Macroscopic behavior of ferronematic gels and elastomers

We present the derivation of the macroscopic equations for uniaxial ferronematic gels and elastomers. We deal with the superparamagnetic case, where no permanent magnetization is present and the anisotropy is provided by the nematic director. We include the magnetization as an independent dynamic degree of freedom. As a consequence special emphasis is laid on possible static and dynamic cross-couplings between magnetization and the non-magnetic degrees of freedom, as director reorientations, flow, elastic strains and relative rotations between director and the elastic network. In particular, we find reversible dynamic cross-couplings among rotations of the magnetization, the director, relative rotations, and deformational flow that allow for new possibilities to manipulate such materials. Application of simple (oscillatory) shear induces, in general, a finite magnetization normal to the shear plane and a relative rotation in the shear plane, whose amplitudes are linear in the shear rate. Induced magnetization, induced relative rotation and the director are mutually orthogonal, with the director aligned obliquely to the flow direction. This orientation is independent of the shear rate and is a material property.