Hydrodynamics of complex fluids with multiple order parameters is governed by a set of dynamic equations with many material constants, of which only some are easily measurable. We present a unique example of a dynamic magneto-optic coupling in a ferromagnetic nematic liquid, in which long-range orientational order of liquid crystalline molecules is accompanied by long-range magnetic order of magnetic nanoplatelets. We investigate the dynamics of the magneto-optic response experimentally and theoretically and find out that it is significantly affected by the dissipative dynamic cross-coupling between the nematic and magnetic order parameters. The cross-coupling coefficient determined by fitting the experimental results with a macroscopic theory is of the same order of magnitude as the dissipative coefficient (rotational viscosity) that governs the reorientation of pure liquid crystals.

We investigate dynamic magneto-optic effects in a ferromagnetic nematic liquid crystal experimentally and theoretically. Experimentally we measure the magnetization and the phase difference of the transmitted light when an external magnetic field is applied. As a model we study the coupled dynamics of the magnetization, M, and the director field, n, associated with the liquid crystalline orientational order. We demonstrate that the experimentally studied macroscopic dynamic behavior reveals the importance of a dynamic cross-coupling between M and n. The experimental data are used to extract the value of the dissipative cross-coupling coefficient. We also make concrete predictions about how reversible cross-coupling terms between the magnetization and the director could be detected experimentally by measurements of the transmitted light intensity as well as by analyzing the azimuthal angle of the magnetization and the director out of the plane spanned by the anchoring axis and the external magnetic field. We derive the eigenmodes of the coupled system and study their relaxation rates. We show that in the usual experimental setup used for measuring the relaxation rates of the splay-bend or twist-bend eigenmodes of a nematic liquid crystal one expects for a ferromagnetic nematic liquid crystal a mixture of at least two eigenmodes.

We present a model of ultrasonic metafluids -acoustic metamaterials in the form of suspensions of discrete microscopic oscillators coupled to the embedding fluid. Contrary to a common assumption about metamaterials, and as already established in the field of metafluids, the metafluid concept need not be based on position periodicity or correlation of the suspended micro-oscillators, and in this case not even on ideally designed micro-oscillators. For the speculation that metafluids may one day be produced as solutions of macromolecules, it is essential that the micro-oscillators be allowed to be randomly distributed in the host fluid and generally have irregular (modal) shapes. We formulate the detailed operating principle of such a metafluid model, give explicit formulae for its effective dynamic moduli in terms of the modal structure of the micro-oscillators, and discuss basic practical issues of performance optimization in terms of their mass and size.