A constitutive equation of co-rotational type for liquid crystalline polymer and influence of orientation on material functions

Abstract

A continuum theory of constitutive equation of co-rotational type is developed for the anisotropic viscoelastic fluid-liquid crystalline (LC) polymer. According to the new concept of anisotropic viscoelastic simple fluid, the stress tensor is considered as a functional on whole history of deformation gradient and hole history of spin tensor measured with respect to co-rotational coordinates. Using the concept and generalizing the co-rotational Oldroyd fluid B model, a continuum theory of constitutive equation of co-rotational type is developed for the fluid. The theory is specialized to constitutive equations of LCP-H model and LCP-Qs model. The orientational motion and the anisotropic material functions are introduced in the equation to describe behaviour of the anisotropic effects of LC polymer fluid. Using the equation analytical expressions of apparent viscosity, first and second normal stress differences and extensional viscosity are given which are in a good agreement with the experimental results. The bifurcation of extrusion-extensional flow is observed for the fluid flow.

Keywords

constitutive equation of co-rotational type / liquid crystalline polymer / normal stress differences / orientational motion / anisotropic material functions / bifurcation of extrusion-extensional flow

References

[1] OnogiS., AsadaT.AstriaG., MarrucciG., Nicolai. Rheology and rheo-optics of polymer liquid crystal[C]. Rheology, 1980, New York, Plenum: 127-147

[2] BaekS. G., MagdaJ. J., LarsonR. G.. Rheological differences among liquid-crystalline polymers I: The first and second normal stress differences of PBG solutions[J]. Journal of Rheology, 1993, 37(6): 1201-1224

[3] BaekS. G., MagdaJ. J., LarsonR. G., et al.. Rheological differences among liquid-crystalline polymers II: Disappearance of nagative N₁ in densely packed lyotropic and thermotropes [J]. Journal of Rheology, 1994, 38(5): 1473-1503

[4] DoiM., EdwardsS. F.The Theory of Polymer Dynamics[M], 1986, London, Oxford

[5] EricksenJ. L.. Anisotropic fluids[J]. Arch Rational Mech Anal, 1960, 4: 231-237

[6] LeslieF. M.BrownG. H.. Theory of flow phenomena in liquid crystals[C]. Advances in Liquid Crystals, 1979, New York, Academic: 1

[7] ChandrasekharS.Liquid Crystals[M], 1977, Cambridge Univ Press, Cambridge

[8] BaleoJ. N., VincentM., NavardP.. Finite element simulation of flow and dirctor orientation of viscous anisotropic fluids in complex 2D geometries[J]. Journal of Rheology, 1992, 36(4): 663-701

[9] VolkovV. S., KulichikhinV. G.. Anisitropic viscoelasticity of liquid crystaline polymers[J]. Journal of Rheology, 1990, 34(3): 281-293

[10] VolkovV. S., KulichikhimV. G.. Non-symmetric viscoelasticity of anisotropic polymer liquids[J]. Journal of Rheology, 2000, 39(3): 360-370

[11] HanS.-fang.Constitutive Equation and Computatinal Analytical Theory of Non-Newtonian Fluids[M], 2000, Beijing, Science Press

[12] HanS.-fang.ZhangF.-g.. Constitutive equation of Maxwell-Oldroyd type for liquid crystalline polymer and its fluid flow[C]. Proc of 3rd Int Conference on Fluid Mechanics, 1998, Beijing, Beijing Institute of Technology Press: 723-728

[13] HanS.-fang.. Constitutive equation of liquid crystalline polymer—anisotropic viscoelastic fluid.[J]. Acta Mechanica Sinica, 2001, 33(5): 588-600

[14] HanS.-fang.. Constitutive equation of co-rotational derivative type for anisotropic viscoelastic fluid.[J]. Acta Mechanica Sinica, 2004, 20(1): 46-53

[15] HanS.-fang.. An unsymmetric constitutive equation for anisotropic viscoelastic fluid[J]. Acta Mechanica Sinica, 2007, 23(2): 149-158

[16] GotsisA. D., OdriozolaM. A.. Extensional viscosity of a thermotropic liquid crystalline polymer[J]. Journal of Rheology, 2000, 44(5): 1205-1225