Upper Bounds on Electrorheological Properties

Electrorheological (ER) fluids are a class of materials whose rheological properties transform from liquid-like to solid-like upon the application of an external electric field. We consider the simplest model of ER fluids: a collection of identical dielectric solid spheres dispersed in a liquid. By transforming the problem to one of effective dielectric constant optimization, it is shown that the ground state of the ER fluid and its various electrical and rheological properties may be calculated from first principles through the Bergman-Milton representation. In particular, we obtain the upper bounds on the dielectric constant, the shear modulus, and the static yield stress of the ER fluid in its high field (solid) state.