Research advances of un-symmetric constitutive theory of anisotropic viscoelastic liquids and its hydrodynamic behavior

Abstract

Research advances of un-symmetric constitutive equation of anisotropic fluid, influence of un-symmetric stress tensor on material functions, vibrational shear flow of the fluid with small amplitudes and rheology of anisotropic suspension were reported. A new concept of simple anisotropic fluid was introduced. On the basis of anisotropic principle, the simple fluid stress behaviour was described by velocity gradient tensor F and spin tensor W instead of velocity gradient tensor D in the classic Leslie-Ericksen continuum theory. Two relaxation times analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equation of co-rotational type was introduced. More general model LCP-H for the fluid was developed. The unsymmetry of the shear stress was predicted by the present continuum theory for anisotropic viscoelastic fluid-LC polymer liquids. The influence of the relaxation times on material functions was specially studied. It is important to study the unsteady vibrational rotating flow with small amplitudes, as it is a best way to obtain knowledge of elasticity of the LC polymer, i.e. dynamic viscoelasticity. For the shear-unsymmetric stresses, two shear stresses were obtained thus two complex viscosities and two complex shear modulus (i.e. first and second one) were introduced by the constitutive equation which was defined by rotating shear rate introduced by author. For the two stability problems of fluid, such as stability of hydrodynamic flow and orientational motion, were discussed. The results show that the polymer suspension systems exhibit anisotropic character. The PNC systems can exhibit significant shear-thinning effects. For more concentrated polymer nano-suspensions, the first normal stress difference change from positive to negative, which is similar to LC polymer behavior.