CONSTITUTIVE EQUATION FOR LIQUID CRYSTALLINE POLYMER ANISOTROPIC VISC-ELASTIC FLUID1)
液晶高分子各向异性粘弹性流体本构方程理论

In non-Newtonian fluid mechanics, the convected time derivative approach to the constitutive equation is frequently used for the general non-Newtonian fluid, i.e. isotropic polymer solution or melt, but rarely for the anisotropic liquid crystalline (LC) polymer fluid. The convected time derivative approach is used by this author to develop the constitutive equation of Oldroyd for LC polymer. The Oldroyd B fluid model is generalized for the co-rotational time deriVative called by co-rotational Oldroyd fluid B. The LC polymer is regarded as anisotropic viscoelastic fluid. The relaxation processes are observed in LC polymer. to extend the co-rotational Oldroyd fluid B, a constitutive equation of Oldroyd type is developed for the liquid crystalline (LC) polymer. The microrheological effects are described by the macrorheological material functions. In the constitutive equation the anisotropic non-linear viscosities, relaxation and retardation times are introduced in order to describe non- linear nature of the material. Following the approach for continuum theory of nematic fluid, the general form of the constitutive equation of Oldroyd type is given, which is then specialized for two LC polymer fluid models: LCP fluid A and LCP fluid B. The results of the present investigation show that the orientational, anisotropic behaviour of LC polymer fluid may be described by the constitutive eqttation of Oldroyd-Maxwell type. Following Baleo, the nematic density p1 is assumed to be of a small value, the nematic inertia is neglected, for the orientational motion of the director the transport equation is used. In order to show the availability of a constitutive equation, usually the equation is used for some typical flow. As an example of application of above investigation, the Poiseulle flow in tube is considered. For the Poiseulle flow the shear stress and normal stress are calculated from the constitutive equation LCP-B, then the material functions such as apparent viscosity,the first and the second normal stress differences are obtained. For flow of the LCP fluid B, the change of the apparels viscosity is shown by Fig.2. The first and the second normal stress differences are shown in Fig.3 to Fig.6 calculated by the LC fluid B. Present constitutive eqttation predicts that the first normal stress changes from positive to negative then to positive, the second normal stress differences changes from negative to positive then to negative. The anisotropic retardation time has more important influence on the change of the first and the second normal stress differences. The results of present investigation with the assumption of the constant director vector are in good agreement with experimental results by Baek and Larson. An important conclusion can be drawn that the rhelogical behaviour of the LC polymer can be described by the constitutive equa- tion of rate type by using the convected time derivative and introducing the anisotropic material functions.