Orientation mode selection mechanisms for sheared nematic liquid crystalline materials

An extensive analysis of the flow orientation modes of sheared liquid crystalline materials is performed using a complete nonlinear nonequilibrium theory that takes into account short and long range order elasticity and viscous flow effects. It is found that there are two main orientation modes in shear flow: (i) in-plane modes, where the average molecular orientation is in the shear plane ($\mathbf{v}-\mathbf{\nabla }\mathbf{v}$ plane, where $\mathbf{v}$ is the velocity vector); and (ii) out-of-plane modes where the average molecular orientation has a nonzero component along the vorticity $(\mathbf{\nabla }\times \mathbf{v})$ axis. It is found that there are four in-plane orientation modes, and five out-of-plane modes, depending on the magnitude of the ratio of short to long range elasticity $\mathrm{}\left(R\right),$ and the magnitude of the ratio of viscous force to long range elastic force (Ericksen number: Er). The spatial configuration of the orientation field shows a bulk region and two boundary layers, which are smoothly and continuously connected by the action of compatibilization mechanisms. The system has two different compatibilization mechanisms at the boundary between the bulk and surface layer regions: (i) scalar order parameter adjustment, and (ii) director orientation changes. The activations of these two mechanisms are self-selected, and depend on the parametric ($R,$ Er) conditions. At lower $R$ the system easily adopts the scalar order parameter compatibilization mechanism, and at higher $R$ and at moderate Er the system adopts the director compatibilization mechanism. Multistable nonplanar orientation modes arise in certain parametric regions. Multistability in nonplanar modes arises due to possible choices in the direction of the director escape from the shear plane (i.e., left or right), and the nucleation time of the out-of-plane orientation. These two degrees of freedom cause the appearance of chirality in the director field. The nonplanar mode selection and its chirality are stochastic, although the equations are deterministic. The complete theory unifies previously used classical theories (Doi and Leslie-Ericksen), but its predictions transcend in number and nature the predictions of the classical theories.