Rheology of electrorheological fluids.

We present experimental and theoretical results on the shear thinning of electrorheological fluids. Rheological measurements on a model fluid consisting of monodisperse silica spheres immersed in a dielectric liquid show a power-law dependence \ensuremath{\mu}\ensuremath{\propto}\ensuremath{\gamma}${\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\Delta}}}$ of the apparent viscosity \ensuremath{\mu} on the strain rate \ensuremath{\gamma}\ifmmode \dot{}\else \.{}\fi{}, with \ensuremath{\Delta} in the range \ensuremath{\Delta}=0.68--0.93. We present a theoretical treatment of steady-state cluster formation in applied electric and shear fields, which correctly predicts the observed power-law shear thinning albeit with an exponent \ensuremath{\Delta}=2/3. We observe no true yield stress in this material.