On the ow - phase diagram for discotic liquid crystals in uniaxial extension and compression

A mesoscopic, extended Doi theory for  ows of nematic liquid crystals (LCs) has been successfully applied by Rey to study extensional  ow-induced, homogeneous phase transitions both for rod-like and disc-like molecular geometry. Rey analysed the two order parameters (eigenvalues) of the orientation tensor. Recently the authors generalized the  ow-phase diagram (nematic concentration vs.  ow rate) for rod-like nematics by analysing all tensor degrees of freedom, i.e. by coupling the three director (eigenvector) degrees of freedom. Here we record and discuss subtleties of the corresponding diagram for discotic LCs in uniaxial extension and uniaxial compression. We focus here on the induced stable orientation conŽ gurations. Uniaxial extension (an idealization of Ž bre  ow) yields a low concentration region of unique oblate uniaxial states at every  ow rate; a very small Ž nite region of bi-stable oblate and biaxial states; and the predominant region, encompassing all concentrations above the pure I–N transition and all  ow rates, where the only stable steady state is a biaxial pattern. Furthermore, whereas uniaxial states are ‘unique’, all biaxial states occur in a continuous family, corresponding to an arbitrary positioning of the director pair in the plane transverse to the  ow axis of symmetry. Uniaxial compression (an idealization of Ž lm stretching  ow) of discotic LCs exclusively yields stable prolate uniaxial patterns.