A Hydrodynamic Theory for Solutions of Nonhomogeneous Nematic Liquid Crystalline Polymers With Density Variations

The hydrodynamic theory developed in [31] for solutions of nonhomogeneous nematic liquid crystalline polymers (LCPs) of spheroidal molecular configurations is extended to account for translational diffusion and the related spatial density variation. The new theory augments the added effect of the density variation to the Smoluchowski equation and the elastic stress. It accounts for the molecular aspect ratio as well as the finite range molecular interaction so that it is applicable to liquid crystals ranging from the rodlike liquid crystal at large aspect ratios to the discotic one at small aspect ratios. It also exhibits enhanced shape effects in the viscous stress and warrants a positive entropy production, thereby, the second law of thermodynamics. Moment averaged, approximate, mesoscopic theories for complex flow simulations are obtained via closure approximations.