<title>Constitutive models of electrorheological and magnetorheological fluids using viscometers</title>

Abstract

A key aspect of application of electrorheological (ER) and magnetorheological (MR) fluids is the characterization of rheological properties. For this purpose, two rotational viscometers are theoretically analyzed. One is a rotational coaxial cylinder viscometer, and the second is a rotational parallel disk viscometer. A key goal is to determine the shear stress and shear rate of ER/MR fluids for both viscometers from the torque and angular velocity data. To do this, the equations between shear stress and torque as well as shear rate and angular velocity are derived on the basis of the Bingham-plastic, biviscous, and Herschel-Bulkley constitutive models. For simplicity in mathematical form, the Bingham-plastic model is used to describe the flow behavior of ER/MR fluids. The biviscous model characterized by static and dynamic yield stresses is used to capture the preyield behavior. The preyield region where the local shear stress is smaller than the static yield stress has much larger viscosity than the postyield region. In order to account for the shear thinning or thickening in postyield region, the Herschel-Bulkley constitutive model is used in this study. The shear stress for a rotational coaxial cylinder viscometer can be calculated directly from measured torque. However, three approximation methods are applied to determine the shear rate. For rotational parallel disk viscometers, the shear rate and shear stress can be obtained directly from the torque and angular velocity data. In order to comprehensively understand the flow behavior of ER/MR fluids with respect to the constitutive models, the nondimensional analyses are undertaken in this study.