Evaluation of a constitutive equation for magnetorheological fluids in shear and elongational flows

A microstructural model of the motion of particle pairs in MR fluids is proposed that accounts for both hydrodynamic and magnetic field forces. A fluid constitutive equation is derived from the model that allows prediction of velocity and particle structure fields. Results for simple shear and elongational flows are presented for cases where particle pairs remain in close contact so they are hydrodynamically equivalent to an ellipsoid of aspect ratio two. Additionally, only the magnetic force component normal to the vector connecting the centers of a particle pair affects motion. Shear flow results indicate particle pairs rotate continuously with the flow at low magnetic fields while a steady state is reached at high fields. For elongational flows, when the applied magnetic field is parallel to the elongation direction, particle pairs orient in the field/flow direction. Either orientation is possible when the field is perpendicular to the flow.