Viscosity of an electro-rheological suspension with internal rotations

The rheological behavior of a suspension of insulating particles dispersed in a slightly conducting liquid under the action of a DC electric field is studied. The polarization of the particles induced by the field is shown to be responsible for a rotation of the particles (Quincke rotation) which, in turn, leads to a drastic decrease of the apparent viscosity of the suspension. The purpose of the paper is to provide a relation between the apparent viscosity of the suspension and the electric (E) field intensity. First, the steady-state solutions are searched for the angular velocity of a particle subjected to both DC E field and simple shear flow. Since the solutions are multivalued, their stability is studied using a linear stability analysis. Then the stable solution for the particle angular velocity is used to deduce the value of the apparent viscosity of the suspension. The predictions of the model are compared to experimental data which have been obtained on a suspension of polymethylmethacrylate particles dispersed in a low polar dielectric liquid. The agreement between experiments and theory is rather good even if the model overestimates the viscosity decrease induced by the field.