(untitled) (Communications in Computational Physics, 2018)
A general nonhomogeneous extension of the Doi's kinetic theory with translational diffusion and nonlocal potential is proposed to describe the microstructures and defect dynamics of Liquid Crystal Polymer (LCP) solutions. The long-range elasticity of polymer molecules is depicted by a kernel type potential, from which one can derive the well-known Marrucci-Greco potential with weak spatial distortion assumption. Applying quasi-equilibrium closure approximation, we get a second-order moment model for isotropic long-range elasticity, and this reduced moment model maintains the energy dissipation. Implemented by the invariant-based fitting method, the moment model is a decent tool for numerical simulations of defect dynamics and texture evolution in LCP solutions. The numerical results of in-plane rotational case show that the reduced second-order moment model qualitatively predicts complicated nonhomogeneous director dynamics under moderate nematic potential strength, and the translational diffusion plays an important role in defect dynamics.