Modeling of the temperature effects on magnetorheological fluids over a wide temperature range based on free volume theory

As a smart material with controllable rheological properties, magnetorheological fluids (MRFs) have been increasingly used in various fields. The temperature of MRFs inevitably changes during operation, which markedly affects the rheological properties; thus, the modeling of temperature effects is critical for the control and design of magnetorheological devices. However, most studies only examine the temperature effects of MRFs in a narrow temperature range, which fails to effectively cover the operating temperature range of MRFs, and the viscosity-temperature models used have notable limitations. This paper proposes to use free volume theory, in the form of the universal Doolittle equation, to study the viscosity-temperature behavior of MRFs and their base oils over a wide temperature range. Compared with the existing Reynolds and Arrhenius equations, the Doolittle equation achieves an accuracy improvement of up to 17 times and eight times, respectively. It predicts the overall viscosity-temperature behavior of liquids based on four data points taken over a narrow temperature range, with a relative root-mean-square error (RMSE) of no more than 5%. Ignoring the limited effect of off-state yield stress, the Doolittle equation with strong expandability can be used to establish temperature-dependent MRF constitutive equations. It can even develop multiphysics models based on the highly similar viscosity-temperature characteristics between MRFs and their base oils, which will greatly facilitate the development and optimization of MRFs.