Magnetization dynamics, rheology, and an effective description of ferromagnetic units in dilute suspension

The rheological properties of a dilute suspension of ellipsoidal ferromagnetic particles in the presence of a magnetic field are studied on the basis of a kinetic model, where the flow and magnetic external fields couple in qualitatively different ways to the orientational behavior of the suspension. In the uniaxial phase the stress tensor is found to be of the same form as in the Ericksen-Leslie theory for nematic liquid crystals in the steady state. Expressions for a complete set of viscosity coefficients in terms of orientational order parameters are worked out. In the low Péclet number regime, the viscosity coefficients are given as explicit functions of the magnetic field and a particle shape factor, where the shape factor may equally represent a nonspherical unit (agglomerate, chain) composed of spherical particles. Effects due to possible flow-induced breakup of units are not covered in this work. Further, by considering the magnetization as the only relevant variable, a magnetization equation within an effective field approach is derived from the kinetic equation and compared to existing magnetization equations. The alignment angle of the magnetization and the first and second normal stress coefficient are studied for the special case of plane Couette flow. The assumptions employed are tested against a Brownian dynamics simulation of the full kinetic model, and a few comparisons with experimental data are made.