Berlin 2008 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 6: Ferrofluids

DY 6.4: Talk

Monday, February 25, 2008, 15:15–15:30, A 053

Rolling ferrofluid drop on the surface of a liquid — •Verena Sterr¹, Konstantin Morozov², and Andreas Engel¹ — ¹Institut für Physik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg — ²Institute of Continuous Media Mechanics, 1 Korolev Street, 614013 Perm, Russia

A ferrofluid drop (∼ mm) floats on the surface of a viscous non-magnetic liquid. Due to the properties of ferrofluids, an external magnetic field, whose vector rotates in a plane orthogonal to the fluid surface, makes the drop rotate and "roll" over the surface with velocity v_drop. This drift velocity is determined by use of a simplifying model which treats the ferrofluid drop either as a solid sphere (a) or as a liquid half-sphere (b). The velocity fields are expanded in vector spherical harmonics and the result v(r,ϑ,ϕ) for r→∞ gives v_drop in terms of experimental parameters.

In case a), the usual no-slip boundary condition is employed at the sphere surface which leads to a logarithmically diverging viscous torque, so that the last boundary condition cannot be used. In order to relieve the singularity, the Navier slip condition is applied, which allows for a finite velocity at the sphere surface and leads to a result for the drop speed which, however, depends on an unknown parameter, the slip length. Calculations for case b) are more complex, but the result does not depend on any unknown parameters.

Considering the simplifications of this model, the agreement with experimental data is surprisingly accurate.