The dependence on applied shear of the morphological and rheological properties of diffusive binary systems after a quench from the disordered state into the coexistence region is investigated. In particular the behavior of the late-time transversal size of domains L_{y} and of the maximum of excess viscosity (Deltaeta)_{M} is considered. Numerical results show the existence of two regimes corresponding to weak and strong shear separated by a shear rate of the order of gamma_{c} approximately 1t_{D} where t_{D} is the diffusive time. L_{y} and (Deltaeta)_{M} behave as L_{y} approximately gamma;{-alpha} and (Deltaeta)_{M} approximately gamma;{nu} with alpha=alpha_{s}=0.18+/-0.02 , nu=nu_{s}=-2.00+/-0.01 and alpha=alpha_{w}=0.25+/-0.01 , nu=nu_{w}=-0.68+/-0.04 in the strong- and weak-shear regimes, respectively. Differently from what was found in systems with fluctuating velocity field, it is confirmed that domains continue to grow at all times.
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