A particle based constitutive model for MR (magnetorheological) fluids

A microstructural model of the motion of particle pairs in MR fluids is proposed. The model considers the relative motion of particle aggregates and the evolution of aggregates of two particles as opposed to tracking individual particles as the existing constitutive models do. The model accounts for both hydrodynamic and magnetic field forces. The magnetic force expression is consistent with the dipole-dipole approximation, unlike in the existing models that consider an ad-hoc expression for it in order to fit model predictions to experimental data. In addition, the effect of interparticle dipole interactions, i.e. the effect of dipoles from the same chain, has been included in the expression of the magnetic force.;A fluid constitutive equation that allows prediction of velocity and particle structure is derived. Results for cases of no flow and flow condition, when the magnetic field is on, are discussed. Simple shear and elongational flows are analyzed assuming that either the particle pairs remain in close contact so that they are hydrodynamically equivalent to an ellipsoid of aspect ratio two, or they separate during flow. Shear flow results, for the close contact condition, indicate that particle pairs rotate continuously with the flow at low magnetic fields while a steady state is reached at high fields. The steady state orientation is tilted toward the direction of the larger magnitude force.;The analysis of particle separation during flow provides needed information for fluid's yield stress calculation. The yield stress is determined by the stress level required to separate any two particles, inside the fluid, exposed to a certain shear rate and magnetic field strength. The particles separation is assumed dependent on the local shear rate, rather than the apparent shear rate. Predictions of the yield stress, for low to moderate magnetic fields, are in good agreement with experimental results and predictions made with other models reported in literature. At higher magnetic fields, the differences between model predictions and experimental data are attributed to possible changes in the assumed chain breakage mechanism, and in the neglect of the particle pair interactions with neighboring particle clusters.