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 of the motion and equilibrium of magnetizable and polarizable media

Because of the features of the basic system of equations, the steady flow of an isotropically magnetizable medium along magnetic lines of force can be associated with a certain gas-dynamic flow. A gas-dynamic analogy can also be established by considering the laws of the hydrostatics of a barotropic magnetizable medium. The “equation of state” of the gas-dynamic flow is determined by the law of magnetization of the medium whose motion or equilibrium is associated with this flow. All the conclusions about a magnetizable nonconducting medium can be transferred to the case of a liquid dielectric without space charges.     

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.     

Flow of magnetizable fluid through long pipes

International Applied Mechanics -     

Sound waves in a magnetizable medium

This article considers the propagation of small perturbations in a medium which can be inhomogeneously and isotropically magnetized under the action of an electromagnetic field. It is shown that in such a medium there is the possibility of sound waves of the same kind as in a medium with a constant magnetic susceptibility. However, the phase velocities of fast and slow magnetosonic waves can take on imaginary values so that, in strong magnetic fields, there may arise the phenomenon of instability. Investigations were made of the diagrams of the phase velocities for para- and diamagnetic substances for a medium with magnetic saturation; the case of an incompressible medium is discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 15–22, January–February, 1973.     

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.     

Stationary simple waves in an electrically conducting magnetizable fluid

A study is made of the analog of Prandt1—Meyer flow in an incompressible electrically conducting ideal fluid that is magnetizable in accordance with an arbitrary isotropic law. It is shown that inhomogeneity of the magnetization in a conducting fluid makes possible the existence of stationary simple waves with varying magnetic permeability. For a paramagnetic fluid magnetized to saturation, the equations of these waves are integrated completely in the case of a magnetic field parallel to the velocity. Some regions of such flows of magnetizable fluids are discussed in the present paper for the example of the problem of flow around a perfectly conducting profile.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 136–143, September–October, 1980.I thank I.E. Tarapov for his interest in the work and valuable comments made in a discussion.     

Hydrodynamics of wetting

Fluid motion along a smooth, solid surface is examined when the free surface forms a final visible angle with the solid boundary. The dependence of this angle on the velocity with allowance for capillary forces is determined. The Reynolds number is small. The problem of the motion of the phase interface in a capillary and the spreading of viscous fluid drops on solid surfaces are solved. Experimental results are explained. Up to now, not only were analytical results lacking in this field, but also there was not even a precise formulation of the problem (see the review in [1]).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 76–84, September–October, 1976.     

A dynamic theory for magnetizable elastic solids with thermal and electrical conduction

A general dynamical theory of magnetizable, electrically and thermally conducting media is developed for soft ferromagnetic or paramagnetic materials in external electromagnetic fields. The general equations are linearized by assuming infinitesimal strains, linear constitutive equations and that all field variables may be divided into two parts: a "rigid body state" and a "perturbation state". The former is the same as the one in rigid body electrodynamics, and the latter which accounts for electromagnetic interaction with the deformable continuum is coupled with stress and strain through linearized field equations. The theory is developed for general anisotropy but specialized for materials with uniaxial, or higher, symmetry.     

Surface waves and stability of free surface of a magnetizable liquid

Linear theory of surface waves in a magnetizable liquid is examined. A stability criterion for a plane-free surface of a magnetizable liquid is studied for an arbitrary magnetization law.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 35–40, July–August, 1974.     

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.