanics of mutually penetrating continua hold [1], whereby it is possible to describe the flow of each phase of the mixture within the framework of the mechanics of a continuous medium. We assume that the solid phase consists of identical, incompressible, and nondeformable particles of spherical shape. It is assumed that the temperature inside the particles is homogeneous. Collisions between particles and their Brownian motion are ignored. It is assumed that the carrier phase is an ideal gas (the viscosity is only allowed for in the interaction forces between phases). The contribution of the volume of the particles is not considered. On the basis of these assumptions, the following problems are considered: the propagation of a detonation wave in a mixture of a detonating gas and chemically inert particles and the motion of a dust-gas mixture in a shock tube in the presence of combustion of the particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 93–99, November–December, 1984.     

Two-phase couette flow

A study is made of plane laminar Couette flow, in which foreign particles are injected through the upper boundary. The effect of the particles on friction and heat transfer is analyzed on the basis of the equations of two-fluid theory. A two-phase boundary layer on a plate has been considered in [1, 2] with the effect of the particles on the gas flow field neglected. A solution has been obtained in [3] for a laminar boundary layer on a plate with allowance for the dynamic and thermal effects of the particles on the gas parameters. There are also solutions for the case of the impulsive motion of a plate in a two-phase medium [4–6], and local rotation of the particles is taken into account in [5, 6]. The simplest model accounting for the effect of the particles on friction and heat transfer for the general case, when the particles are not in equilibrium with the gas at the outer edge of the boundary layer, is Couette flow. This type of flow with particle injection and a fixed surface has been considered in [7] under the assumptions of constant gas viscosity and the simplest drag and heat-transfer law. A solution for an accelerated Couette flow without particle injection and with a wall has been obtained in [6]. In the present paper fairly general assumptions are used to obtain a numerical solution of the problem of two-phase Couette flow with particle injection, and simple formulas useful for estimating the effect of the particles on friction and heat transfer are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1976.     

Electrization of dielectric liquids flowing in tubes

The methods of the mechanics of continuous media [1] are used to consider the problem of electrization of dielectric liquids flowing in tubes [2–6]. According to modern ideas [2–6], there is always dissolved in such liquids a slight admixture of an electrolyte, whose molecules in such a dilute solution dissociate to a certain extent into positively and negatively charged ions. On the walls, oxidizing and reducing reactions take place, as a result of which the negative and positive ions, respectively, give up to the wall surplus electrons or take missing electrons from it. Thus, a positive (respectively, negative) total electric charge is induced in the liquid by the flow. We consider in this paper the electrization of a dielectric liquid in laminar flow in a circular cylindrical tube. We find the distribution of the electric charge in the liquid, the maximal electric current, and the dependence of the length over which the distribution of the electric charge in the tube is established on the tube radius, the Debye radius of the liquid, and the Péclet diffusion number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 41–47, November–December, 1979.We thank V. V. Gogosov for helpful comments made in a discussion of thwe work.     

Convective combustion of aerosuspensions in fuel that contains the oxidant

The convective combustion of porous gunpowder and high explosives is an intermediate stage in the transition from layered combustion to detonation [1, 2]. The theory of convective combustion of such systems is developed in [3–6]. It has now become necessary to analyze the possibility of convective combustion of aerosuspensions. The present paper develops the theory of the combustion of such systems on the basis of an analysis of the equations of gas dynamics with distributed supply of mass and heat; the problem of nonstationary motion of a convective combustion front is formulated. In the homobaric approximation [7], when the pressure is assumed to be spatially homogeneous, an analytic solution to the problem is found; this determines the law of motion of the front and the distribution of the parameters that characterize the gas and the particles in the combustion zone. Necessary conditions for the transition from convective combustion to explosion are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 49–56, September–October, 1980.I thank R. I. Nigmatulin for helpful comments and advice, and also V. A. Pyzh and V. K. Khudyakov for discussing the work.     

Boundary layer on a blunt body in a flow of dusty gas

The problem of interaction of gas-dust flows with solid surfaces arose in connection with the study of the motion of aircraft in a dusty atmosphere [1–2], the motion of a gas suspension in power generators, and in a number of other applications [3]. The presence of a disperse admixture may lead to a significant increase in the heat fluxes [4] and to erosion of the surface [5]. These phenomena are due to the joint influence of several factors — the change in the structure of the carrier-phase boundary layer due to the presence of the particles, collisions of the particles with the surface, roughness of the ablating surface, and so forth. This paper continues an investigation begun earlier [6–7] into the influence of particles on the structure of the dynamical and thermal two-phase boundary layer formed around a blunt body in a flow. The model of the dusty gas [8] has an incompressible carrier phase. The method of matched asymptotic expansions [9] is used to obtain the equations of the two-phase boundary layer. In the frame-work of the refined classification made by Stulov [6], it is shown that the form of the boundary layer equations is different in the presence and absence of inertial precipitation of the particles. The equations are solved numerically in the neighborhood of the stagnation point of the blunt body. The temperature and phase velocity distributions in the boundary layer, and also the friction coefficients and the heat transfer of the carrier phase are found for a wide range of the determining parameters. In the case of an admixture of low-inertia particles that are not precipitated on the body, it is shown that even when the mass concentration of the particles in the undisturbed flow is small their accumulation in the boundary layer can lead to a sharp increase in the thermal fluxes at the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1985.I thank V. P. Strulov for a discussion.     

