Dr. Hanns Walter Müller


Flow behavior of ferrofluids

A ferrofluid is a stable colloidal suspension of ferromagnetic mono-domain particles in a liquid carrier. To avoid agglomeration due to attractive dipole-dipole or Van der Vaals forces each particle is coated by long-chain molecules or by an electrostatic layer (see figure). Due to the smallness of the particles (diameter ~ 10nm) the properties of ferrofluids are substantially affected by thermal Brownian motion. When exposed to a magnetic field, a ferrofluid behaves like a paramagnetic gas of high permeability (Rosensweig).

In a static magnetic field normal to the surface, the dispersion relation for free surface waves of the form exp[i (kx-wt)] may become non-monotonous with an anomalous branch at which the frequency w decreases with the wave number k (see lines in the figure beside). If the magnetic field is sufficiently strong this phenomenon gives rise to the so called "Rosensweig instability", which is a spontaneous static deformation of the surface (Cowley & Rosensweig).

In a Faraday experiment surface waves are excited parametrically by a modulation of the effective gravity field. A careful choice of the filling depth h permits the normal and the anomalous dispersion branches to be measured (see symbols in the figure beside it) . Furthermore the parametric driving  is predicted to delay of the Rosensweig instability.  This situation is analogous to the stabilization of a rigid pendulum in its unstable rest state by a modulation of the suspension point [1,2].

One of the most exciting properties of ferrofluids is related to the coupling of the microscopic particle rotation to the macroscopic vorticity of the flow.  In a static magnetic field the magnetic torque prevents particles from rotating and thus causes an extra viscous dissipation in the carrier liquid,  which leads to an enhanced effective viscosity, the so called rotational viscosity (Mc Tague, Shliomis). When measuring this quantity, the experimental data is usually superimposed by the shear viscosity, whose contribution is typically  two orders of magnitude larger. In collaboration with the Theoretische Physik and the Technische Physik of the Universität Saarbrücken we have constructed a device by which the rotational viscosity can be measured without a parasitic shear flow [3].

The reverse situation, in which an oscillating magnetic field pumps energy into a macroscopic ferrofluid flow, can also be observed (Barci, Zeuner). This effect, first predicted theoretically (Shliomis) leads to a negative viscosity increment, denoted as "negative viscosity". The negative and the rotational viscosity are intimately related to the presence of suspended particles in the fluid. In a situation in which the determinsitic forces  (magnetic torque, viscous torque on each particle) prevail over thermal fluctuations, it is possible to design an experimental arrangement, by which the onset of particle rotation can be detected in a magnetometric resonance experiment [4].

My acivities on ferrofluids are performed in the framework and with support of the  Sonderforschungsbereich  277 "Grenzflächenbestimmte Materialien" of the Universität Saarbrücken.

Recent publications:

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Hanns Walter Müller
Last modified: March 16, 2001