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.     

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.     

Investigation of surfaces of discontinuity in perfectly conducting magnetizing media

Relationships on discontinuities in magnetizing perfectly conducting media in a magnetic field are investigated. The magnetic permeabilities before and after the discontinuity are assumed to be constant, but unequal, quantities. It is shown that shocks of two kinds, fast and slow, are possible in the formulation under consideration in the hydrodynamics of magnetizing media, as in magnetic hydrodynamics: It is shown that the entropy decreases on the rarefaction shocks diminishing the magnetic permeability, but can grow on the rarefaction shocks increasing the magnetic permeability, but such waves are not evolutionary. The relationships on discontinuities in the mechanics of a continuous medium are written down in general form in [1] with the electromagnetic field, polarization, and magnetization effects taken into account. Relationships on discontinuities in the ferrohydrodynamic and elec trohydrodynamic approximations were written down in [2] and [3–5], respectively, for the cases when the magnetic permeability and dielectric permittivity of the medium ahead of and behind the discontinuity are arbitrary functions of their arguments and are identical. A system of relationships on discontinuities propagated into a magnetizing perfectly conducting medium is investigated in this paper. The method proposed in [6] is used in the investigation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 104–110, January–February, 1976.We are grateful to A. A. Barmin for discussing the paper and for valuable remarks.     

Coupled magnetoacoustic waves in a conducting paramagnetic fluid

We consider the propagation of small disturbances in a paramagnetic conducting fluid in a uniform constant magnetic field. Because of coupling of the mechanical and magnetic effects, coupled magnetoacoustic oscillations of a wave nature develop in a certain (resonant) frequency region. The usual MHD waves and uniform magnetization oscillations occur far from resonance. Dissipative processes are accounted for.The equations of motion for a conducting paramagnetic fluid in which interaction of the hydrodynamic velocity with the magnetization and the magnetic field was taken into account phenomenologically were obtained in [1], One of the consequences of this interaction is the propagation of coupled magnetoelastic waves in the fluid; this phenomenon is examined in the present paper.     

Transverse waves and discontinuities in an ideal magnetized fluid

Suppose that a constant and uniform field B₀ exists within an ideal fluid medium, that is, a medium in which dissipative processes are absent. If this medium is a conducting one and its magnetization and polarization can be neglected, then finite perturbations of the transverse (perpendicular to B₀) components of the velocity and the magnetic field propagate a-long b₀ with a constant velocity without change of form [1], These plane transverse waves, called Alfven waves, are linear and cannot lead to discontinuities if there are no discontinuities in the initial conditions. In this paper we shall consider plane transverse waves in an ideal fluid medium which is not only electrically conducting, but which can also be magnetized by the magnetic field. In such a medium transverse waves are no longer linear and they can develop into jumps in the magnitudes of the field and the velocity. Like Alfven waves, these waves leave the density of the medium unchanged, so that they can also exist in an incompressible fluid. This circumstance is reflected in the nature of the discontinuity, which is analyzed in Section 5.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 116–124, November–December, 1973.The author thanks A. G. Kulikovskii and A. A. Barmin for their valuable remarks contributed during discussions of the work.     

Statics of a magnetic fluid containing magnetic field concentrators

Various static surface shapes of a magnetic fluid containing bodies made of easily magnetizable materials (magnetic field concentrators) in a uniform applied magnetic field are numerically calculated with account for the gravity force, surface tension, and the dependence of the magnetic-fluid magnetization on the magnetic field strength. The possibility of a sudden change in surface shape is shown. Hysteresis in the surface shape with a cyclic increase and decrease in the applied field is predicted.     

Study of propagation of linear and non-linear Alfvén-gravity waves in rotating medium

Travelling waves in an incompressible, infinitely conducting, inviscid fluid of variable density are investigated under the influence of a horizontal magnetic field and Coriolis force. Periodic solutions are found in the limit of infinite vertical wave length. Phase diagrams are drawn to show the solution.     

