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