Ericksen’s transversely isotropic fluid

Comparison with Ericksen s Transversely Isotropic Fluid Theory... 

Ericksen proposed a theory for fluids such as nematic liquid crystals which could become anisotropic during flow. By assuming symmetry around the director, the expression for the stress tensor was somewhat simplified. We compare here briefly Ericksen s transversely isotropic fluid theory with the transient behavior observed for thermotropic copolyesters of PHB/PET. 

Fig. 10. Prediction of the shear stress using Ericksen s transversely isotropic fluid theory. The domains were assumed to be initially oriented along 2-direction (i.e. perpendicular to the shear surface).

The shear stress growth on the inception of shear flow may reflect the orientation of the liquid crystalline domains. Orientation seems to occur within less than 2 strain units in shear flow. This primary normal stress difference can exhibit different phenomena from the shear stress response. In particular for the 60 mole % PHB/PET system, values of N are positive and rise gradually to the equilibrium values whereas the 80 mole % PHB/PET system can exhibit negative values of N. Ericksen s transversely isotropic fluid theory can qualitatively handle some of the observed phenomena. Further studies which couple the transient flow behavior to the orientation and morphology need to be carried out. 

The first rheological theory for Uquid crystals was developed by LesUe and Ericksen, building on Ericksen s earUer transversely isotropic fluid. The theory is formulated in terms of a director field n, and it is similar to the fiber theory in the preceding section, except that it includes a contribution to the free energy from an interactive potential that causes the molecules to align at rest. The usual form of the free energy F resulting from distortions of the director field is... 

---