The viscosity behavior in electric fields was measured for dilute suspensions of p-[perfluoro(2-isopropyl-1,3-dimethyl-1-butenyl)oxy]benzoic acid particles (PFNA) in silicone oils. The application of electric fields causes a viscosity increase in a wide range of shear rates. Since the electrorheological (ER) effect is much stronger at low shear rates, the flow becomes shear-thinning. However, contrary to conventional ER suspensions which are reversibly converted between Newtonian fluids and Bingham solids, the PFNA suspensions are fluids even in electric fields. When the particle concentration is increased to 5 wt.%, the ER effect reaches saturation. Further increase does not contribute to additional viscosity enhancement. These results cannot be explained through the chain formation mechanism established for conventional systems. After the ER experiments, the bob surface of the rheometer is covered with several stripes of aggregated particles. Although the strength of electric and shear fields is constant in the rheometer, the periodic structure may be formed in the flow of electrified suspensions. When a dielectric liquid is subjected to high electric fields, the secondary motion of liquid can be induced by the Coulomb force acting on free charge. The electrohydrodynamic (EHD) convection is responsible for the periodic distribution of particles concentration. The ER effect of PFNA suspensions may be generated by a combined effect of EHD convection and external shear.