Experimental investigation of the decomposition of a cylindrical layer of a magnetizing liquid under the action of magnetic forces

Arkhipenko, V. I.; Barkov, Yu. D.

doi:10.1007/bf00920775

Cited by 2 publications

(3 citation statements)

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“…These authors identified soliton solutions to this model and showed that they are elevation waves (with a central hump) if 1 < B < 3/2 and are depression waves (with a central dip) if 3/2 < B < 9, where B denotes the magnetic Bond number. For B < 1, the jet is unstable (Arkhipenko and Barkov, 1980). More recently, Bourdin et al (2010) reported the first experimental observation of such axisymmetric waves and found a good agreement with the KdV predictions.…”

Section: Introductionmentioning

confidence: 62%

“…Due to surface tension, it is well-known that an inviscid liquid jet (in the absence of gravity) is unstable to long-wave disturbances with wavelength greater than the jet circumference, eventually leading to the formation of disconnected droplets (Rayleigh, 1878). It has been observed however that a magnetic field can be used to suppress this Rayleigh instability for a jet composed of a ferrofluid (Arkhipenko and Barkov, 1980). Ferrofluids are colloidal liquids made of ferromagnetic nano-particles suspended in a carrier Newtonian fluid (e.g.…”

Section: Introductionmentioning

confidence: 99%

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An operator expansion method for computing nonlinear surface waves on a ferrofluid jet

Guyenne

Pźrźu

2016

Journal of Computational Physics

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We present a new numerical method to simulate the time evolution of axisym- metric nonlinear waves on the surface of a ferrofluid jet. It is based on the reduction of this problem to a lower-dimensional computation involving surface variables alone. To do so, we describe the associated Dirichlet–Neumann op- erator in terms of a Taylor series expansion where each term can be efficiently computed by a pseudo-spectral scheme using the fast Fourier transform. We show detailed numerical tests on the convergence of this operator and, to illus- trate the performance of our method, we simulate the long-time propagation and pairwise collisions of axisymmetric solitary waves. Both depression and elevation waves are examined by varying the magnetic field. Comparisons with weakly nonlinear predictions are also provided

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Section: Introductionmentioning

confidence: 62%

Section: Introductionmentioning

confidence: 99%

An operator expansion method for computing nonlinear surface waves on a ferrofluid jet

Guyenne

Pźrźu

2016

Journal of Computational Physics

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“…When Bo m ≤ 1, the capillary effects are greater than the magnetic ones, and an instability occurs [ω 2 ≤ 0 in Eq. ( 1)]: the cylindrical ferrofluid layer is unstable to disturbances whose wavelengths λ ≥ 2πR/ √ Bo m − 1, and breaks up into a string of connected drops [9,12]. This is the magnetic analogue of the surface-tension-driven Rayleigh-Plateau instability when a thin cylindrical jet of a usual fluid breaks into a set of drops [13].…”

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confidence: 99%

Observation of Axisymmetric Solitary Waves on the Surface of a Ferrofluid

2010

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We report the first observation of axisymmetric solitary waves on the surface of a cylindrical magnetic fluid layer surrounding a current-carrying metallic tube. According to the ratio between the magnetic and capillary forces, both elevation and depression solitary waves are observed with profiles in good agreement with theoretical predictions based on the magnetic analogue of the Korteweg-deVries equation. We also report the first measurements of the velocity and the dispersion relation of axisymmetric linear waves propagating on the cylindrical ferrofluid layer that are found in good agreement with theoretical predictions.PACS numbers: 47.65.Cb,47.35.Fg Solitary waves or solitons are localized nonlinear waves that propagate almost without deformation due to the balance between the nonlinearity and the dispersion. Since the first observation of a solitary wave on the freesurface of water by Russel [1], and its interpretation using the Korteweg-de Vries equation (KdV) [2], it has been shown that the KdV equation describes a large class of solitons observed in various situations: acoustic waves on a crystal lattice, plasma waves, hydrodynamics internal or surface waves, elastic surface waves, and waves in optical fibers [3]. Most of them involve a localized elevation disturbance propagating within a quasi-one-dimensional plane system. Observations of axisymmetric solitary waves governed by the KdV equation are scarce [4], and mainly concern waves in rotating fluids confined in a tube or on vortex lines. More recently, Bashtovoi et al. derived a KdV equation with an axisymmetric solitary waves solution propagating on the surface of a cylindrical magnetic fluid layer submitted to a magnetic field [5,6]. Without gravity, the stability of the cylindrical magnetic fluid layer is governed by the ratio between the magnetic force and the capillary one. According to its ratio, axisymmetric elevation (hump-like) or depression (hole-like) solitary waves are predicted with a subsonic or supersonic velocity [5,6]. To our knowledge, direct observation of axisymmetric magnetic solitary waves have never been reported.In this Letter, we report the first observation of axisymmetric solitary waves on the surface of a cylindrical ferrofluid layer submitted to an azimuthal magnetic field. Depending on the strength of the field, elevation or depression solitary waves are observed on the ferrofluid surface. A ferrofluid is a stable suspension of nanometric magnetic particles diluted in a carrier liquid (water or oil) that responds to an external applied magnetic field [7,8]. Although the solitary waves are damped by viscous dissipation, we have shown that they keep the self-similar profile given by the solution of the KdV equation on a propagation length larger than their typical scale. Moreover, we also report the first measurement of the velocity and dispersion relation of axisymmetric magnetic linear waves in this system in good agreement with the theoretical predictions [9].The experimental setup is shown in Fig. 1. It consists...

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Experimental investigation of the decomposition of a cylindrical layer of a magnetizing liquid under the action of magnetic forces

Cited by 2 publications

References 7 publications

An operator expansion method for computing nonlinear surface waves on a ferrofluid jet

An operator expansion method for computing nonlinear surface waves on a ferrofluid jet

Observation of Axisymmetric Solitary Waves on the Surface of a Ferrofluid

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