We consider the behavior of the Doi-Marrucci-Greco (DMG) model for nematic liquid crystalline polymers in planar shear flow. We found the DMG model to exhibit dynamics in both qualitative and quantitative agreement with experimental observations reported by Larson and Mead [Liq. Cryst. 15, 151 (1993)] for the Ericksen number and Deborah number cascades. For increasing shear rates within the Ericksen number cascade, the DMG model displays three distinct regimes: stable simple shear, stable roll cells, and irregular structure accompanied by disclination formation. In accordance with experimental observations, the model predicts both and disclinations. Although defects form via the ridge-splitting mechanism first identified by Feng, Tao, and Leal [J. Fluid Mech. 449, 179 (2001)], a new mechanism is identified for the formation of defects. Within the Deborah number cascade, with increasing Deborah number, the DMG model exhibits a streamwise banded texture, in the absence of disclinations and roll cells, followed by a monodomain wherein the mean orientation lies within the shear plane throughout the domain.
REFERENCES
1.
S.
Chandrasekhar
, Liquid Crystals
, 2nd ed. (Cambridge University Press
, Cambridge, UK, 1992
).2.
P. G.
de Gennes
and J.
Prost
, The Physics of Liquid Crystals
, 2nd ed. (Oxford University Press
, London, 1993
).3.
A. M.
Donald
and A. H.
Windle
, Liquid Crystalline Polymers
(Cambridge University Press
, Cambridge, UK, 1992
).4.
F. C.
Frank
, “On the theories of liquid crystals
,” Discuss. Faraday Soc.
25
, 19
(1958
).5.
6.
G.
Kiss
and R. S.
Porter
, “Rheo-optical studies of liquid-crystalline solutions of helic polypeptides
,” Mol. Cryst. Liq. Cryst.
60
, 267
(1980
).7.
B.
Ernst
and P.
Navard
, “Band textures in mesomorphic (hydroxypropyl) cellulose solutions
,” Macromolecules
22
, 1419
(1989
).8.
M.
Srinivasarao
and G. C.
Berry
, “Rheo-optical studies on aligned nematic solutions of a rodlike polymer
,” J. Rheol.
35
, 379
(1991
).9.
J. T.
Gleeson
, R. G.
Larson
, D. W.
Mead
, G.
Kiss
, and P. E.
Cladis
, “Image analysis of shear-induced textures in liquid-crystalline polymers
,” Liq. Cryst.
11
, 341
(1992
).10.
R. G.
Larson
and D. W.
Mead
, “Development of orientation and texture during shearing of liquid-crystalline polymers
,” Liq. Cryst.
12
, 751
(1992
).11.
R. G.
Larson
and D. W.
Mead
, “The Ericksen number and Deborah number cascades in sheared polymeric nematics
,” Liq. Cryst.
15
, 151
(1993
).12.
J.
Vermant
, P.
Moldenaers
, S. J.
Picken
, and J.
Mewis
, “A comparison between texture and rheological behaviour of lyotropic liquid crystalline polymers during flow
,” J. Non-Newtonian Fluid Mech.
53
, 1
(1994
).13.
Z.
Tan
and G. C.
Berry
, “Studies on the texture of nematic solutions of rodlike polymers. 3. Rheo-optical and rheological behavior in shear
,” J. Rheol.
47
, 73
(2002
).14.
G.
Sgalari
, L. G.
Leal
, and E.
Meiburg
, “Texture evolution of sheared liquid crystalline polymers: Numerical predictions of roll-cells instability, director turbulence, and striped texture with a molecular model
,” J. Rheol.
47
, 1417
(2003
).15.
G.
Marrucci
and F.
Greco
, “The elastic constants of Maier-Saupe rodlike molecule nematics
,” Mol. Cryst. Liq. Cryst.
206
, 17
(1991
).16.
J.
Feng
, G.
Sgalari
, and L. G.
Leal
, “A theory for flowing nematic polymers with orientational distortion
,” J. Rheol.
44
, 1085
(2000
).17.
R.
Zhou
, M. G.
Forest
, and Q.
Wang
, “Kinetic structure simulations of nematic polymers in plane Couette cells. I: The algorithm and benchmarks
,” Multiscale Model. Simul.
3
, 853
(2005
).18.
G.
Sgalari
, L. G.
Leal
, and J. J.
Feng
, “The shear flow behaviour of LCPs based on a generalized Doi model with distortional elasticity
,” J. Non-Newtonian Fluid Mech.
102
, 361
(2002
).19.
R.
Kupferman
, M. N.
Kawaguchi
, and M. M.
Denn
, “Emergence of structure in a model of liquid crystalline polymers with elastic coupling
,” J. Non-Newtonian Fluid Mech.
91
, 255
(2000
).20.
T.
Tsuji
and A. D.
Rey
, “Effect of long range order on sheared liquid crystalline materials: Flow regime transitions and rheological phase diagrams
,” Phys. Rev. E
62
, 8141
(2000
).21.
T.
Tsuji
and A. D.
Rey
, “Orientational mode selection mechanisms for sheared nematic liquid crystalline materials
,” Phys. Rev. E
57
, 5609
(1998
).22.
A. D.
Rey
and T.
Tsuji
, “Recent advances in theoretical liquid crystal rheology
,” Macromol. Theory Simul.
7
, 623
(1998
).23.
T.
Tsuji
and A. D.
Rey
, “Effect of long range order on sheared liquid crystalline materials. Part 1: Compatability between tumbling and behaviour and fixed anchoring
,” J. Non-Newtonian Fluid Mech.
