A Nonhomogeneous Kinetic Model of Liquid Crystal Polymers and Its Thermodynamic Closure Approximation (Communications in Computational Physics, 2018)
A general nonhomogeneous extension of the Doi's kinetic theory with translationaldiffusion and nonlocal potential is proposed to describe the microstructuresand defect dynamics of Liquid Crystal Polymer (LCP) solutions. The long-range elasticityof polymer molecules is depicted by a kernel type potential, from which onecan derive the well-known Marrucci-Greco potential with weak spatial distortion assumption.Applying quasi-equilibrium closure approximation, we get a second-ordermoment model for isotropic long-range elasticity, and this reduced moment modelmaintains the energy dissipation. Implemented by the invariant-based fitting method,the moment model is a decent tool for numerical simulations of defect dynamics andtexture evolution in LCP solutions. The numerical results of in-plane rotational caseshow that the reduced second-order moment model qualitatively predicts complicatednonhomogeneous director dynamics under moderate nematic potential strength, andthe translational diffusion plays an important role in defect dynamics.