A 2-DIMENSIONAL APPROACH TO THE CONSTITUTIVE EQUATION OF NEMATIC POLYMERS

On the basis of the rod-like polymer theory of the nematic phase, originally formulated by Doi, an attempt is made to develop a constitutive equation for the stress tensor which does not require a preliminary determination of the distribution function of rod orientations and yet is capable of predicting well-known pecularities of the rheological behaviour of many liquid crystalline polymers, such as the negative normal stress effect. In view of the intrinsic difficulties of this task, the work developed in this paper is fictitiously restricted to a shear flow in two dimensions, with the aim of understanding, in this relatively simple case, what kind of approximations are permissible. It is found that closure approximations at the lowest possible level are inadequate, whereas a suitable closure at the next level works satisfactorily.