Interparticle force in polydisperse electrorheological fluids: Beyond the dipole approximation

We have developed a multiple image method to compute the interparticle force for a polydisperse electrorheological (ER) fluid. We apply the formalism to a pair of dielectric spheres of different dielectric constants and calculate the force as a function of the separation. The results show that the point-dipole (PD) approximation errs considerably because many-body and multipolar interactions are ignored. The PD approximation becomes even worse when the dielectric contrast between the particles and the host medium is large. From the results, we show that the dipole-induced-dipole (DID) model yields very good agreements with the multiple image results for a wide range of dielectric contrasts and polydispersity. The DID model accounts for multipolar interaction partially and is simple to use in computer simulation of polydisperse ER fluids.