Abstract
A continuum extensible director theory was formulated to describe the isothermal, incompressible flow of uniaxial rodlike semiflexible liquid crystalline polymers. The model is strictly restricted to material that flow-align in shear, and that, in the absence of flow, are sufficiently far from the nematic-isotropic phase transition. The microstructure of the continuum is described by a variable length director, but the extensibility is finite. The model is an extension of the TIF (Transversely Isotropic Fluid) model of Ericksen (1960). The thermodynamic restrictions on the model parameters are found using the non-negative definiteness of the entropy production. The rheological material functions predicted by the model are calculated for steady simple shear and steady uniaxial extensional flows. In the rigid rod limit the model predictions agree with those of the TIF model, and for the finite extensibility case the model predictions are in agreement with those associated with flexible isotropic polymers: strong non-Newtonian shear viscosity, positive first normal stress differences, recoverable shear of order one, negative second normal stress differences, and a maximum in the steady uniaxial extensional viscosity.
Similar content being viewed by others
References
Ahmadi G (1978) On the theory of extensible nematic liquid crystals. Mol Cryst Liq Cryst 47:209–223
Bhave AV, Menon RK, Armstrong RC, Brown RA (1993) A constitutive equation for liquid crystalline polymers solutions. J Rheol 37:413–441.
Barnes HA, Hutton JF, Walters K (1989) An Introduction to Rheology. Elsevier, Amsterdam, p 58
Boyce WE, DiPrima RC (1977) Elementary differential equations and boundary value problems, third edition. Wiley, New York, p 397
Calderer MC (1992) Stability of shear flows of polymeric liquid crystals. J Non-Newtonian F. Mech. 43:351–368
DeGennes PG (1974) The physics of liquid crystals. Clarendon Press, Oxford
Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon Press, Oxford
Edwards BJ, Beris AN, Grmela M (1991) The dynamical behaviour of liquid crystals: a continuum description through generalized brackets. Mol Cryst Liq Cryst 201:51–86
Ericksen JL (1960) Transversely isotropic fluids. Kolloid-Z 5:117–122
Ericksen JL (1989) Liquid crystals with variable degree of orientation. IMA Preprint Series No 559, 1–25
Eringen C (1992) Continuum theory of microstretch liquid crystals. J Math Phys 33:4078–4086
Farhoudi Y, Rey AD (1993) Shear flow of nematic polymers. I. Orienting modes, bifurcations, and steady rheological predictions. J Rheol 37:289–314
Farhoudi Y, Rey AD (1993) Shear flow of nematic polymers. II. J Non Newt Fluid Mech (in press)
Kneppe H, Schneider F, Sharma NK (1982) Rotational viscosity γ1 of nematic liquid crystals. J Chem Phys 77:3203–3209
Han WH, Rey AD (1992) Stability analysis of a non-aligning nematic in simple shear flow. Proceedings XIth Congr on Rheology, Moldenares P, Keunigs R (eds) Elsevier, Amsterdam, pp 531–533
Larson RG (1990) Arrested tumbling in shearing flows of liquid crystal polymers. Macromolecules 23:3983–3992
Larson RG (1988) Constitutive equations for polymer melts and solutions. Butterworths, Stoneham, p 145.
Leslie FM (1968) Some constitutive equations for liquid crystals. Arch Rational Mech Anal 28:265–283
Leslie FM (1979) Theory of flow phenomena in liquid crystals, in: GH Brown (ed) Advances in liquid crystals. Academic Press, New York 4:1–81
Lipscomb GG (1987) Analysis of suspension rheology in complex flows, PhD thesis. University of California, Berkeley, p 38
MacMillan EH (1989) Slow flows of anisotropic fluids. J Rheol 33:1071–1105
Maffettone PL, Marrucci G (1992) The nematic dumbbell model. J Rheol 36:1547–1562
Marrucci G (1991) Rheology of nematic polymers, in liquid crystallinity in polymers, Ciferri, A., ed. VCH Publishers, New York, pp 395–423
Marrucci G, Maffettone PL (1989) Description of the liquid-crystalline phase of rodlike polymers at high shear rates. Macromolecules 22:4076–4082
Marrucci G, Maffettone PL (1990a) Nematic phase of rodlike polymers. I. Prediction of transient behavior at high shear rates. J Rhol 34:1217–1230
Marrucci G, Maffettone PL (1990b) Nematic phase of rodlike polymers. II. Polydomain predictions in the tumbling regime. J Rheol 34:1231–1244
Maugin GA (1993) Thermomechanical equations of magnetic fluids. Int J Eng Sci 31:27–39
Semenov AN (1983) Rheological properties of a liquid-crystal solution of rodlike molecules. Sov Phys JETP 58:321–326
Semenov AN (1987) Rheological predictions of a nematic solution of semiflexible macromolecules. Sov Phys JETP 66:712–716
Subbotin A (1993) Dynamics of slightly flexible rods in the liquid crystalline state. Macromolecules 26:2562–2565
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rey, A.D. Rheological predictions of a transversely isotropic fluid model with extensible microstructure. Rheol Acta 32, 447–456 (1993). https://doi.org/10.1007/BF00396175
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00396175