Electrochemical characterization of Ni–Fe alloy codeposition under MHD control

The nickel–iron alloy electrodeposition is affected by a superimposed magnetic field. Some previous papers [Msellak et al., Magnetohydrodynamics, 39:487–493, 2003 and Msellak et al., J Magn Magn Mat, 281:295–304, 2004] have exhibited some dramatic changes in iron amount and morphology of these deposits. As it is usual for a magnetic field up to 1 T, no charge transfer effect can be expected, and the observed modifications can be explained by the magnetohydrodynamic convection that controls the iron species flux during the electrochemical reaction. By electrochemical impedance spectroscopy and physical investigations (scanning electron microscopy, X-ray diffraction, and inductively coupled plasma), the reduction process is analyzed, the characteristic parameters of the mechanism are determined, and the magnetic field effects can be quantified. Contribution to special issue on “Magnetic field effects in Electrochemistry”.     

Poloidal–toroidal decomposition in a finite cylinder. I: Influence matrices for the magnetohydrodynamic equations

The Navier–Stokes equations and magnetohydrodynamics equations are written in terms of poloidal and toroidal potentials in a finite cylinder. This formulation insures that the velocity and magnetic fields are divergence-free by construction, but leads to systems of partial differential equations of higher order, whose boundary conditions are coupled. The influence matrix technique is used to transform these systems into decoupled parabolic and elliptic problems. The magnetic field in the induction equation is matched to that in an exterior vacuum by means of the Dirichlet-to-Neumann mapping, thus eliminating the need to discretize the exterior. The influence matrix is scaled in order to attain an acceptable condition number.     

Aharonov–Bohm effects in magnetohydrodynamics

It is shown that an Aharonov–Bohm (AB) effect exists in magnetohydrodynamics (MHD). This effect is best described in terms of the MHD variational variables (Kats, 2004; Yahalom and Lynden-Bell, 2008; Yahalom, 2010) [1], [10], [12]. If a MHD flow has a non-trivial topology some of the functions appearing in the MHD Lagrangian are non-single-valued. These functions have properties similar to the phases in the AB celebrated effect (Aharonov and Bohm, 1959; van Oudenaarden et al., 1998) [2], [3]. While the manifestation of the quantum AB effect is in interference fringe patterns (Tonomura et al., 1982) [4], the manifestation of the MHD Aharonov–Bohm effects are through new dynamical conservation laws.     

Application of Reynolds stress transport turbulence closure models to flows affected by Lorentz and buoyancy forces

The effect of magnetic field strength and orientation on two types of electromagnetically influenced turbulent flows was studied numerically under the Reynolds averaged Navier–Stokes (RANS) framework. Previous work (Wilson et al., 2014) used an electromagnetically extended linear eddy-viscosity model, whilst the current paper focuses on the performance of a more advanced Reynolds stress transport type model both with and without electromagnetic modifications proposed by Kenjereš et al. (2004). First, a fully-developed 2D channel flow is considered with a magnetic field imposed in either the wall-normal or streamwise direction. Both forms of the RSM gave good agreement with the DNS data for the wall-normal magnetic field across the range of Hartmann numbers with the additional electromagnetic terms providing a small, but noticeable, difference. For the streamwise magnetic field, where electromagnetic influence is only through the turbulence, the electromagnetically extended RSM performed well at moderate Hartmann numbers but returned laminar flow at the highest Hartmann number considered, contrary to the DNS. The RSM results were, however, significantly better than the previous eddy-viscosity model predictions. The second case is that of unsteady 3D Rayleigh–Bénard convection with a magnetic field imposed in either a horizontal or vertical direction. Results revealed that a significant reorganization of the flow structures is predicted to occur. For a vertically oriented magnetic field, the plume structures increase in number and become thinner and elongated along the magnetic field lines, leading to an increase in thermal mixing within the core in agreement with Hanjalić and Kenjereš (2000). With a horizontal magnetic field, the structures become two-dimensional and a striking realignment of the roll cells’ axes with the magnetic field lines occurs. The results demonstrate the capability of the Reynolds stress transport approach in modelling MHD flows that are relevant to industry and offer potential for those wishing to control levels of turbulence, heat transfer or concentration without recourse to mechanical means.     

Hydromagnetic parametric resonance instability of two superposed conducting fluids in porous medium

