Analysis of particle-particle forces in electrorheological fluids

The Rayleigh identity, based on a multipole expansion theory, is extended t o analyse the forces between particles in an electrorheological system. The shear modulus for chains of particles arrayed on a square lattice is calcu lated. It is found that the modulus increases linearly with the ratio of di electric constants of the dispersed particles to that of the continuous pha se; as the ratio becomes larger, contrary to the expectations from a simple dipole approximation, the modulus would saturate. In the case of conductin g particles, the modulus varies with the frequency of the applied field. In a limiting case of perfectly conducting particles, the conductivity is als o considered. It is found that the particle-particle forces are extremely s ensitive to their separations from each other.