A computational study on power law and weibull models applied to magnetorheological fluids

Abstract

Magnetorheological fluids (MRFs) are smart materials of increasing interest in research and industry due to their versatility in mechanical and mechatronic systems. As main rheological features, MRFs must present low viscosity in the absence of a magnetic field (0.1 - 1.0 Pa.s) and high yield stress (50 - 100 kPa) when magnetized in order to optimize the magnetorheological effect, which is responsible for its most important properties. These properties, in turn, are directly influenced by the composition, volume fraction (concentration), size, and size distribution (polydispersity) of the suspended particles, the latter being one of the most important factors in improving their quality. As is well known in the literature, widening the size distribution of the solid phase increases the maximum packing fraction and reduces the viscosity of concentrated suspensions. Therefore, by carefully adjusting the polydispersity, it is possible to increase the magnetorheological effect of concentrated MRFs. However, there is no known analytical model to calculate the so-called packing efficiency of particulate materials, and a numerical approach is often necessary. In this context, many functions can be used in these approximations, and this work aims to study via simulations three common models from science and engineering: the Andreasen-Andersen distribution, the Dinger-Funk distribution (modified Andreasen-Andersen), and the Weibull distribution. Simulations in 1D and 3D were carried out to compute the packing fractions, and their data were compared. The simulation results show that when the distribution modulus of the Dinger-Funk distribution is 𝑞≈0.5, there is a maximum packing fraction that should lower the relative viscosity. Also, the results show that by widening the particle size distribution, it is possible to get an even greater polydispersity of the solid phase. These data suggest that it may be possible to optimize the viscosity of MRFs by carefully adjusting the size distribution, paving the way for preparing MRFs with a stronger magnetorheological effect.