Identification of dominant modes in the interface between two conducting fluids (original) (raw)
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Interface reconstruction between two conducting fluids applying genetic algorithms
IEEE Transactions on Magnetics, 2004
In magnetic fluid dynamics, there appears the problem of reconstruction of free boundary between conducting fluids, e.g., in aluminum electrolysis cells. We have investigated how the interface between two fluids of different conductivity of a highly simplified model of an aluminum electrolysis cell could be reconstructed by means of external magnetic field measurements using a simple genetic algorithm.
Surface current reconstruction using magnetic field tomography
IEEE Transactions on Magnetics, 2004
The identification of characteristics or shape reconstruction of boundary surfaces are inverse problems arising in industrial applications, e.g., in magnetic fluid dynamics. We have investigated the identification of the interface between two conducting fluids using multichannel magnetic field measurements (magnetic field tomography). We considered a highly simplified model of an aluminum electrolysis cell consisting of a cylinder containing two compartments with different conductivities. Numerical simulations using the finite element method (FEM) have been evaluated. Additionally, magnetic field measurements taken from an experimental setup of this cylindrical object have been used as a reference for comparison. We propose a new test problem for the evaluation of inverse methods which consists in the estimation of the interface shape characteristics based on the current density distribution in the vicinity of the deformed interface using magnetic field measurements.
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We develop a systematic method to derive all orders of mode couplings in a weakly nonlinear approach to the dynamics of the interface between two immiscible viscous fluids in a Hele-Shaw cell. The method is completely general: it applies to arbitrary geometry and driving. Here we apply it to the channel geometry driven by gravity and pressure. The finite radius of convergence of the mode-coupling expansion is found. Calculation up to third-order couplings is done, which is necessary to account for the time-dependent Saffman-Taylor finger solution and the case of zero viscosity contrast. The explicit results provide relevant analytical information about the role that the viscosity contrast and the surface tension play in the dynamics of the system. We finally check the quantitative validity of different orders of approximation and a resummation scheme against a physically relevant, exact time-dependent solution. The agreement between the low-order approximations and the exact solution is excellent within the radius of convergence, and is even reasonably good beyond this radius.
Journal of Fluid Mechanics, 2007
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Forward simulations for free boundary reconstruction in magnetic fluid dynamics
Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2003
In many industrial applications of magnetic fluid dynamics it is important to control the motion of the surface of liquids. In aluminium electrolysis cells, large surface deformations of the molten aluminium are undesired, and it would be useful to have the possibility to recognize the surface deviation. This includes the problem of reconstructing a free boundary between the conducting fluids. We have investigated how the interface between two fluids of different conductivity assumed in a highly simplified model of an aluminium electrolysis cell could be reconstructed by means of external magnetic field measurements. Forward simulations of the magnetic field generated by the impressed current are done by applying the FEM software code FEMLAB. Several interface shapes which can be realized in experiments are investigated and a strategy for identifying the main interface characteristics using magnetic field measurements as an initial guess to the solution of the inverse problem is proposed.
Waves and instability at the interface of two flows of miscible magnetic and non-magnetic fluids
Journal of Fluid Mechanics, 2023
This study presents the results of a numerical simulation of two horizontal flows of miscible magnetic and non-magnetic fluids at low Reynolds numbers in a vertical uniform magnetic field. The problem is solved by taking into account the dependence of the viscosity and magnetization of the fluid on the concentration of the magnetic phase, and the dependence of the magnetic field on the concentration. Four flow modes are found: the diffusion mixing mode with a flat diffusion front, the wave mode and two different plug flow modes. In the first of them, the growing wave instability forms the plugs, whereas in the second, the growing magnetostatic instability does. A combination of dimensionless criteria is found that determines the transition from one mode to another. The dependences of the phase velocity of the waves on the diffusion front and the period of the oscillations of the front near the point of the confluence of the two flows on dimensionless criteria are found.
Theoretical models for AC-field probing of complex magnetic fluids
Journal of Magnetism and Magnetic Materials, 2003
Description of the magneto-orientational dynamics of single-domain ferroparticles embedded in a viscoelastic fluid or in a weak gel is constructed on the basis of the Langevin equation that takes into account the non-Newtonian properties of the matrix and the Brownian motion of the particle. For the mentioned complex media, dynamic magnetic susceptibilities are obtained and shown to possess some interesting quasi-resonance properties. r (Y.L. Raikher). 0304-8853/03/$ -see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 -8 8 5 3 ( 0 2 ) 0 1 0 9 7 -1
Magnetohydrodynamic instability of a two fluid interface
Journal of Magnetism and Magnetic Materials, 1992
The stability of a gas cylinder (density p) immersed in a liquid (density p') subjected to capillary, pressure gradient, inertia and electro-magnetic forces has been developed analytically and numerically. A general hydromagnetic eigenvalue relation describing the characteristics of that model is deri,,ed based on the linearized perturbation technique, in the abscence of a magnetic field, the model is only unstable to axisymmetric disturbances whose wavelength is longer than the circumference of the gas cylinder and stable in all other disturbance states. The instability of the model rapidly decreases with increasing (if~p) but can never be suppressed, however large the (if~p) value is. The magnetic field has a strong stabilizing effect on all perturbation modes for all wavelengths. Its influence is to decrease the wavelength at which the capillary instability occurs. The latter could be completely suppressed above a certain value of the applied magnetic field strength, independent of (if~p) values, then the stability arises. However, in a two-dimensional perturbation (k = 0, k is the axial wavenumber) it is found that the capillary force remains unaffected by such a magnetic field. The present resulls coincide with our results [A.E. Radwan, J. Magn. Magn. Mater. 72 (1988) 219] if we neglect here the gas inertia force and with some Chandrasekhar's results [S. Chandrasekh,~,, Hydrodynamic and Hydromagnetic Stability (Dover. New York, 1981)] with appropriate choices. 0304-8853/92/$05.00