Theoretical Study on Equation of Motion and Yield Stress of Electrorheological Fluid

Abstract

The flow of electrorheological(ER)fluids has been analyzed theoretically based on the constitutive equation for Bingham fluids. However, it is necessary to take account of internal rotation in ER fluids, because they are suspensions of particles. The equation of motion of an ER fluid is derived based on not only the constitutive equation of stress for a Bingham fluid but also on the theory of micropolar electrically conducting fluids, assuming the equilibrium equation of angular momentum. With respect to the yield stress, which is a characteristic of ER fluids, we consider that the interaction of particles, which are polarized by an applied electric field, is based on a two-body problem at the cutting surface of a cluster of particles. As a result, a new equation is derived based on the theory of dipole-dipole interaction. Yield stress in this study is not dynamic yield stress but static yield stress.