73
, 127
(1997
).24.
P. T.
Mather
, D. S.
Pearson
, and R. G.
Larson
, “Flow patterns and disclination-density measurements in sheared nematic liquid crystals II: Tumbling 8CB
,” Liq. Cryst.
20
, 539
(1996
).25.
Calculations performed by
W. H.
Han
and A. D.
Rey
[Macromolecules
28
, 8401
(1995
)] using the phenomenologically based Leslie-Ericksen theory, in which gradients along the spanwise direction are neglected and the domain lies within the shear plane, predict a flow and orientation structure that corresponds to a spanwise-oriented banded texture.26.
R. G.
Larson
, “Roll-cell instabilities in shearing flows of nematic polymers
,” J. Rheol.
37
, 175
(1993
).27.
J. J.
Feng
, J.
Tao
, and L. G.
Leal
, “Roll cells and disclinations in sheared nematic polymers
,” J. Fluid Mech.
449
, 179
(2001
).28.
J. L.
Ericksen
, “Conservation laws for liquid crystals
,” Trans. Soc. Rheol.
5
, 23
(1961
).29.
F. M.
Leslie
, “Some constitutive equations for liquid crystals
,” Arch. Ration. Mech. Anal.
28
, 265
(1968
).30.
M.
Doi
, “Molecular dynamics and rheological properties of concentrated solutions of rodlike polymers in isotropic and liquid crystalline phases
,” J. Polym. Sci., Polym. Phys. Ed.
19
, 229
(1981
).31.
M.
Doi
and S. F.
Edwards
, The Theory of Polymer Dynamics
(Oxford University Press
, New York, 1986
).32.
R. B.
Bird
, C. F.
Curtis
, R. C.
Armstrong
, and O.
Hassager
, Dynamics of Polymeric Fluids, Vol. 2: Kinetic Theory
, 2nd ed. (John Wiley and Sons
, New York, 1987
).33.
W.
Maier
and A.
Saupe
, “Eine einfache molekular-statistische theorie der nematischen kristallinflüssigen phase. I
,” Z. Naturforsch. A
, 14
, 882
(1958
).34.
W.
Maier
and A.
Saupe
, “Eine einfache molekular-statistische theorie der nematischen kristallinflüssigen phase. I
,” Z. Naturforsch. A
, 15
, 288
(1960
).35.
S.
Prager
, “Stress-strain relationship in a suspension of dumbbells
,” Trans. Soc. Rheol.
1
, 53
(1957
).36.
C. V.
Chaubal
and L. G.
Leal
, “A closure approximation for liquid-crystalline polymer models based on parametric density estimation
,” J. Rheol.
42
, 177
(1998
).37.
J.
Feng
, C. V.
Chaubal
, and L. G.
Leal
, “Closure approximations for the Doi theory: Which to use in simulating complex flows of liquid-crystalline polymers
,” J. Rheol.
42
, 1095
(1998
).38.
J.
Feng
and L. G.
Leal
, “Pressure-driven channel flows of a model liquid-crystalline polymer
,” Phys. Fluids
11
, 2821
(1999
).39.
M.
Vinokur
, “On one-dimensional stretching functions for finite-difference calculations
,” J. Comput. Phys.
50
, 215
(1983
).40.
H. A.
van der Vorst
, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
13
, 631
(1992
).41.
D. H.
Klein
, C. J.
Garcia-Cervera
, H. D.
Ceniceros
, and L. G.
Leal
, “Computational studies of the shear flow behavior of a model for liquid crystalline polymers
,” Proceedings of the 12th Computational Techniques and Applications Conference CTAC-2004
(ANZIAM
, 2005
), Vol. 46
, pp. C210
–C244
.42.
C.
Shu
and S.
Osher
, “Efficient implementation of essentially non-oscillatory shock-capturing schemes
,” J. Comput. Phys.
, 77
, 439
(1988
).43.
P.
Manneville
and E.
Dubois-Violette
, “Shear flow instability in nematic liquids: Theory steady simple shear flows
,” J. Physique
37
, 285
(1976
).44.
P.
Pieranski
and E.
Guyon
, “Instability of certain shear flows in nematic liquids
,” Phys. Rev. A
9
, 404
(1974
).45.
P.
Manneville
, “The transition to turbulence in nematic liquid crystals
,” Mol. Cryst. Liq. Cryst.
70
, 1501
(1981
).46.
P. E.
Claudis
and S.
Torza
, “Flow instabilities in Couette flow in nematic liquid crystals
,” in Colloid and Interface Science
, edited by M.
Kelker
(Academic
, New York, 1976
), Vol. 4
, p. 487
.47.
P. E.
Cladis
and W.
van Saarloos
, “Some nonlinear problems in anisotropic liquids
,” in Solitons in Liquid Crystals
, edited by L.
Lam
and J.
Prost
(Springer-Verlag
, New York, 1990
).48.
S.
Guido
, P.
Frallicciardi
, N.
Grizzuti
, and G.
Marrucci
, “Rheo-optics of hydroxypropylcellulose solutions in Poiseuille flow
,” Rheol. Acta
33
, 22
(1994
).49.
Computational Techniques for Fluid Dynamics: Fundamental and General Techniques
, edited by C. A. J.
Fletcher
, R.
Glowinski
, and M.
Holt
(Springer-Verlag
, New York, 1991
), Vol. 1
.© 2007 American Institute of Physics.
2007
American Institute of Physics
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