A phenomenological model of electrorheological fluids

Abstract

The fundamental assumption of the paper is that the extra stress tensor τ of an electrorheological fluid is an isotropic tensor valued function of the rate of strain tensor D and the vector n (which characterizes the orientation \({\mathbf{\hat{n}}}\) and length N of the fibers formed by application of an electric field). The resulting constitutive equation for τ is supplemented by the solution of the previously studied time evolution equation for n. Plastic behavior for the shear and normal stresses is predicted. Anticipating that the action of increasing shear rate \( \dot{\gamma } \) is i) to orient the fibers more and more in the direction of flow and ii) simultaneously to break up the fibers leads to the conclusion that for \( \dot{\gamma } \to \infty \) the same behavior is encountered as without an electric field. Using realistically possible approximation formulas for the dependence of \({\mathbf{\hat{n}}}\) and N on \( \dot{\gamma } \) leads to the Bingham behavior for \( \dot{\gamma } \to 0 \) and power law behavior for large shear rates.