A new constitutive theory for extrusion-extensional flow of anisotropic liquid crystalline polymer fluid

A new continuum theory of the constitutive equation of co-rotational derivative type was developed by the author for anisotropic viscoelastic fluid-liquid crystalline (LC) polymers (S.F. Han, 2008, 2010) . This paper is a continuation of the recent publication [1] to study extrusion-extensional flow of the fluid. A new concept of simple anisotropic fluid is introduced. On the basis of anisotropic simple fluid, stress behavior is described by velocity gradient tensor F and spin tensor W instead of the velocity gradient tensor D in the classic Leslie?Ericksen continuum theory. A special form of the constitutive equation of the co-rotational type is established for the fluid. Using the special form of the constitutive equation in components a computational analytical theory of the extrusion-extensional flow is developed for the LC polymer liquids - anisotropic viscoelastic fluid. Application of the constitutive theory to the flow is successful in predicting bifurcation of elongational viscosity and contraction of extrudate for LC polymer liquids–anisotropic viscoelastic fluid. The contraction of extrudate of LC polymer liquids may be associated with the stored elastic energy conversion into that necessary for bifurcation of elongational viscosity in extrusion extensional flow of the fluid.

An unsymmetric constitutive equation for anisotropic viscoelastic fluid

A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline （LC） polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie-Ericksen theory is described by the first Rivlin-Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion-extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extru- date of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a seriesof new anisotropic non-Newtonian fluid problems can be addressed.

Vibrational shear flow of anisotropic viscoelastic fluid with small amplitudes

Using the constitutive equation of co-rotational derivative type for anisotropic viscoelastic fluid-liquid crystalline(LC),polymer liquids was developed.Two relaxation times are introduced in the equation:λn represents relaxation of the normal-symmetric stress components;λs represents relaxation of the shear-unsymmetric stress components.A vibrational rotating flow in gap between cylinders with small amplitudes is studied for the anisotropic viscoelastic fluid-liquid crystalline polymer.The time-dependent constitutive equation are linearized with respect to parameter of small amplitude.For the normal-symmetric part of stress tensor analytical expression of the shear stress is obtained by the constitutive equation.The complex viscosity,complex shear modulus,dynamic and imaginary viscosities,storage modulus and loss modulus are obtained for the normal-symmetric stress case which are defined by the common shear rate.For the shear-unsymmetric stress part,two shear stresses are obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) are given by the constitutive equation which are defined by rotating shear rate introduced by author.The dynamic and imaginary viscosities,storage modulus and loss modulus are given for each complex viscosities and complex shear modulus.Using the constituive equation the rotating flow with small amplitudes in gap between two coaxial cylinders is studied.

CONSTITUTIVE EQUATION OF CO-ROTATIONAL DERIVATIVE TYPE FOR ANISOTROPIC-VISCOELASTIC FLUID

A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientational motion on the material behavior and neglecting the influence,the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation,retardation times and anisotropic viscosi- ties are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid.Using the equation for the shear flow of LC polymer fluid,the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al.For the fiber spinning flow of the fluid,the analytical expression of the extensional viscosity is given.

黏弹性流体在油藏孔隙中的流动特性

针对油藏孔隙中黏弹性流体的流动特性,选取了黏弹性流体中的上随体Maxwell本构方程描述以第一法向应力差为主要特征的聚合物溶液的流变性,同时使用计算流体有限元分析软件Polyflow对收缩流道内的黏弹性聚合物溶液流动过程进行等温数值模拟分析。从理论上研究了不同雷诺数(Re)和韦森博格数(We)条件下聚合物溶液黏弹性对孔隙内速度场和应力场的影响规律。确定当Re数和We数较大时,流体在收缩流道中流动时,流体的流速和应力随韦森博格数的增大而增大;第一法向应力随We的增大而增大,且在出口窄流道内最大,而在入口宽流道处最小;越靠近壁面,We数对第一法向应力的影响越大;黏弹性对流速的影响在靠近中心线处较大,靠近壁面处影响较小。

黏弹流体流动的数值模拟研究进展

综述了黏弹流体流动数值模拟的研究进展．突出介绍近十年来有限元法在黏弹流体流动数值模拟研究中取得的成果．通过动量方程的适当变形和本构方程离散权函数的合理选择，可以显著增强数值计算的稳定性，得到较高Ｗｅｉｓｓｅｎｂｅｒｇ数下的解．同时文中对黏弹流体流动数值模拟中本构方程的应用、非等温情况和三维空间下的研究进行了介绍。

筒型基础负压沉贯流固耦合渗流分析模型

分析筒型基础沉贯作用的土层,利用J2流动理论各项同性硬化原理,研究海积软土颗粒本构关系,结合离散元方法计算土体体应变,并将其引入海积软土的物性参数动态计算模型。根据筒型基础沉贯特征,结合体应变以及物性参数动态模型,由有效应力原理和瞬时质量守恒原理分别确定应力和渗流方程,并给出上述模型的定解条件。建立了新的流固耦合渗流的数学模型,求解筒型基础沉贯渗流场分布。

扰动本构方程及粘弹流体拉伸流动不稳定性

提出“准衰退记忆”新概念,发展了非牛顿流体扰动本构理论,并研究了粘弹流体拉伸流动的不稳定性规律。