Equilibrium configurations of the surface of a perfectly conducting fluid in the magnetic field of a current-carrying linear conductor

This paper considers the problem of the possible equilibrium configurations of the free surface of a perfectly conducting fluid deformed by a nonuniform magnetic field. A family of exact solutions of the problem is obtained using conformal mappings; equilibrium is achieved due to the balance of capillary and magnetic pressures. According to these solution, the surface strain amplitude increases with increasing current and the hole is transformed into a two-dimensional bubble covering the linear conductor.     

Instability of binary nanofluids with magnetic field

The present paper investigates the effects of a vertical magnetic field on the double diffusive nanofluid convection. The effects of the Brownian motion and thermophoresis due to the presence of nanoparticles and the effects of the Dufour and Soret parameters due to the presence of solute are included in the investigated model. The normal mode technique is used to solve the conservation equations. For the analytical study, valid approximations are made in the complex expression for the Rayleigh number to get useful and interesting results. The bottom heavy binary nanofluids are more stable than the regular binary fluids, while the top heavy binary nanofluids are less stable than the regular binary fluids. The critical wave number and the critical Rayleigh number increase whereas the frequency of oscillation (for the bottom heavy configuration) decreases when the Chandrasekhar number increases. The numerical results for the alumina-water nanofluid are studied by use of the MATHEMATICA software.     

Interaction of a magnetic liquid with a conductor containing current and a permanent magnet

The present study investigates the force exerted by a magnetic liquid on a conductor with a current or a permanent magnet located near its infinite free surface. It is shown that this force is equal to the weight of the liquid raised by the magnetic field above the original horizontal level. The force is found for the cases when the liquid is weakly magnetic and when the shape of its surface differs little from plane. Consideration is given to the equilibrium of a magnet suspended on a small spring near the surface of the magnetic liquid. The critical height is found at which the magnet ceases to be held by the spring and is torn off into the liquid. The experimentally obtained values of the magnitude of of the force acting on the magnet and the height of collapse of the magnet into the liquid are in good agreement with the theoretical results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–181, March–April, 1988.The authors are grateful to V. V. Gogosov for valuable discussion of the study.     

Instability of an electron beam in a magnetic field

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 10–17, March–April, 1990.     

The fields of a line source of current over a stratified conductor

Summary The problem of a line source of alternating current situated over a stratified dissipative medium is theoretically investigated. Special cases of the general solution are studied in detail and several illustrative curves are given. The results have application to stratigraphic investigations of the earth's crust.     

Yield stress of a magnetic fluid in a magnetic field

The yield stress ₀ of a magnetic fluid in a plane channel and the shape of the chains restraining the motion of the fluid are determined. The equilibrium problem for a magnetic fluid in a plane channel in the presence of an external magnetic field perpendicular to the plane of the channel and a pressure difference between the channel ends is solved within the framework of the structured fluid model. It is shown that equilibrium is possible only when the pressure difference does not exceed a certain limit p _cr at which the shear stress on the channel wall has a maximum. In weak fields p _cr and the corresponding ₀ depend quadratically on the field and in strong fields tend to saturation. The phenomenological parameters of the model are estimated for the case in which the microstructure is a system of chains of magnetic particles. The results obtained are found to be in qualitative agreement with the experimentally observed dependence of p _cr and ₀ on the field and the magnetic phase concentration.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 4–10, May–June, 1992.The authors are grateful to V. V. Gogosov for useful discussions and his interest in 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.     

Instability of structured magnetic films in the absence of an external magnetic field

A phenomenological theory is proposed to describe the equilibrium of a thin structured film of magnetic fluid on the surface of another non-magnetic fluid in the absence of an external magnetic field. The stability of a semi-infinite plane magnetic film is considered on the basis of the theory proposed. The result obtained can serve as a qualitative explanation of experiments performed on thin films of magnetic fluid. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 105–110, November–December, 1986. The author is grateful to L. I. Sedov and V. V. Gogosov for useful discussions and their interest in his work.     

