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Electra-rheological materials are suspensions of particles in non-conducting fluids, and all models that have been developed to date describe their behavior by treating them as a homogenized single continuum, and ignoring the multicomponent structure of the material. The theory of interacting continua is ideally suited for modeling such mixtures and in this paper we present a simple theory which takes into account the distribution of the particles in the fluid, the applied electric field, and the relative motion of the two constituents. To illustrate the utility of such a theory we study the flow of an electro-rheological material between two parallel plates under the application of an electrical field normal to the plates.

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