Phenomenological model for rheological characterization of magnetorheological fluids

Magnetorheological fluid converts into semisolid under the action of the magnetic field. Yield stress is the minimum external stress required to initiate the flow in the presence of a magnetic field. Predicting yield stress is vital for analyzing the performance of any MR application. Various yield stress models are available in the literature. However, they are valid for a particular composition of MRF or magnetic field strength range. Here, the yield stress model is derived using magnetostatics principles. Further, the characteristic magnetic field strength is used to introduce the non-linear magnetization of MRF. The Herschel-Bulkley model is used to present the post-yield nature of MRF flow. The constants of the proposed model are determined using the gradual reduced gradient method. They can predict shear stress with ± 10% accuracy irrespective of magnetic field strength zone.