Fluids with microstructure often show fascinating flow behavior. In particular, the rheological behavior of ferrofluids - stable suspensions of nano--sized ferromagnetic particles in a carrier liquid - can be manipulated by external magnetic fields. Anisotropic viscosities are observed in ferrofluids depending on the relative orientation of the applied magnetic field to the flow field. For a plane shear flow, these are the so called Miesovicz viscosities. As has been noticed [1,2], the stress tensor of ferrofluids can be described phenomenologically by the same set of viscosity coefficients used to describe uniaxial (or generally biaxial) nematic liquid crystals in the presence of an orienting field [3-7]. The microscopic mechanisms leading to the anisotropic viscosities are, however, rather different in these systems [2]. To understand the origin of various viscosity coefficients for ferrofluids, a simple model system is studied here. The model is formulated on the level of kinetic theory, in accordance with kinetic models of nematic fluids. General expressions for the viscosity coefficients are obtained from the model. For the special case of uniaxial symmetry, the expressions are worked out in detail and compared with the result of phenomenological approaches to uniaxial nematic liquid crystals as well as findings from simulations, other theoretical approaches and experiments.
[1] S. Hess, J.F. Schwarzl, D. Baalss, J. Phys. Condens. Matter 2 (1990) SA279.
[2] S. Hess, T. Weider, M. Kröger, Magnetohydrodynamics 37 (2001) 297.
[3] M.I. Shliomis, Sov. Phys. 34 (1972) 1291.
[4] S. Hess, Z. Naturforsch. 31A (1976) 1034.
[5] N. Kuzuu, M.Doi, J. Phys. Soc. Jpn. 52 (1983) 3486.
[6] S. Hess, J. Non--Equilib. Thermodyn. 11 (1986) 175.
[7] M. Kröger, S. Sellers, J. Chem. Phys. 103 (1995) 807; Phys. Rev. E 56 (1997) 1804
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