Interparticle Force in Nonlinear Electrorheological Fluids

The prediction of the strength of the electrorheological (ER) effect is the main concern in a theoretical investigation of ER fluids. The ER effect originates from the induced interaction between the polarized particles in an ER fluid. As the mismatch in material parameters (either conductivities or dielectric constants) is responsible for the ER effects, previous theoretical studies have taken the point-dipole approximation, which is now believed to be over-simplified. Since the many-body and multipole interactions have been ignored in these studies, the predicted yield stress has been off by an order in magnitude. The gap between theory and experiment further widens rapidly because the technological applications of ER fluids have stimulated many experiments which measure directly the interactions between particles of various materials under different experimental conditions. It is now known that for crystalline particles, not only force but also torque are exerted on the particles due to crystalline anisotropy. It is also known that particles coated with different materials have a significant impact on the ER response. Because of the inadequacy of the point-dipole approximation, substantial effort has been made to sort out more accurate models. Klingenberg and coworkers proposed an empirical force expression for the interaction between isolated pairs of equal spheres from the numerical solution of Laplace’s equation. Davis used the finite-element method, which is proved to be effective. Clercx and Bossis constructed a fully multipolar treatment to account for the polarizability of spheres up to 1,000 multipolar orders. Recently, Yu and coworkers developed an integral