Orientational dynamics of nematic liquid crystals under shear flow

The orientational dynamics of low molecular weight and polymeric nematic liquid crystals in a flow field is investigated, based on a nonlinear relaxation equation for the second rank alignment tensor. Various approximations are discussed: Assuming uniaxial alignment with a constant order parameter, the results of the Ericksen–Leslie theory are recovered. The detailed analysis to be presented here for plane Couette flow concerns (i) uniaxial alignment with a variable degree of order and (ii) the tensorial analysis involving the three symmetry-adapted components of the five components of the alignment tensor. The transitions between tumbling, wagging and aligning behavior observed in polymeric liquid crystals and described by the Doi theory of rod-like nematic polymers are recovered. Consequences for the rheological behavior are indicated.