INTERACTION BETWEEN PARTICLES AND PARTICLE CHAINS IN ELECTRORHEOLOGICAL FLUIDS
The electric potential in a granular system consisting of spherical inclusions in the presence of an external applied electric field is studied in detail within the framework of the Rayleigh identity. The effects of induced charges on the inclusions are taken into account explicitly. The method, in principle, includes the effects of all multipoles. The method is applied to study the interaction between two inclusions. The standard form of interaction between inclusions widely used in studying ER fluids is recovered as an approximation of our general approach. We then apply the method to a chain of inclusions. Analytic expressions for the electrostatic energy per inclusion and the electric field are obtained for the case in which the chain is parallel to the applied field. Our result reduces to the form used in the literature when appropriate approximation is taken. The method is further extended to study the interaction between chains of inclusions. An approximate expression is obtained for the force between two chains of inclusions. Our approach provides a rigorous framework for determining the interaction between inclusions and chains of inclusions to arbitrary accuracy.