Rosensweig instability of ferrogel thin films or membranes
Max Planck Institute for Polymer Research, 55021, Mainz, Germany
2 Theoretische Physik III, Universität Bayreuth, D 95440, Bayreuth, Germany
Accepted: 22 April 2008
Published online: 26 May 2008
We derive the dispersion relation of surface waves for magnetic gel membranes or thin films at the interface between two fluids in the presence of an external magnetic field normal to the free surface. Above a critical field strength surface waves become linearly unstable with respect to a stationary pattern of surface protuberances. This linear stability criterion generalizes that of the Rosensweig instability for ferrofluid and ferrogel free surfaces to take into account bending elasticity and intrinsic elastic and magnetic surface properties of the film or membrane, additionally. The latter is of interest for uniaxial ferrogel film or membranes, which show a locked-in permanent magnetization.
PACS: 47.20.Ma Interfacial instabilities (e.g. , Rayleigh-Taylor) – / 46.70.Hg Membranes, rods, and strings – / 47.65.Cb Magnetic fluids and ferrofluids –
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2008