Yield stresses in electrorheological fluids

Abstract

We describe and determine the static and dynamic (Bingham) yield stresses in an electrorheological (ER) fluid from a microstructural model. The model relates both these yield stresses to the electrostatic energy determined from the suspension capacitance matrix, which we developed previously for the dynamic simulation of an ER fluid. The static yield stress is determined from nonlinear elasticity strain‐energy theory applied to an ER fluid for a variety of volume fractions and particle‐to‐fluid dielectric constant ratios. The static yield stress increases with the dielectric constant ratio and exhibits a maximum at 40 Vol % particles for dielectric constant ratios of 4 or less. From the capacitance of the suspension we also compute the zero‐frequency birefringence of the ER fluid and show that it follows a nonlinear stress‐optical rule. The dynamic yield stress, as we have observed in our previous simulations, dominates the rheology of the ER fluid at large electric field strengths. At the same time the e...