New conception in continuum theory of constitutive equation for anisotropic crystalline polymer liquids

Abstract

A new continuum theory of the constitutive equation of co-rotational derivative type is developed for anisotropic viscoelastic fluid—liquid crystalline (LC) polymers. A new concept of simple anisotropic fluid is introduced. On the basis of principles of anisotropic simple fluid, stress behaviour is described by velocity gradient tensor and spin tensor instead of the velocity gradient tensor in the classic Leslie—Ericksen continuum theory. Analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equ- ation of co-rotational type is established for the fluid. A special term of high order in the equation is introduced by author to describe the sp- ecial change of the normal stress differences which is considered as a result of director tumbling by Larson et al. Analyzing the experimental results by Larson et al., a principle of Non- oscillatory normal stress is introduced which leads to simplification of the problem with relaxation times. The special behaviour of non- symmetry of the shear stress is predicted by using the present model for LC polymer liquids. Two shear stresses in shear flow of LC polymer liquids may lead to vortex and rotation flow, i.e. director tumbling in the flow. The first and second normal stress differences are calculated by the model special behaviour of which is in agree- ment with experiments. In the research, the com- putational symbolic manipulation such as computer software Maple is used. For the anisotropic viscoelastic fluid the constitutive equation theory is of important fundamental significance.