Magnetic Faraday instability

Abstract

In a magnetic fluid, parametrically driven surface waves can be excited by an external oscillating magnetic field. A static magnetic field changes the restoring forces and damping coefficients of the various surface waves. This property enables the excitation of both subharmonic and harmonic responses of the standing waves.

Tunable diffusion of magnetic particles in a quasi-one-dimensional channel

“…Recently there has been an increased interest in the study of the structural and the dynamical properties of magnetic confined (in particular on the meso-and nano-scale) systems due to the possibility of biomedical [1][2][3] and engineering applications [4]. Examples of these magnetic systems are ferrofluid nanofilms [5][6][7] and magnetorheological (MR) fluids [8,9]. For instance, the translational dynamics of a mesoscopic 3D system of permanent magnetic dipoles was studied in Ref.…”

On the Hill Equation Describing Oscillations of a Ferrofluid Free Surface in a Vertical Magnetic Field

“…For a very simple form of the oscillating part of the magnetic field, the deformation is described by a more complex law than for the mechanical vibration at the origin of the Faraday instability. We illustrate that discussion further for an experimentally realized situation (Mahr 1998;Pi et al 2000). Adapting the method developed originally by Ince (1915Ince ( /1916 and Erdelyi (1934), we show first that the necessary condition to have a possible oscillating solution differs from the well known CowleyRosensweig criterion for static instability (Rosensweig 1997), and secondly that the marginal state leads to two possible independent resonant conditions.…”

“…We limit the discussion to m h = 0, as it corresponds to some experiments at δ B = 1 (Mahr 1998;Pi et al 2000), and also to the theoretical situation considered by Blums et al (1997) d z + a 2 y(z) = 0, where a 2 must be a positive integer n 2 to obtain a periodic solution in the variable z in the form of cos(n z) or sin(n z). Therefore, the periodic solution of the equation…”

“…However, they failed to show the difference between a case where the magnetic field contains an oscillating part (Mahr 1998;Pi et al 2000) and the one where a classical vertical vibration is combined with a constant vertical magnetic field. In the first situation, the magnetic field introduces the Kelvin force in the momentum balance as proportional to the square of the magnetic field (Hennenberg et al 2009(Hennenberg et al , 2010 whereas for the second one, the classical Faraday vibration adds simply to the gravity external force.…”

Modelling of an Oscillatory Magnetic Field Action on a Ferrofluid Layer

“…Indeed, as we will show, the momentum balance will introduce a function containing also the square of the magnetic field pulsation in the Laplace equation. This is the main difference between the simplest Faraday vertical vibration and the oscillating magnetic field (Müller 1998;Mahr and Rehberg 1998;Embs et al 2007). Years ago, Mahr and Rehberg (1998) studied such an oscillating magnetic field and exciting experiences appeared recently to illustrate parametric forcing due to an oscillating magnetic field with a very low frequency, in the study of patterns (Pi et al 2000;Ko et al 2002).…”