Surface waves in ferrofluids under vertical magnetic field (original) (raw)
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Non-monotonic dispersion of surface waves in magnetic fluids
Journal of Magnetism and Magnetic Materials, 1996
The dispersion relation of surface waves of a magnetic fluid in a magnetic field is studied experimentally. We verify the theoretically predicted existence of a non-monotonic dispersion relation. In particular, we demonstrate the existence of two different wave numbers occuring at the same frequency in an annular geometry.
Letter to the Editor Non-monotonic dispersion of surface waves in magnetic fluids
1996
The dispersion relation of surface waves of a magnetic fluid in a magnetic field is studied experimentally. We verify the theoretically predicted existence of a non-monotonic dispersion relation. In particular, we demonstrate the existence of two different wave numbers occuring at the same frequency in an annular geometry.
Parametrically Excited Surface Waves in Magnetic Fluids: Observation of Domain Structures
Physical Review Letters, 1998
Observations of parametrically excited surface waves in a magnetic fluid are presented. Under the influence of a magnetic field these waves have a non-monotonic dispersion relation, which leads to a richer behavior than in ordinary liquids. We report observation of three novel effects, namely: i) domain structures, ii) oscillating defects and iii) relaxational phase oscillations.
Surface waves created by low-frequency magnetic fields
European Journal of Mechanics - B/Fluids, 2005
This paper analyses the effects of a low frequency A.C. magnetic field on the free surface of a liquid metal. The action of the vertical and uniform magnetic field is twofold. First it creates forced standing surface waves which generally exhibit symmetry related to that of the container; second it triggers non-symmetric free surface instabilities superimposed on the forced regime. A previous paper considered the case of a circular cylindrical tank where axisymmetric forced standing waves caused an electric current perturbation which then excited non-axisymmetric waves at a critical A.C. field intensity. Nonlinear interaction between the symmetric and non-symmetric modes was not taken into account. The present work treats the problem from a more general standpoint. Equilibrium perturbations are developed systematically to order N 2 (where N is the magnetic interaction parameter) and at this level of approximation we also need to consider nonlinear mode interactions and electromagnetic damping. The theory applies to tanks of arbitrary shape and the O(N) irrotational motion may be described by the torsion function for the particular pool cross-section. For circular and annular tanks we then derive a system of coupled Mathieu-Hill equations for the time-development of non-symmetric surface modes. Two main types of parametric resonance are predicted, namely the single or combination mode, and the particular type observed may depend on the geometry of the tank. Results of the stability analysis are confirmed by experimental work carried out in mercury pools.
Study of small-amplitude magnetohydrodynamic surface waves on liquid metal
Physics of Plasmas, 2005
Magnetohydrodynamic (MHD) surface waves on liquid metal are studied theoretically and experimentally in the small magnetic Reynolds number limit. A linear dispersion relation is derived when a horizontal magnetic field and a horizontal electric current is imposed. Waves always damp in the deep liquid limit with a magnetic field parallel to the propagation direction. When the magnetic field is weak, waves are weakly damped and the real part of the dispersion is unaffected, while in the opposite limit waves are strongly damped with shortened wavelengths. In a table-top experiment, planar MHD surface waves on liquid gallium are studied in detail in the regime of weak magnetic field and deep liquid. A noninvasive diagnostic accurately measures surface waves at multiple locations by reflecting an array of lasers off the surface onto a screen, which is recorded by an intensified-CCD (charge-coupled device) camera. The measured dispersion relation is consistent with the linear theory with a reduced surface tension likely due to surface oxidation. In excellent agreement with linear theory, it is observed that surface waves are damped only when a horizontal magnetic field is imposed parallel to the propagation direction. No damping is observed under a perpendicular magnetic field. The existence of strong wave damping even without magnetic field suggests the importance of the surface oxide layer. Implications to the liquid metal wall concept in fusion reactors, especially on the wave damping and a Rayleigh-Taylor instability when the Lorentz force is used to support liquid metal layer against gravity, are discussed.
Journal of Fluid Mechanics, 2007
The normal field instability in magnetic liquids is investigated experimentally by means of a radioscopic technique which allows a precise measurement of the surface topography. The dependence of the topography on the magnetic field is compared to results obtained by numerical simulations via the finite element method. Quantitative agreement has been found for the critical field of the instability, the scaling of the pattern amplitude and the detailed shape of the magnetic spikes. The fundamental Fourier mode approximates the shape to within 10 % accuracy for a range of up to 40 % of the bifurcation parameter of this subcritical bifurcation. The measured control parameter dependence of the wavenumber differs qualitatively from analytical predictions obtained by minimization of the free energy.
Effect of magnetic field on parametrically driven surface waves
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 2007
Effect of magnetic field on parametrically driven References ml#ref-list-1 Stability analysis of parametrically driven surface waves in liquid metals in the presence of a uniform vertical magnetic field is presented. Floquet analysis gives various subharmonic and harmonic instability zones. The magnetic field stabilizes the onset of parametrically excited surface waves. The minima of all the instability zones are raised by a different amount as the Chandrasekhar number Q is raised. The increase in the magnetic field leads to a series of bicritical points at a primary instability in thin layers of a liquid metal. The bicritical points involve one subharmonic and another harmonic solution of different wavenumbers. A tricritical point may also be triggered as a primary instability by tuning the magnetic field.
Dynamics and stability of three-dimensional ferrofluid films in a magnetic field
Journal of Engineering Mathematics, 2017
We consider the interfacial dynamics of a thin, ferrofluid film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. The fluid is assumed to be weakly conducting, and its dynamics are governed by a coupled system of the steady Maxwell, Navier-Stokes, and continuity equations. The magnetization of the film is a function of the magnetic field, and is prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure, velocity, and magnetic fields inside the film. The potential in the gas phase is solved by means of Fourier Transforms. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape, via use of the kinematic condition, and the magnetic field. We study the three-dimensional evolution of the film to spanwise perturbations by solving the nonlinear equations numerically. The constant-volume configuration is considered, which corresponds to a slender drop flowing down an incline. A parametric study is then performed to understand the effect of the magnetic field on the stability and structure of the interface.