| A constitutive model for dispersions of acicular magnetic particles has been developed by modeling the particles as rigid dumbbells dispersed in a solvent. The effects of Brownian motion, anisotropy hydrodynamic drag, a steric force in the form of the Maier-Saupe potential, and most importantly a magnetic mean-field potential are included in the model. The development is similar to previous models for liquid-crystalline polymers. The phase behavior is studied in terms of an orientational order parameter S, and an average polarity parameter J; the latter is introduced because the magnetic particles have distinguishable direction due to polarity. Predictions for microstructure are obtained by using closure approximations as well as a numerical solution technique involving an expansion in terms of spherical harmonic functions. The use of a bifurcation software (AUTO) to solve the resulting equations enables prediction of rich solution behavior. A transition from isotropic to nematic phases at equilibrium is predicted. Multiple phases—stationary as well as periodic—are predicted in the presence of steady shear flow and magnetic field for dispersions initially in nematic equilibrium. The effects of magnetic interactions and external magnetic field on the microstructure are also investigated.; The theory also yields a constitutive equation in which the stress tensor can be expressed as a function of the velocity gradient, the orientational order, average alignment, and any imposed external magnetic field. The constitutive equation is used to calculate material functions for steady shear flow as well as those for unsteady shear flows. The importance of effects of concentration, equilibrium nematic ordering in the dispersion, and anisotropy in the hydrodynamic drag are emphasized. Data comparisons are presented for material functions in steady shear flow, inception of steady shear flow, and small-amplitude oscillatory shear flow. The rheological predictions from the model for dispersions initially in isotropic equilibrium compare well with experimental data for magnetic inks. Incorporating neglected dispersion characteristics like polydispersity, clustering, spatial non-homogeneity, and including a better magnetic mean-field potential will allow the model to be more effective in complementing experimental studies. |