Rayleigh–Taylor instability of a heavy fluid supported by a lighter one through porous medium, in the presence of a uniform, horizontal and oscillating magnetic field is studied. The fluids are taken as viscous (obeying Darcy's law), uniform, incompressible, and infinitely conducting. The amplitude of the oscillating part of the field is taken to be small compared with its steady part. The dispersion relation is obtained in the form of a third-order differential equation, with time as the independent variable and with periodic coefficients, for the vertical displacement of the surface of separation of the two fluids from its equilibrium position. The oscillatory magnetic field of frequency ω$\omega$ and steady part _H0$H_0$ has a stabilizing influence on a mode of disturbance which is unstable in a steady magnetic field of strength _H0$H_0$. It is found that the oscillatory magnetic field and porosity of the porous medium have stabilizing effects, while the medium permeability has a destabilizing influence on the considered system. For a constant value of any of these physical parameters, the system has been found to be unstable (for small wavenumbers) as well as stable afterwards after a definite wavenumber value. The marginal stability case of parametric resonance holds when _M1=_M2=0$M_1=M_2=0$ (and hence m=0$m=0$), in which the characteristic exponents, and the corresponding solutions for u$u$ break down, is also investigated in detail. It is found, to order ?$?$, that the effect of an oscillating magnetic field has no stabilizing influence on a disturbance which is marginally stable in the steady magnetic field; while to order ?²${?}^2$, and when the magnetic field oscillates, a resonance between this mode of disturbances and the oscillating field leads to instability when _ρ2>_ρ1${\rho }_2>{\rho }_1$. It is found also, in this resonant case, that all the constant or varied physical parameters, mentioned above, have destabilizing influences on the considered system. Finally, the other two resonance points appear in non-porous media (i.e., when m=±iω$m=\pm \mathrm{i}\omega$ and m=±2iω$m=\pm 2\mathrm{i}\omega$), are disappeared here due to the presence of the porous medium.     

Electrically induced flows in the vicinity of a dielectric stripe on a conducting plane

We report a theoretical and experimental study of the hydrodynamic flow induced by an a.c. electric field in the vicinity of a dielectric stripe deposited on a conducting plate. In the theoretical part, we model the stripe as a small change of the surface capacitance of the plate, and a perturbative approach is used to perform the calculations. This approach predicts an outwards rectified electro-osmotic slip along the surface that generates two steady counter-rotating rolls, the size of which decreases with the frequency. In the experimental section, we use tracers to determine the structure of the flow and investigate its dependence on the frequency and the amplitude of the applied voltage. The structure and amplitude of the observed flow compares satisfactorily with the theoretical analysis. This could guide the design of surface-controlled flows and help to understand the collective behavior of colloids near electrodes. Received 20 June 2002 RID="a" ID="a"e-mail: nadal@crpp.u-bordeaux.fr     

A stability criterion for an infinitely long Hall-Héroult cell

This study is concerned with the stability of a Hall-Héroult cell which is assumed to be infinitely long. The modelling used leans on the magnetohydrodynamic theory for incompressible fluids. The presence of longitudinal electrical current inside the cell are taken into account. The influences of these last ones, on the stability of the cell, are studied.     

Slow magnetohydrodynamic flow past a circular cylinder

Oseen’ approximations are used to study the slow motion of a viscous, incompressible, electrically conducting fluid past a circular cylinder in the presence of a uniform aligned magnetic field. Using series truncation method, the analytical solutions for the first three terms in the Fourier sine series expansion of the stream function are obtained. Numerical values of the tangential drag for different values of magnetic interaction parameter and viscous Reynolds number are calculated.     

Numerical study of homogeneous dynamo based on experimental von Kármán type flows

A numerical study of the magnetic induction equation has been performed on von Kármán type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von Kármán sodium (VKS) experiment designed to study dynamo action in an unconstrained flow. The mean velocity fields have been measured for different configurations and are introduced in a periodic cylindrical kinematic dynamo code. Depending on the driving configuration, on the poloidal to toroidal flow ratio and on the conductivity of boundaries, some flows are observed to sustain growing magnetic fields for magnetic Reynolds numbers accessible to a sodium experiment. The response of the flow to an external magnetic field has also been studied: The results are in excellent agreement with experimental results in the single propeller case but can differ in the two propellers case.     

Electroweak interactions between intense neutrino beams and dense electron-positron magnetoplasmas

The electroweak coupling between intense neutrino beams and strongly degenerate relativistic dense electron-positron magnetoplasmas is considered. The intense neutrino bursts interact with the plasma due to the weak Fermi interaction force, and their dynamics is governed by a kinetic equation. Our objective here is to develop a kinetic equation for a degenerate neutrino gas and to use that equation to derive relativistic magnetohydrodynamic equations. The latter are useful for studying numerous collective processes when intense neutrino beams nonlinearly interact with degenerate, relativistic, dense electron-positron plasmas in strong magnetic fields. If the number densities of the plasma particles are of the order of 10³³ cm^-3, the pair plasma becomes ultra-relativistic, which strongly affects the potential energy of the weak Fermi interaction. The new system of equations allows several neutrino-driven streaming instabilities involving new types of relativistic Alfvén-like waves. The relevance of our investigation to the early universe and supernova explosions is discussed. Received 11 September 2002 Published online 4 February 2003 RID="a" ID="a"Permanent address: Department of Physics, Tbilisi State University, Chavchavadze 3, Tbilisi 38028, Georgia. RID="b" ID="b"Also at the Department of Plasma Physics, Ume? University, 90187 Ume?, Sweden; and the Center for Interdisciplinary Plasma Science, Max-Planck Institut für Plasmaphysik und extraterrestrische Physik, Postfach 1312, 85741 Garching, Germany. e-mail: ps@tp4.ruhr-uni-bochum.de RID="c" ID="c"Permanent address: Department of Plasma Physics, Ume?University, 90187 Ume?, Sweden.