Non-conducting Fluid Research Articles

Theory of lifting surface in fluids of high electrical conductivity

This paper examines the motion of an inviscid and perfectly conducting fluid past an airfoil in the presence of a magnetic field orthogonal to the motion direction. The integral equation of the theory of lifting surface is deduced and the limit case of the lifting line is also studied. For the latter case a simple relation is given which permits the calculation of the lift in the case of a conducting fluid as a function of the lift of an equivalent airfoil placed in a non-conducting fluid.

On space-time permeated by the relativistic charged fluid

The behaviour of the self-gravitating charged fluid with constant electric conductivity and constant magnetic permeability is investigated by choosing a suitable orthonormal tetrad frame. The properties of the charged fluid with the electric field orthogonal to the magnetic field admitting groups of motion with respect to the flow vector are studied. It is proved that this fluid degenerates into non-conducting fluid if it allows groups of motion with respect to its flow vector. Moreover, for the convection-free charged fluid with electric field orthogonal to the magnetic field a necessary and sufficient condition for null conductivity is found.

Small oscillations of a liquid drop with surface charge

A viscous incompressible non-conducting fluid forms a spherical drop with an electric charge distributed uniformly over its surface. Small oscillations about the spherical shape are possible because of surface tension; a transcendental equation is given, to determine their frequency and damping. If the electric charge is sufficiently large, the drop is unstable. But the principle of exchange of stabilities is valid, and the maximum charge consistent with stability is given by Rayleigh's calculation for a conducting, inviscid fluid drop.

The motion of magnetizable fluid in a rotating homogeneous magnetic field: PMM vol. 42, no. 4, 1978, pp. 668–672

A general steady solution of cylindrically symmetric form is obtained for equations that define the motion of a magnetizable incompressible nonconducting fluid in a homogeneous magnetic field rotating at constant angular velocity. The obtained solution is used for determining the velocity and internal moment of momentum of a magnetizable fluid between two coaxial cylinders rotating at different angular velocities. It is shown that in the case of fixed cylinders a fluid posessing an internal moment of momentum is in motion, unlike the conventional viscous fluid, various limit cases are considered when either the inner or outer cylinder is absent, when one of the cylinder is fixed and the other freely rotates, and when the two cylinders freely rotate.

Influence of a uniform magnetic field on the hydroelastic instability of a ferromagnetic plate

The static hydroelastic instability of a two-dimensional ferromagnetic panel in a uniform oblique magnetic field, one side of which is exposed to a high velocity flow of a non-conducting incompressible fluid is investigated. The elastic panel is considered to be thin, of infinite width, simply supported along its edges and composed of soft linear magnetic material. The analysis is based on the small bending theory of thin plates, a simple model of the magnetoelastic interaction and classical potential flow theory. Galerkin's method and Fourier transforms are used. The divergence velocity is determined for various values of the magnetic field. It is found that there exists a critical angle, βcr, of the oblique magnetic field at which the effect of the magnetic field on the divergence velocity vanishes. For β βcr, the divergence velocity increases with an increase in the magnetic field.

Hydroelastic Instability of Infinitely Long Magnetoelastic Plates

The hydroelastic instability of an infinitely long ferromagnetic plate exposed on one side to a high velocity flow of a heavy nonconducting fluid and placed in a uniform magnetic field normal to the plate is soft linear material. The analysis is based on the small deflection plate theory, a quasistatic model of the magnetoelastic interaction and the classical linearized potential flow theory. Assuming a plate deflection in the form of traveling waves, Galerkin's method and Fourier transforms are used to derive a characteristic equation, from which both the velocities of divergence and flutter are determined for a wide range of mass ratio and magnetic field. An increase in the transverse magnetic of mass ratio and magnetic field. An increase in the transverse magnetic field is found to decrease both the velocities of divergence and flutter.

A novel form of the MHD Rayleigh–Taylor instability

When a mutually perpendicular horizontal magnetic field and electric current are imposed upon an electrolytic liquid in a tank covered by a lighter nonconducting fluid, the interface can become unstable. In the experiment described in this paper the tank floor is stepped so that only part of the interface becomes unstable. The result is a distinctive arch-like configuration of the electrolyte, which finally disintegrates to break the current path, but which will continue to repeat itself.

