We analyze the electro-rheological effect in immiscible fluid mixtures with dielectric mismatch. By taking the electric field effect into account, which couples to the dynamics of domain morphology under flow, we propose a set of electro-rheological constitutive equations valid under the condition where the relative magnitude of the flow field is stronger than that of the electric field. Through the comparison with recent experiment, we point out a unique dynamical stress response inherent in

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... tuations, where the cross-coupling between different fields is essential.