According to the rheological principles and previous studies, the rheological behavior of magnetorheological fluids (MRFs) at high shear rates conforms to the Bingham model. Due to its simple form and clear physical meaning, the Bingham model has gained the most widespread applications^[1-4]. However, the nonlinearity of MRFs at low and medium shear rates makes it difficult for the Bingham model to accurately describe and predict its rheological behavior over a wide range of shear rates. The exponential linear mixed analytical (ELMA) model not only accommodates the Bingham model but also has excellent descriptive and predictive capabilities for the rheological behavior of MRFs over a wide range of shear rates^{[3, 4]}. By analyzing the rheological data of the MRF over a wide range of shear rates, we find that the deviation between the MRF rheological behavior and the converged Bingham model is exponentially decaying, in agreement with the ELMA model. In addition, to solve the problem that the traditional dimensionless analysis based on the Mason number cannot describe the nonlinear rheological behavior of MRFs under off-state conditions, we propose a modified Mason number. Finally, a multivariable model of MRF considering the applied magnetic field is developed based on the ELMA model and the modified Mason number.

Mason number,Magnetorheological fluid,Bingham model,Exponential linear mixed analytical model