磁流体在铁谱技术中的应用研究

通过对某矿井提升机滑动轴承工况的实际监测 ,考察了磁流体对铁谱仪中非铁磁性颗粒沉积的影响 .结果表明 :磁流体可以使非铁磁性颗粒有效地沉积在铁谱仪的谱片上 ,使谱片携带更加全面的信息 ;磁流体对非铁磁性颗粒的“磁化”作用具有选择性 .磁流体可以用于监测非铁磁性颗粒     

Peristaltic flow of MHD Jeffrey fluid through finite length cylindrical tube

The present investigation studies the peristaltic flow of the Jeffrey fluid through a tube of finite length. The fluid is electrically conducting in the presence of an applied magnetic field. Analysis is carried out under the assumption of long wavelength and low Reynolds number approximations. Expressions of the pressure gradient, volume flow rate, average volume flow rate, and local wall shear stress are obtained. The effects of relaxation time, retardation time, Hartman number on pressure, local wall shear stress, and mechanical efficiency of peristaltic pump are studied. The reflux phenomenon is also investigated. The case of propagation of a non-integral number of waves along the tube walls, which are inherent characteristics of finite length vessels, is also examined.     

Effect of a Magnetizable Surfactant on the Motion of a Liquid Film on the Horizontal Surface

The motion of a thin liquid film of viscous incompressible fluid on the horizontal surface in the presence of a magnetizable surfactant on the free boundary in the external inhomogeneous magnetic field is investigated. Surfactant diffusion along the free surface and the dependence of the surface tension on the magnetic field strength are taken into account. The system of evolutionary equations is derived in the lubricant approximation and steady-state film flows and their stability in the case of constant film thickness and constant surfactant number density are investigated with regard to the Marangoni effect.     

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.     

Growth and decay of weak shock waves in magnetogasdynamics

The purpose of the present study is to investigate the problem of the propagation of weak shock waves in an inviscid, electrically conducting fluid under the influence of a magnetic field. The analysis assumes the following two cases: (1) a planar flow with a uniform transverse magnetic field and (2) cylindrically symmetric flow with a uniform axial or varying azimuthal magnetic field. A system of two coupled nonlinear transport equations, governing the strength of a shock wave and the first-order discontinuity induced behind it, are derived that admit a solution that agrees with the classical decay laws for a weak shock. An analytic expression for the determination of the shock formation distance is obtained. How the magnetic field strength, whether axial or azimuthal, influences the shock formation is also assessed.     

Nonlinear waves on the free surface of an electrically conducting liquid

Gravity waves of small but finite amplitude on the free surface of an electrically conducting liquid are examined. For the waves whose propagation is described by the Korteweg-de Vries equation (in the absence of a magnetic field), equations are derived. In addition to nonlinearity and dispersion, these equations include the influence of applied magnetic fields. As an example, the effect of magnetic damping on a solitary wave is presented.     

Motion of a slender body made of magnetizable composite in a traveling magnetic field

The motion of a slender body made of magnetizable composite in a channel, along which coils producing a heterogeneous “traveling” magnetic field are mounted, is investigated. The coil axes are vertical and lie in the same plane. A mathematical model of a slender body made of viscoelastic magnetizable material is proposed. The magnetic force is calculated from a formula used in ferrohydrodynamics of magnetic fluids with equilibrium magnetization. The problem of the motion of this body in a channel in a vertical plane under the action of the magnetic field produced in an experimental setup is numerically solved. The dependence of the body velocity on the coil switching frequency is calculated and the effect of different problem parameters on the form of this dependence is studied. The theoretical results are compared with the experimental data.     

Unsteady flows with a constant total pressure,described by the equations of ideal magnetohydrodynamics

Exact solutions of the equations of ideal magnetohydrodynamics describing the class of unsteady flows of an electrically conducting fluid with a constant total pressure are constructed. The solutions are written in the Lagrange coordinate system; arbitrariness in its choice was used to parameterize magnetic field lines. The wide functional arbitrariness the solutions provide a significant variation in the picture of the described fluid motions. An example of unsteady flow of an ideal electrically conducting fluid in a cylindrical channel with fixed magnetic tubes is given.     

