Hydrodynamics of magnetizable and polarizable media

An analysis is made of the general equations for the equilibrium of magnetizable and polarizable media. The problem of the equilibrium of a finite volume of a magnetizable medium is reduced to a system of one differential and two integral equations, which are solved numerically. It is shown that the interface of a magnetizable liquid mass in a homogeneous field extends along the lines of force of the field, with the subsequent formation of a neck of the division.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 141–144, September–October, 1974.The author thanks I. V. Sukharevskii for his interest in the work and his valuable advice, and A. B. Isers for making the computer computations.     

Simple waves and small perturbations in magnetizable or polarizable media

The system of equations describing the behavior of the electrically polarizable media in the case of a sufficiently weak magnetic field and the system of equations for magnetizable media in a weak electric field coincide except for the notations. These equations are used for the investigation of Riemann waves and small perturbations for different given dependences of ε and Μ on ρ and T. The case when the velocity of propagation of simple waves takes complex values is considered. Similar investigation has been carried out in [1, 2] in the case where the dependence of Μ on ρ and T is in the form Μ?1/Μ=cρT (Mossoti formula) and μ=1+4πρk(θ-T)/H. The same problems are investigated here for an infinitely conducting magnetizable gas, whose behavior is described by another system of equations reminiscent of the equations of magnetohydrodynamics.     

Gas-dynamic analogy in the theory of stratified liquid flows with a free boundary

Novel approximate mathematical models of long-wave theory describing flows of a density-stratified liquid with a free boundary are proposed. It is shown that in certain cases the equations of the novel models coincide with either the equations of nonisentropic gas dynamics with a polytropic equation of state for γ = 2 or the equations describing the dynamics of a mixture of two perfect gases.     

Magnetooptical, electrooptical and photoelastic effects in an elastic polarizable and magnetizable isotropic continuum

The magnetooptical, electrooptical and photoelastic behaviour of an elastic polarizable and magnetizable isotropic continuum are investigated from a dynamical point of view, starting from balance equations and constitutive relations. The most original result of the theory is the fact that the continuum exhibits the Cotton-Mouton effect, together with linear birefringence of transverse sound waves. This is compared with experimental data and quantum theory results.As expected, the continuum does not exhibit Faraday rotation.     

Integrals of the equations of motion of a magnetizable ideal medium

Clebsch type representations are used to find integrals of the hydrodynamic equations for magnetizable media of the type of the Bernoulli and Cauchy-Lagrange integrals in hydrodynamics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 165–169, March–April, 1984.     

Calculation of the motion of two-component media

The one-dimensional motion of a viscous incompressible liquid in which particles are suspended is described by the mathematical model used in [1], Two examples are discussed: the precipitation of particles from the suspension, and a boiling layer. The results are presented in the form of graphs.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 102–108, November–December, 1973.     

On the stability of an equilibrium position and rotational motion of a gyrostat

This article is devoted to study the compulsory stability of equilibrium position and rotational motion of a rigid body containing fluid with the help of three rotors carried on the body. The control moments on the rotors using that condition which impose the stabilization of equilibrium position of the rigid body and rotational motion are obtained.     

Structure and stability of the interface in a magnetizable fluid

The problems of interface stability in magnetizable and polarizable fluids are considered in the case of the surface tension tensor dependent on the electromagnetic field strength. For describing this dependence the model proposed by A.N. Golubyatnikov (1986) is used. The investigation of the internal interface structure showed that for single-component systems, as a rule, the dependence of the surface tension on the field strength corresponds to surface phase properties paramagnetic in the normal and diamagnetic in the tangential direction. It is shown that within the framework of the model adopted the thermodynamic stability of the surface depends on the thickness of the interphase layer. Necessary stability conditions are obtained for plane interfaces in media with a constant magnetic permeability outside the interphase layer. The problem of stability of the horizontal free surface of an ideal magnetic field in an external magnetic field (similar to the problem of stability of the horizontal interface of two polarizable fluids in an external electric field) is solved for an arbitrary orientation of the external field relative to the interface. The stability loss is now accompanied by qualitative effects absent in the case of the surface tension tensor independent of the electromagnetic field strength.     

Stabilization of the interface instability of moving magnetizable fluids

A study is made of the stabilization of the interface between two moving magnetizable fluids by means of an external magnetic field H={H₀ cos t, H₀ sin t, 0} of circular polarization. The fluids are assumed to be ideal, incompressible, nonconducting, and electrically neutral. An equation of motion is derived for the perturbed interface. The Borg criterion is used to obtain sufficient conditions of stability of small perturbations of the interface; these conditions relate the amplitude H₀ and the frequency of the external magnetic field to the characteristic parameters of the problem and the wave vector k. The dependence of H₀ and on the modulus of the wave vector is investigated. The obtained results are compared with the results of [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 118–122, July–August, 1980.     

On equilibrium and primary variables in transport in porous media

Thermodynamic equilibrium, which involves mechanical, thermal, and chemical equilibria, in a multiphase porous medium, is defined and discussed, both at the microscopic level, and at the macroscopic one. Conditions are given for equilibrium in the presence of forces between the surface of the solid matrix and the fluid phases. The concept ofapproximate thermodynamic equilibrium is introduced and discussed, employing the definition of athermodynamic potential. This discussion serves as the basis for the methodology of determining the number of degrees of freedom in models of phenomena of transport (of mass, energy, and momentum) in porous media. Equilibrium and nonequilibrium cases are considered. The proposed expressions for the number of degrees of freedom in macroscopic transport models, represent the equivalent ofGibbs phase rule in thermodynamics. Based on balance considerations and thermodynamic relationships, it is shown that the number of degrees of freedom, NF, in a problem of transport in a deformable porous medium, involving NP fluid phases and NC components, under nonisothermal conditions, with equilibrium among all phases and components, is $${\text{NF = NC + NP + 4}}{\text{.}}$$ Under nonequilibrium conditions among the phases, the rule takes the form $${\text{NF = NC }} \times {\text{ NP + 2NP + NC + 4}}{\text{.}}$$ In both cases, when fluid phase velocities are determined by Darcy's law, NF is reduced by NP. When the solid matrix is nondeformable, NF is reduced by 3. The number of degrees of freedom is also determined for conditions of approximate chemical and thermal equilibria, and for conditions of equilibrium that prevail only among some of the phases present in the system. Examples of particular cases are presented to illustrate the proposed methodology.     

Percolation model of equilibrium three-phase flow through porous media

Percolation models of one-phase and two-phase flow through porous media are extended to the three-phase case. The characteristic regions of realization of one-phase, two-phase and three-phase flow are determined, Relative phase permeability calculations are presented for a model capillary radial density function. The theory is compared with the available experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 109–114, January–February, 1989.     

Gas-dynamic spraying. An experimental study of the spraying process

We present results of an experimental study of the specific features of the gas-dynamic formation of coatings from metallic powders (d_p<50 μm) on substrates of various materials depending on the particle velocity (200–1200m/sec), the jet temperature (300–700K), and other parameters. Results of a prospecting study of the implementation of the methods of particle acceleration in supersonic (M=2.0–3.0) rectangular nozzles are described. The rate of bond formation in a cold particle-cold substrate contact occurring in gas-dynamic spraying is estimated within the framework of the concepts applied in analysis of gas-dynamic spraying. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 182–188, March–Apil, 1998.