On the Possibility of a Hydrodynamic Model of the Electron

We explore the possibility that the mutual repulsive forces of a uniformly charged sphere could be kept in balance dynamically by a steady circulation of the material, which is assumed to be a nonconducting perfect fluid of uniform density. An exact solution is obtained of Maxwell's equations and of the hydrodynamic equations in the nonrelativistic approximation, which satisfies the boundary conditions on the surface of the sphere. In this solution all the components of the velocity and of the magnetic field are found to vanish on the surface, but not the electric field. The pressure can also be made to vanish on the surface, but in the interior it turns out to be negative, which makes the present solution unacceptable.

Anisotropic surface waves under a vertical electromagnetic force. Part 2. Experimental demonstration

It was shown theoretically in part 1 (Shercliff 1969) that, when a horizontal magnetic field and electric current field are imposed upon a conducting liquid with a free surface, waves excited at the surface have an anisotropic dispersion relation. Here the possibility of demonstrating this phenomenon in the laboratory is considered. The analysis is completed for waves a t the interface between a conducting and non-conducting fluid of similar density, taking full account of surface tension, and then viscosity. Surface tension is found to have a considerable influence in reducing the degree of anisotropy to be expected. The problem of choosing suitable experimental parameters is discussed, and an apparatus is described in which it was possible to demonstrate the existence of anisotropic surface waves, and to compare the phase velocity with the theoretical results. Also, an experiment is described which verifies the relationship between the orientation of the anisotropy and the relative orientation of the imposed magnetic and current fields.

On the spin-up of a stably stratified, electrically conducting fluid. Part 1: Spin-up controlled by the hartmann layer

Abstract The linear spin-up of a stably stratified, electrically conducting fluid within an electrically insulating cylindrical container in the presence of an applied axial magnetic field is analyzed for those cases in which electric currents generated within the steady Hartmann boundary layer control the fluid interior. It is shown how to obtain the known spin-up times for a homogeneous, nonconducting fluid (τ = E -½), a stably stratified, nonconducting fluid (τ = (σS/E, E −1) and a homogeneous conducting fluid (τ = α−1 E -½) from the present formulation where τ = v/ωt, E = v/ωL 2, σS = vN2/κω2 and 2α2 = σB2/pω. The problem is solved in the parameter range E≪α2≪1, α2/E≪σS using the Laplace transform and two new spin-up times are obtained. Combined into one expression, they are τ = (1 + δ)α−1E-½ where δ = σμv. The spin-up mechanism is investigated and it is found that, in contrast to the homogeneous, conducting case, torsional Alfven waves may be instrumental in the spin-up of a stratified conducting flu...

The velocity of magnetohydrodynamic waves in general relativity

The energy-momentum tensor for a perfect fluid with infinite conductivity is modified slightly by attributing a proper energy content to a field of tension, as proposed by Cattaneo, for a perfect nonconducting fluid, and it is shown that with this modification the velocities of the hydrodynamic waves in the fluid do not exceed C. This contrasts with the standard theory in which a lower limit must be placed on the compressibility of the fluid to prevent the velocity of the ‘fast’ hydrodynamic wave fron exceeding c. The velocity of the Alfven wave is changed only slightly and is always less than c as in the standard theory.

On laminar two-phase flows in magnetohydrodynamics

We consider the Hartmann flow of a conducting fluid in the channel between two horizontal insulating plates of infinite extent, there being a layer of non-conducting fluid between the conducting liquid and the upper channel wall. A suitable volumetric flow-rate factor is defined, and it is shown that significant increases can be obtained in the flow-rate of the conducting fluid for suitable ratios of the depths and viscosities of the two fluids.

Heat-Up of Rotating Stratified Fluid

A heat-up process of a rotating stratified fluid in a circular cylinder which occurs as a response to a small change of the side wall temperature is analyzed in a framework of the linearized Boussinesq approximation. A meridional circulation induced by the buoyancy layer along the side wall causes both a heat-up and a spin-up process of the inner, non-conducting inviscid fluid. These processes continue until a quasi-steady asymptotic state is reached. The time scale of the transient process tends to the heat-up time of a non-rotating stratified fluid for the case of the strong stratification, and to the spin-up time of the homogeneous fluid for the case of the order unity stratification. The initial meridional circulation, and the asymptotic distribution of the azimuthal velocity and the temperature are also given.

