Electrostatic field and force calculation for a chain of identical dielectric spheres aligned parallel to uniformly applied electric field

We apply the re-expansion method proposed by Washizu to a linear particle chain aligned in the direction of a uniform electric field. The calculated results show that the potential distribution around the particles becomes very complicated and the electric field is highly concentrated near the contact points of particles. The pearl-chain forming force rapidly increases with increasing number of particles and reaches a saturation value for chains consisting of some tens of particles. The force at a contact point in a particle chain is reduced near both the ends of the chain but is still much stronger than the interaction force of the two particles. The present method can be extended to cases of coated particles. One example of the application is a new model for the surface roughness of electro-rheological (ER) particles. A layered particle model, in which the surface roughness is replaced with an equivalent surface layer, provides a more reasonable method for the force calculation, because the existing gap model is too sensitive to the fictitious interstice representing the roughness. Another example is the effect of surface coating to reduce the electric field at the contact points. Such a coating will be preferable for ER particles to prevent electrical breakdown in the fluid.