Onsager-theory-based dynamic model for nematic phases of bent-core molecules and star molecules

We construct the molecular model and the tensor model for the dynamics of the nematic phases of bent-core molecules and star molecules in incompressible fluid. We start from the molecular interaction and the molecule--fluid friction, and write down a general formulation based on the molecular shape and the free energy. Then we incorporate an Onsager-theory-based static tensor model that is determined by the molecular shape. In this way, the terms in the molecular model are fully determined by the molecular shape and expressed by physical parameters. For bent-core molecules and star molecules, the model shares the same form, but is different in the coefficients. With the polar interaction and elastic energy taken into account, and the convection and diffusion included both spatially and orientationally, the model is suitable for inhomogeneous flows. We adopt the quasi-equilibrium approximation to derive the tensor model with energy dissipation maintained. Numerical simulation is carried out focusing on the shear flow problem using both the molecular and the tensor models. We choose the parameters near the transition region of different equilibrium nematic phases and examine the effect of molecular shape on the flow modes. The tensor model proves to exhibit all the flow modes found in the molecular model.