液晶高分子各向异性黏弹流体本构方程研究

CONSTITUTIVE EQUATION FOR LIQUID CRYSTALLINE POLYMER——ANISOTROPIC VISC-ELASTIC FLUID

将液晶高分子－各向异性流体的本构方程，建立在Ｏｌｄｒｏｘｄ随体导数观点基础上．推 广上随体 Ｏｌｄｒｏｓｄ Ｂ流体模型，提出共转 Ｏｌｄｒｏｓｄ Ｂ流体模型，同时将微观结构的影响通过 宏观参数表示出来，使在宏观理论中包含微观结构的贡献，即引入取向物质函数，非线性各向 异性黏度函数和各向异性松弛时间及推迟时间等，表征取向运动对黏度和松弛及推迟现象的影 响，在此基础上发展了一类新的液晶高分子－Ｏｌｄｒｏｒｄ型本构方程理论，由该类型本构方程得 出的物质函数，液晶高分子流体的第一、第二法向应力差与实验结果一致，解释了液晶高分子 溶液的第一、第二法向应力差的特殊流变学行为．

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.