Plane nonstationary gas flow with a strong discontinuity

The problem of plane, nonstationary gas motion under the effect of a piston in the shape of a dihedral angle moving at constant velocity in the gas is considered. In contrast to one-dimensional motion under the effect of a flat piston, a curvilinear shockwave originates here, and the flow becomes nonisentropic and vortical. This problem is examined herein in a linear formulation when the angle of the piston breakpoint is assumed small. The linear problem reduces to an inhomogeneous Riemann—Hilbert problem whose solution is found explicitly. The problem under consideration adjoins a circle of problems associated with shockwave diffraction and reflection studied by Lighthill [1], Smyrl [2], Ter-Minassiants [3], etc.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 45–50, May–June, 1971.The author is grateful to L. V. Ovsyannikov for interest in the research and useful comments.     

Investigation of electrogasdynamic jet behind a source of charged particles

We have investigated theoretically and experimentally a submerged jet emerging from a source of charged particles (corona-producing system). Simplest scaling laws are established for the distribution of the electric parameters in a unipolarly charged gas jet in the case of grounded and insulated sources. It is shown that the current from a grounded source and the floating potential to which an insulated system is charged depend strongly on the ambient conditions. Methods of decreasing the floating potential were investiated experimentally. The distributions of the local electric parameters in the jet were measured using a probe method. The propagation of viscous unipolarly-charged jets and the phenomenon of electric wind formation were investigated in [1, 2] and [2–5], respectively. The distinguishing features of the flows considered in the article consisted of their organization (blowing of a jet of uncharged gas over the corona-producing system), absence of walls to limit the flow, and the weak influence of electrostatic forces on the gas motion. The developed setup has made it possible to simulate the processes of accumulation of electric charge on a body as a result of the escape of a jet stream.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–13, September–October, 1971.In conclusion, the authors thank G. M. Bam-Zelikovich for useful discussions.     

Kinetic theory of disperse systems

A kinetic equation for the motion of solid particles in a liquid or gas is derived on the basis of the Fokker-Planck-Kolmogorov diffusion equation for the N particle distribution function. It is shown that, under appropriate assumptions, Bogolyubov's method can also be applied to equations of diffusion type. The obtained kinetic equation is a generalization of the one proposed earlier in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 128–132, January–February, 1980.I thank V. P. Myasnikov for suggesting the problem and for helpful discussions.     

On stream inhomogeneities in a pulsed electromagnetic accelerator

In a number of papers [1–7] carried out on various pulsed electromagnetic accelerators the appearance of a lamellar structure in the stream of accelerated ionized gas occurs having an oscillation frequency of several megahertz. The majority of authors relate the development of irregularities in the stream with local peculiarities in the flow of electric currents (secondary breakdowns [6], the formation of micropinches [3–5], the motion of a current spiral [2], etc.). Notwithstanding the generality of many properties of the irregularities recorded under various conditions, no unified point of view exists as yet concerning the nature of their development.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 143–149, July–August, 1970.     

Hydrodynamics of a liquid with deformable and interacting particles

Interest in the hydrodynamics of a liquid with particle rotations and microdeformations has recently intensified [1–9] in connection with the technical applications of different artificially synthesized structured media. A model of a liquid with deformable microstructure was first proposed in [4] and was thermodynamically analyzed in [6], in which a model of a liquid was constructed by means of methods from the thermodynamics of irreversible processes. A model of a macro- and microincompressible liquid with particle rotations and deformations has been proposed [7, 8] based on constitutive equations from [6]. Below we will solve the sphere rotation problem in an infinite liquid given different boundary conditions on the rates of particle rotation and microdeformation within the context of the system of equations presented in [7]. The solution of an analogous problem for a micropolar liquid simulating a suspension with solid particles has been obtained [9] and the solution for a viscous liquid was found by Stokes in [10].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnieheskoi Fiziki, No. 1, pp. 79–87, January–February, 1976.     

