Combined slit and plate–plate magnetorheometry of a magnetorheological fluid (MRF) and parameterization using the Casson model

We describe a magneto-slit die of 0.34 mm height and 4.25 mm width attached to a commercial piston capillary rheometer, enabling the measurement of apparent flow curves of a magnetorheological fluid (MRF) in the high shear rate regime (apparent shear rates 276 up to 20,700 s^− 1, magnetic flux density up to 300 mT). The pressure gradient in the magnetized slit is measured via two pressure holes. While the flux density versus coil current without MRF could directly be measured by means of a Hall probe, the flux density with MRF was investigated by finite element simulations using Maxwell® 2D. The true shear stress versus shear rate is obtained by means of the Weissenberg–Rabinowitsch correction. The slit die results are compared to plate–plate measurements performed in a shear rate regime of 0.46 up to 210 s^− 1. It is shown that the Casson model yields a pertinent fit of the true shear stress versus shear rate data from plate–plate geometry. Finally, a joint fit of the slit and plate–plate data covering a shear rate range of 1 up to 50,000 s^− 1 is presented, again using the Casson model. The parameterization of the MRF behavior over the full shear rate regime investigated is of relevance for the design of MR devices, like, e.g., automotive dampers. In the Appendix, we demonstrate the drawbacks of the Bingham model in describing the same data. We also show the parameterization of the flow curves by applying the Herschel–Bulkley model.