Slow steady flows of a conducting fluid at large Hartmann numbers

We consider slow steady flows of a conducting fluid at large values of the Hartmann number and small values of the magnetic Reynolds number in an inhomogeneous magnetic field. The general solution is obtained in explicit form for the basic portion (core) of the flow, where the inertia and viscous forces may be neglected. The boundary conditions which this solution must satisfy at the outer edges of the boundary layers which develop at the walls are considered. Possible types of discontinuity surfaces and other singularities in the flow core are examined. An exact solution is obtained for the problem of conducting fluid flow in a tube of arbitrary section in an inhomogeneous magnetic field.The content of this paper is a generalization of some results on flows in a homogeneous magnetic field, obtained in [1–8], to the case of arbitrary flows in an inhomogeneous magnetic field. The author's interest in the problems considered in this study was attracted by a report presented by Professor Shercliff at the Institute of Mechanics, Moscow State University, in May 1967, on the studies of English scientists on conducting fluid flows in a strong uniform magnetic field.     

Oblique collision of a plane-polarized Alfvén discontinuity and a slow shock wave propagating in opposite directions in magnetohydrodynamics

Collision of plane fronts of a plane-polarized Alfvén discontinuity and a slow shock wave propagating in opposite directions at a certain angle is considered within the framework of an ideal magnetohydrodynamic model. The initial state of an infinitely conducting medium at rest with a frozen-in magnetic field is assumed to be given. Calculations are carried out for various values of the shock wave Mach number and the magnetic field strength using a special software which makes it possible to find an exact solution of the Riemann problem of breakdown of a discontinuity between the states downstream of the interacting waves by means of a computer. The wave flow structure is investigated and a bifurcation map of flow restructuring is constructed. Domains of the initial parameters for which the interaction differs qualitatively are distinguished. The parameters of the medium and magnetic field are found as functions of the angle between the colliding discontinuities and the inclination of the magnetic field. The results obtained may be used in investigations of magnetic reconnection.     

Influence of magnetic field on wave propagation at liquid-microstretch solid interface

The reflection and refraction of a longitudinal wave at an interface between a perfectly conducting nonviscous liquid half-space and a perfectly conducting microstretch elastic solid half-space are studied. The appropriate solutions to the governing equations are obtained in both the half-spaces satisfying the required boundary conditions at the interface to obtain a system of five non-homogeneous equations in the amplitude ratios of various reflected and transmitted waves. The system is solved by a Fortran program of the Gauss elimination method for a particular example of an interface between water and aluminum-epoxy composite. Numerical values of the amplitude ratios are computed for a certain range of the incidence angle both in the presence and absence of an impressed transverse magnetic field. The effects of the presence of the transverse magnetic field on the amplitude ratios of various reflected and transmitted waves are shown graphically.     

Deformation of an Inviscid Magnetizable Liquid Drop in a Non-Stationary Magnetic Field

Fluid Dynamics - Variation in the shape of a magnetizable liquid drop suspended in another immiscible magnetizable liquid in the presence of a non-stationary uniform magnetic field is theoretically...     

Absolute instability of an interface between two magnetic fluids in the presence of a tangential velocity discontinuity and an external magnetic field

The nature of the instability of the surface of a tangential velocity discontinuity between two incompressible, inviscid, capillary, nonconducting, linearly magnetizable fluids in an external magnetic field is considered. An absolute instability criterion is obtained in analytic form. When the gravity force is negligible, this criterion does not depend on the value of the surface tension. When the surface tension is negligible, the absolute instability criterion is obtained for the region of the flow parameters in which the causality condition for the system in question is satisfied. If the magnetic field is tangential to the interface, all the criteria obtained are also applicable to the case of nonmagnetic, perfectly conducting fluids, i.e., to the case of ideal magnetohydrodynamics.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 21–26, September–October, 1995.