Some characteristic features of diffusion of a magnetic field into a moving conductor

The study of the diffusion of a magnetic field into a moving conductor is of interest in connection with the production of ultra-high-strength magnetic fields by rapid compression of conducting shells [1,2]. In [3,4] it is shown that when a magnetic field in a plane slit is compressed at constant velocity, the entire flux enters the conductor. In the present paper we formulate a general result concerning the conservation of the sum current in the cavity and conductor for arbitrary motion of the latter. We also consider a special case of conductor motion when the flux in the cavity remains constant despite the finite conductivity of the material bounding the magnetic field.Notation ₁, * flux which has diffused into the conductor - ₂ flux in the cavity - ₀ sum flux - r radius - r* cavity boundary - thickness of the skin layer - (r) delta function of r - t time - q intensity of the fluid sink - v velocity - flux which has diffused to a depth larger than r - x self-similar variable - dimensionless fraction of the flux which has diffused to a depth larger than r - * fraction of the flux which has diffused into the conductor - a conductivity - c electrodynamic constant - R_m magnetic Reynolds number - dimensionless parameter     

Motion of a deformable droplet of magnetic fluid in a rotating magnetic field

The problem of the magnetic field-driven rotation of a magnetic fluid droplet in a viscous nonmagnetic fluid is solved analytically and experimentally. The shape of the droplet and the magnetic fields and velocities of both fluids are calculated in the weak-field approximation. The droplet is flattened for any relations between the parameters of the system. The instability of the axisymmetric shape of the droplet is established experimentally. A result of the instability is a sudden change in the droplet shape from a flattened ellipsoid of revolution to a triaxial ellipsoid elongated in the equatorial plane. The critical magnetic Bond number is determined. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 22–30, January–February, 2000. The work was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00182).     

Determination of a magnetic field with rotational symmetry about a given line of magnetic force

In certain technical applications when a magnetic field with rotational symmetry has to be calculated, it is often a principal requirement that a given line should be a magnetic line of force (or more accurately, that a given surface of rotation should coincide with a surface of magnetic force).An exact particular solution of the problem is found in the case when the given line of force is straight. This solution is subsequently generalized to the case of an arbitrary smooth line, approximating it by a broken line. A method is also proposed for producing and calculating a magnetic field satisfying the above conditions.The solution of this problem may be used in questions of magneto-hydrodynamics and plasmadynamics as the first approximation for the magnetic field in the case of small magnetic Reynolds numbers, when it is required that a certain line of fluid flow should coincide with a magnetic line of force.The authors would like to mention that it was due to the constant interest of E. S. Kuznetsov and his valuable advice that the present paper was completed.     

Benard convection in a non-linear magnetic fluid under the influence of a non-vertical magnetic field

This work examines the convective instability of a horizontal layer of magnetohydrodynamic fluid of variable permeability when subjected to a non-vertical magnetic field. We use a model proposed by P. H. Roberts [9] in the context of neutron stars but the results obtained are aso relevant to the area of ferromagnetic fluids. The presence of the variable permeability has no effect on the development of instabilities through the mechanism of stationary convection but influences the threshold of overstable convection which is often the preferred mechanism in non-terrestrial applications. In the context of ferromagnetic fluids, both stationary and overstable instability can be expected to be realisable possibilities.     

Instability of the quiescent state of an ideal conducting medium in a magnetic field

The linear stability of the quiescent states of an ideal compressible medium with infinite conductivity in a magnetic field is studied. It is shown by Lyapunov’s direct method that these quiescent states are unstable relative to small spatial perturbations, which decrease the potential energy (the sum of the internal energy of the medium and the energy of the magnetic field in this case). Two-sided exponential estimates of perturbation growth are obtained; the exponents in these estimates are calculated using the parameters of the quiescent states and the initial data for perturbations. A class of the most rapidly growing perturbations is separated and an exact formula to determine the rate of their increase is derived. An example is constructed of the quiescent states and the initial perturbations whose linear stage of evolution in time occurs in correspondence with the estimates. From the mathematical viewpoint, our results are preliminary, because the existence theorems for the solutions of the problems considered are not proved. Deceased. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 148–155, March–April, 1999.     

Viscous lifting of a conducting fluid in the presence of a magnetic field

Summary This paper describes the effect of a magnetic field upon the viscous lifting of a conducting fluid for two types of lifting surfaces; conducting and non-conducting. It is shown that the magnetic field produces very small effects on the film thickness and mass flow rate for the case of the dielectric plate. For the conducting plate, the effects are more pronounced and increase with larger values of the ratio of plate conductivity to fluid conductivity. The analysis employed here is simplified to the extent that the effects of surface tension are not included.