Supersonic two-phase flow around a wedge

Supersonic two-phase flow around bodies is encountered in calculating the flow around the last stages of blades of condensing turbines, in studying the motion of airplanes under cloudy conditions, etc. In the latter case, there is, along with erosion of the forward edges of the wing profiles, a change in the wave structure and interference situation in the flow about the airplane, leading to off-design regimes of motion. Supersonic flow of a two-phase mixture around a wedge, without taking account of the influence of the particles on the flow, was investigated in [1–3]. In [4], also in this kind of simplified setting, a study was made of the interaction of particles with the surface of a wedge in which reflection of the particles from the wall was taken into account. Morganthaler [5] made an experimental study of the flow of a mixture of air and aluminum oxide particles around a wedge. In [6] a theoretical study was made of a supersonic two-phase flow around thin flat axially-symmetric bodies. In particular, for the flow around a wedge, closed form solutions were obtained for the form of the shock wave, the gas streamlines and particle paths, and the distribution of all the parameters along the surface of the wedge. On the basis of the equations given in [7] and the method of characteristics, which were developed for flows consisting of a mixture of a gas and heterogeneous particles in nozzles [8,9], we present below a study of a supersonic two-phase flow around a wedge.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 83–88, March–April, 1972.     

Propagation of an ion jet near a dielectric surface

Difficulties in determining experimentally the local electrical parameters of unipolar-charged jets are arousing interest in the theoretical investigation of electrogasdynamic (EGD) flows. Free EGD jets were examined, for example, in [1–3]. In order to control the charge on the dielectric parts of aircraft surfaces, which results from their static electrification and may have certain negative consequences [4], and, moreover, to influence the flow in the boundary layer use is being made of unipolar-charged jets propagating near the dielectric [5, 6]. In [6] the case of an ion jet near a dielectric surface possessing surface conductivity was investigated. In these circumstances it is possible to neglect charge diffusion, which considerably simplifies the problem. Space charge diffusion was taken into account in [7], but subject to certain very important simplifications. The author has calculated the electrical parameters of a unipolar-charged jet propagating in a viscous incompressible gas near an ideal dielectric plate, with allowance for surface and polarization charges and, moreover, the diffusion processes near the surface. An asymptotic solution is obtained for the equations of the ionic diffusion layer as the ratio of the thickness of the diffusion layer to the thickness of the hydrodynamic boundary layer tends to zero.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–180, September–October, 1984.The author is grateful to V. V. Mikhailov and A. V. Kazakov for valuable advice and comments.     

Joule loss due to compressibility of gas in a channel of variable section

It is known that closed electric currents arise in a conducting medium moving in a non-uniform magnetic field. These currents lead to additional energy loss and adversely affect the characteristics of magnetohydrodynamic channels. (The numerous investigations of these effects are dealt with in the review [2, 3].) Eddy electric currents are also formed, however, when a medium flows in a uniform magnetic field perpendicular to the to the plane of motion if the channel has a variable cross section and the medium is compressible [1], This paper is devoted to an investigation of some features of these flows. It is assumed in the analysis that the gas flows in channels whose geometry varies slightly.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 4, pp. 3–9, July–August, 1968.     

Quasi-three-dimensional calculation of flow in blade passages of turbines

The flow in turbomachines is currently calculated either on the basis of a single successive solution of an axisymmetric problem (see, for example, [1-A]) and the problem of flow past cascades of blades in a layer of variable thickness [1, 5], or by solution of a quasi-three-dimensional problem [6–8], or on the basis of three-dimensional models of the motion [9–11]. In this paper, we derive equations of a three-dimensional model of the flow of an ideal incompressible fluid for an arbitrary curvilinear system of coordinates based on averaging the equations of motion in the Gromek–Lamb form in the azimuthal direction; the pulsation terms are taken into account in the equations of the quasi-three-dimensional motion. An algorithm for numerical solution of the problem is described. The results of calculations are given and compared with experimental data for flows in the blade passages of an axial pump and a rotating-blade turbine. The obtained results are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 69–76, March–April, 1991.I thank A. I. Kuzin and A. V. Gol'din for supplying the results of the experimental investigations.     

Motion of inhomogeneities of a developed fluidized bed at small reynolds numbers

The instability of a fluidized system in which the particles are uniformly distributed in space [1–3] leads to the development of local inhomogeneities in the internal structure, these taking the form of more or less stable formations of packets of particles [4]. In accordance with the existing ideas based on experimental data [5–8, 13], the particle concentration within a packet may vary in a wide range from very small values (10^–2–10^–3 [8]) for bubbles to the concentration of the unfluidized bed for bunches of particles in a nearly closely packed state. The paper considers the steady disturbed motion of the fluid and solid phases near an ascending or descending packet of particles in a developed fluidized bed. It is assumed that the motion of the solid phase corresponds to a creeping flow of viscous fluid, and the viscosity of the fluidizing agent is taken into account only in the terms that describe the interphase interaction. The velocity fields and pressure distributions of the phases inside and outside a packet are determined. If the particle concentration within a packet tends to zero, the solution describes the slow motion of a bubble in a fluidized bed. The results of the paper are compared with results obtained earlier for the model of ideal fluids [9] and Batchelor's model [10], in which the fluidized bed is treated in a simplified form as a viscous quasihomogeneous continuum.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 57–65, July–August, 1984.