Role and nature of high field conduction of the suspending liquid in electrorheological fluids

We examine the interaction force between spheres of a slightly conducting material immersed in a dielectric liquid when subjected to a DC field. An approach is developed which refines the previous two-zone model retaining only the electrical conduction of the solid and liquid phases and taking into account the field enhanced dissociation of electrolytic impurities. Approximations on the shape of the equipotential surfaces inside the solid lead to a system of ordinary differential equations governing the distribution of the electrical potential along the sphere surface. Estimates are derived for the attraction force between spheres in contact, for the current and for the electric stress in the liquid lying between the spheres in the "contact zone". This field takes values in the range 200 - 300 V/mum which correspond to extremely high levels of salts dissociation. The different conduction phenomena in the liquid are then discussed and their role in limiting the interaction force is emphasized.