An analytical model for magnetorheological fluids

Two- and three-dimensional analytical models for the yield stress of magnetorheological (MR) fluids as a function of magnetic field and total volume fraction of particles are developed, which are in accord with experimental data. Important factors are the packing density of the particles in the aggregates, their magnetization saturation and the enhanced field between the particles. Our calculations indicate that the torsional force components due to the anisotropic magnetizability of the entire MR suspension may contribute up to 20% of the resultant shear force. Further, when the particles are completely saturated the yield stress is proportional to the square of the saturation magnetization.