Rosensweig instability of ferrogel thin films or membranes

Abstract

Abstract. 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.

Force-induced elastic matrix-mediated interactions in the presence of a rigid wall

“…For instance, the situation of thin elasto-magnetic membranes could be considered [49,50]. Since linear elasticity theory is a general symmetry-based continuum description, no specific chemical properties of the material need to be satisfied for our approach to apply.…”

“…In the future, our approach opens the way to transfer further related solution methods from the hydrodynamic to the linearly elastic case. For instance, the situation of thin elasto-magnetic membranes could be considered [49,50]. Since linear elasticity theory is a general symmetry-based continuum description, no specific chemical properties of the material need to be satisfied for our approach to apply.…”

Influence of High Viscosity and Magnetoviscous Effect on the Washout Resistance of Magnetic Fluid

“…Based on ferrohydrodynamic analysis (Rosensweig [17]), the magnetic force applied to magnetic fluid can be theoretically calculated in gaseous or liquid environments. As proposed by Rosensweig [17], the Bernoulli equation of ferrofluid dynamics under steady or time-varying magnetic fields is:…”

“…Cui [16] studied the effect of gravity and shear flow on adhesion of magnetic fluid and found that the enhancement of a vertical magnetic field could improve the critical magnetic Bond number and reduce the critical Weber number, which makes the magnetic droplet more susceptible to shear flow. Bohlius [17] deduced the dispersion relationship of interfacial waves in magnetic films under a vertical magnetic field. The influence of surface elasticity, surface magnetism and anisotropic magnetic films on the instability of solid iron gel films under magnetic field was studied.…”