Abstract
The primary objective of this study is to estimate the parameters of a constitutive model characterizing the rheological properties of a ferrous nanoparticle-based magnetorheological fluid. Constant shear rate rheometer measurements were carried out using suspensions of nanometer sized iron particles in hydraulic oil. These measurements provided shear stress vs. shear rate as a function of applied magnetic field. The MR fluid was characterized using both a Bingham-Plastic constitutive model and a Herschel-Bulkley constitutive model. Both these models have two regimes: a rigid pre-yield behavior for shear stress less than a field-dependant yield stress, and viscous behavior for higher shear rates. While the Bingham-Plastic model assumes linear post-yield behavior, the Herschel-Bulkley model uses a power law dependent on the dynamic yield shear stress, a consistency parameter and a flow behavior index. Determination of the model parameters is a complex problem due to the non-linearity of the model and the large amount of scatter in the experimentally observed data. Usual gradient-based numerical methods are not sufficient to determine the characteristic values. In order to estimate the rheological parameters, we have used a genetic algorithm and carried out global optimization. The obtained results provide a good fit to the data and support the choice of the Herschel-Bulkley fluid model.
Published Version
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