Influence of orientation of electric field on shear flow of electrorheological fluids

It is possible, in experimental flows of electrorheological (ER) fluids or in actual ER devices based on shear flows, that the electric field may have a component normal to and/or parallel to the fluid velocity. An analytical study of this possibility is presented here. The analysis is carried out using a constitutive equation for the three‐dimensional response of ER fluids [Rajagopal and Wineman, Acta Mechanica 91 (1992)] in which the electric field influences the response in two ways: (a) by affecting the material parameters, and (b) by contributing to stress components because of the interaction of the electric field vector and the shearing. It is shown that the viscosity is altered by a component of the electric field in the direction of the fluid velocity. Moreover, the viscosity is changed if the shear direction is reversed. The model is used in a study of the flow between parallel plates. It is found that the velocity field need not be symmetric about the midplane and the tractions on the plates ma...