A rheological evaluation of steady shear magnetorheological flow behavior using three-parameter viscoplastic models

Abstract

Knowledge of the complicated flow characteristics of magnetorheological (MR) suspensions is necessary for simulations, calculations in engineering processes, or designing new devices utilizing these systems. In this study, we employed three constitutive equations (three-parameter models) for an evaluation of steady shear behavior of MR suspensions. The predictive/fitting capabilities of the Robertson–Stiff (R–S) model were compared with the commonly used Herschel–Bulkley (as a reference) and the Mizrahi–Berk models. The appropriateness of the models was examined using rheological data for diluted as well as concentrated MR systems. The effect of magnetic field strength on model fitting capabilities was also investigated. The suitability of the individual models was evaluated by observing correlation coefficient, sum of square errors, and root mean square errors. A statistical analysis demonstrated that the best fitting capabilities were exhibited by the R–S model, while others provided less accurate fits with the experimental data. Therefore, shear stresses and the yield stress predicted according to the R–S equation can be considered as the most accurate under defined conditions in comparison with the Herschel–Bulkley and the Mizrahi–Berk model predictions. We also showed that the consistency index obtained from the R–S model increased with increasing magnetic field and particle concentration, which physically reflected more rigid internal structures generated in MR suspensions upon an external magnetic field. This behavior was indistinguishable when other models were applied.