Describing the orientation state of the particles is often critical in fibre suspension applications.Macroscopic descriptors,the so-called second-order orientation tensor(or moment)leading the way,are often preferred ...Describing the orientation state of the particles is often critical in fibre suspension applications.Macroscopic descriptors,the so-called second-order orientation tensor(or moment)leading the way,are often preferred due to their low computational cost.Closure problems however arise when evolution equations for the moments are derived from the orientation distribution functions and the impact of the chosen closure is often unpredictable.In this work,our aim is to provide macroscopic simulations of orientation that are cheap,accurate and closure-free.To this end,we propose an innovative data-based approach to the upscaling of orientation kinematics in the context of fibre suspensions.Since the physics at the microscopic scale can be modelled reasonably enough,the idea is to conduct accurate offline direct numerical simulations at that scale and to extract the corresponding macroscopic descriptors in order to build a database of scenarios.During the online stage,the macroscopic descriptors can then be updated quickly by combining adequately the items from the database instead of relying on an imprecise macroscopic model.This methodology is presented in the well-known case of dilute fibre suspensions(where it can be compared against closure-based macroscopic models)and in the case of suspensions of confined or electrically-charged fibres,for which state-of-the-art closures proved to be inadequate or simply do not exist.展开更多
A general nonhomogeneous extension of the Doi’s kinetic theory with trans-lational diffusion and nonlocal potential is proposed to describe the microstructuresand defect dynamics of Liquid Crystal Polymer (LCP) solut...A general nonhomogeneous extension of the Doi’s kinetic theory with trans-lational diffusion and nonlocal potential is proposed to describe the microstructuresand defect dynamics of Liquid Crystal Polymer (LCP) solutions. The long-range elas-ticity of polymer molecules is depicted by a kernel type potential, from which onecan derive the well-known Marrucci-Greco potential with weak spatial distortion as-sumption. 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.展开更多
文摘Describing the orientation state of the particles is often critical in fibre suspension applications.Macroscopic descriptors,the so-called second-order orientation tensor(or moment)leading the way,are often preferred due to their low computational cost.Closure problems however arise when evolution equations for the moments are derived from the orientation distribution functions and the impact of the chosen closure is often unpredictable.In this work,our aim is to provide macroscopic simulations of orientation that are cheap,accurate and closure-free.To this end,we propose an innovative data-based approach to the upscaling of orientation kinematics in the context of fibre suspensions.Since the physics at the microscopic scale can be modelled reasonably enough,the idea is to conduct accurate offline direct numerical simulations at that scale and to extract the corresponding macroscopic descriptors in order to build a database of scenarios.During the online stage,the macroscopic descriptors can then be updated quickly by combining adequately the items from the database instead of relying on an imprecise macroscopic model.This methodology is presented in the well-known case of dilute fibre suspensions(where it can be compared against closure-based macroscopic models)and in the case of suspensions of confined or electrically-charged fibres,for which state-of-the-art closures proved to be inadequate or simply do not exist.
基金The authors would like to thank Prof.Sharon Murrel for her help in revising English.The research of Pingwen Zhang is partially supported by the State Key Basic Research Project of China 2005CB321704the National Science Foundation of China for Distinguished Young Scholars 10225103The research of Guanghua Ji is partially supported by National Science Foundation of China 10801014.
文摘A general nonhomogeneous extension of the Doi’s kinetic theory with trans-lational diffusion and nonlocal potential is proposed to describe the microstructuresand defect dynamics of Liquid Crystal Polymer (LCP) solutions. The long-range elas-ticity of polymer molecules is depicted by a kernel type potential, from which onecan derive the well-known Marrucci-Greco potential with weak spatial distortion as-sumption. 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.