Some factors affecting the rotation of a dielectric in an electrorheological medium

It has been shown experimentally that the rotational speed of a dielectric in a nonconducting disperse medium depends on the concentration of the disperse phase and on the electrode geometry. The results are compared with those pertaining to the rotation of a dielectric in a pure homogeneous nonconducting fluid.

Note on slow rotation or rotary oscillation of axisymmetric bodies in hydrodynamics and magnetohydrodynamics

Results for three interrelated problems are obtained by making use of solutions of boundary-value problems obtained in a different context. The first one concerns a thin rigid circular disk rotating in a slow stream of viscous fluid, both when the fluid is conducting and when it is non-conducting. For the case of a conducting fluid formulae are given for both small and large Hartmann numbers. The second problem concerns a disk performing simple harmonic rotary oscillations about its axis of symmetry in a non-conducting viscous fluid which is at rest at infinity. The last problem is that of an arbitrary axisymmetric solid oscillating about its axis of symmetry in a bounded viscous fluid, and the solution is illustrated by the case of an oscillating disk.

Electrohydrodynamic instability in plane layers of fluid

The instability of a plane layer of non-conducting fluid which is in hydrostatic equilibrium between two semi-infinite conducting fluids with surface charges is discussed for both inviscid and viscous fluid models. It is shown that for both the inviscid and viscous fluid cases, the criteria for instability are the same. Consideration is given to the relevance of the results in explaining the mechanism by which the presence of an electric field promotes more readily the coalescence of water droplets on a water surface by viewing the onset of disruption of the air film as the instability of the air film under the action of the electrostatic field produced by the surface charges on the water surfaces.

Steady rotation of a body of revolution in a conducting fluid

We investigate the steady rotation of an insulating body of revolution in an unbounded electrically conducting fluid permeated by a uniform axial applied magnetic field. The assumptions of a small magnetic Reynolds number (Rm ≪ 1, i.e. the weakly conducting situation) and negligible inertia forces compared with the magnetic forces (R/M2 ≪ 1) permit us to suppress the inflow at the poles and outflow at the equator, which normally occurs for a non-conducting viscous fluid ((12), pp. 436–439). Thus in the case of the sphere, we find an exact solution of the reduced equations in terms of an infinite series of Legendre polynomials of order 1 with coefficients which are the ratios of modified spherical Bessel functions. This is the canonical problem by which results for arbitrary bodies of revolution are obtained.

Stability of laminar magnetofluid flow along a parallel magnetic field

A perfect magnetofluid model is used, without viscosity or resistivity. The simpler velocity and magnetic profiles are classified into stable and unstable groups. The analysis takes account of exponential and non-exponential time dependence, and of rigid and free boundaries.A variety of stability criteria are established, and related to similar results in non-conducting fluid mechanics. A constant magnetic field is shown to stabilize some velocity profiles but destabilize others.

Calculation of the boundary layer on the electrically conducting wall of a plane channel

There are presently available quite a large number of works devoted to the study of the motion of an electrically conducting fluid in boundary layers formed on electrodes or on the nonconducting walls of various MHD devices. However, the methods of solving the boundary layer equations in these studies are based on various simplifying assumptions which allow the problem to be reduced to the solution of a system of ordinary differential equations. Thus, in [1] there is imposed on the flow the special magnetic fieldH∼1/√x, which enables the problem to be reduced to the self-similar form, while in the studies of other authors [2, 3] either the solution is sought in the form of expansions in x, or it is assumed that the problem is locally self-similar [4]. In the present paper we construct the solution of the MHD boundary layer equations which is obtained by one of the numerical methods which has long been used for solving the boundary layer equations for a nonconducting fluid.

Magnetohydrodynamic flow in a curved pipe

The effect of a transverse magnetic field on the steady motion of a conducting, viscous and incompressible liquid through a pipe of circular crossection, coiled in a circle is studied in this paper. The solution is obtained by successive approximations in ascending powers of the Hartmann number; the first approximation corresponds to the non-magnetic case, formulated and discussed by Dean1). It is assumed that the walls of the pipe are nonconducting and the radius of the cross-section is small in comparison with that of the circle in which the pipe is coiled. The stream-lines in the central plane and the projection of the stream-lines on a normal section are shown graphically and are compared with those of a non-conducting fluid.