Genetic algorithms for rheological parameter estimation of magnetorheological fluids

The primary objective of this study is to estimate the parameters of constitutive models characterizing the rheological properties of ferrous and cobalt nanoparticle-based magnetorheological fluids. Constant shear rate rheometer measurements were carried out using suspensions of nanometer sized particles in hydraulic oil. These measurements yielded shear stress vs. shear rate as a function of applied magnetic field. The MR fluid was characterized using both Bingham-Plastic and Herschel-Bulkley constitutive models. 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 experimental data.