Effect of elongational flow on the orientational order phase transitions and viscosity of hard rod fluids

We consider the generalized Smoluchowski equation for the orientational distribution of interacting hard rod-like particles. Using the Onsager theory of excluded volume in these systems, we solve for steady-state solutions to this equation in the special case of elongational flow. Accordingly, we obtain explicit predictions concerning the effect of such flow on the suppression of orientional ordering phase transitions and on the nonlinear behavior (dependence on velocity gradient) of the viscosity.