Model for the electrorheological effect in flowing polymeric nematics

An analytical model to study the response of a polymeric nematic confined in a rectangular cell, to a dc electric field is presented. The effect of a pressure-driven plane Poiseuille flow and its competition with the electric field is explicitly considered. For the final stationary state where the induced reorientation of the director has already occurred, an aligned structure with a greatly enhanced viscosity (electrorheological effect) is produced. For this same state the first normal stress difference is calculated as a function of position and of the applied field. For this quantity, regions of negative and positive values develop along the direction of the velocity gradient and an increase in the electric field or the flow causes an augmented effect in its profiles. The net force between the plates is also calculated. As the Reynolds number increases, it is found that it also changes sign from positive to negative, and the effect is more pronounced as the strength of the electric field increases. Finally, the paper is closed by discussing the scope and limitations of the model and methods employed. (C) 1999 American Institute of Physics. [S0021-9606(99)51416-5].