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Shearing the I-N phase transition of liquid crystalline polymers: Long-time memory of defect initial data
1. | Department of Biomedical Engineering, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7575, United States |
2. | Departments of Mathematics and Biomedical Engineering, Institute for Advanced Materials, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250, United States |
3. | Department of Mathematics, University of South Carolina, Columbia, SC 29208 |
References:
[1] |
M. G. Forest, Q. Wang and R. Zhou, Kinetic structure simulations of nematic polymers in plane Couette cells, II: In-plane structure transitions, SIAM Multi. Model. Simul., 4 (2005), 1280-1304.
doi: 10.1137/040618187. |
[2] |
J. J. Feng, J. Tao and L. G. Leal, Roll cells and disclinations in sheared nematic polymers, J. Fluid Mech., 449 (2001), 179-200.
doi: 10.1017/S0022112001006279. |
[3] |
J. J. Feng and L. G. Leal, Simulating complex flows of liquid-crystalline polymers using the Doi theory, J. Rheol. 41 (1997), 1317-1335.
doi: 10.1122/1.550872. |
[4] |
D. H. Klein, C. J. Garcia-Cervera, H. D. Ceniceros and L. G. Leal, Ericksen number and Deborah number cascade predictions of a model for liquid crystalline polymers for simple shear flow, Phys. of Fluids, 19 (2007) , 023-101. |
[5] |
D. H. Klein, "Dynamics of a Model for Nematic Liquid Crystalline Polymers in Planar Shear and Pressure-Driven Channel Flows," Ph.D thesis, University of California in Santa Barbara, 2007. |
[6] |
D. H. Klein, C. J. Garcia-Cervera, H. D. Ceniceros and L. G. Leal, Three-dimensional shear driven dynamics of polydomain textures and disclination loops in liquid crystalline polymers, J. Rheol., 52 (2008), 837-863.
doi: 10.1122/1.2890779. |
[7] |
R. G. Larson and D. W. Mead, Development of orientation and texture during shearing of liquid-crystalline polymers, Liq. Cryst., 12 (1992), 751-768.
doi: 10.1080/02678299208029120. |
[8] |
R. G. Larson and D. W. Mead, The Ericksen number and Deborah number casades in sheared polymeric nematics, Liq. Cryst., 15 (1993), 151-169.
doi: 10.1080/02678299308031947. |
[9] |
G. de Luca and A. D. Rey, Dynamic interactions between nematic point defects in the extrusion duct of spiders, Virtual Journal of Biological Physics Research, 124 (2006), 144904/1-8. |
[10] |
J. Shen, Efficient spectral-Galerkin method I. Direct solvers for second and fourth-order equations using Legendre polynomials, SIAM J. Sci. Comput., 15 (1994), 1489-1505.
doi: 10.1137/0915089. |
[11] |
T. Tsuji and A. D. Rey, Effect of long range order on sheared liquid crystalline materials : Flow regimes, transitions, and rheological diagrams, Phys. Rev. E, 62 (2000), 8141-8151.
doi: 10.1103/PhysRevE.62.8141. |
[12] |
X. Yang, M. G. Forest, Q. Wang and W. M. Mullins, Dynamic defect morphology and hydrodynamics of sheared nematic polymers in two space dimensions, J. Rheology, 53 (2009), 589-614.
doi: 10.1122/1.3089622. |
[13] |
X. Yang, M.G. Forest, Q. Wang and W. M. Mullins, 2-D Lid-driven cavity flow of nematic polymers: an unsteady sea of defects, Soft Matter, 6 (2010), 1138-1156.
doi: 10.1039/b908502e. |
[14] |
M. G. Forest and Q. Wang, Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows, Rheologica Acta, 42 (2003), 20-46.
doi: 10.1007/s00397-002-0252-0. |
[15] |
M. G. Forest, Q. Wang and R. Zhou, The weak shear kinetic phase diagram for nematic polymers, Rheol. Acta, 43 (2004), 17-37.
doi: 10.1007/s00397-003-0317-8. |
[16] |
M.G. Forest, S. Heidenreich, S. Hess, X. Yang and R. Zhou, Robustness of pulsating jet-like layers in sheared nano-rod dispersions, J. Non-Newtonian Fluid Mech., 155 (2008), 130-145.
doi: 10.1016/j.jnnfm.2008.06.003. |
show all references
References:
[1] |
M. G. Forest, Q. Wang and R. Zhou, Kinetic structure simulations of nematic polymers in plane Couette cells, II: In-plane structure transitions, SIAM Multi. Model. Simul., 4 (2005), 1280-1304.
doi: 10.1137/040618187. |
[2] |
J. J. Feng, J. Tao and L. G. Leal, Roll cells and disclinations in sheared nematic polymers, J. Fluid Mech., 449 (2001), 179-200.
doi: 10.1017/S0022112001006279. |
[3] |
J. J. Feng and L. G. Leal, Simulating complex flows of liquid-crystalline polymers using the Doi theory, J. Rheol. 41 (1997), 1317-1335.
doi: 10.1122/1.550872. |
[4] |
D. H. Klein, C. J. Garcia-Cervera, H. D. Ceniceros and L. G. Leal, Ericksen number and Deborah number cascade predictions of a model for liquid crystalline polymers for simple shear flow, Phys. of Fluids, 19 (2007) , 023-101. |
[5] |
D. H. Klein, "Dynamics of a Model for Nematic Liquid Crystalline Polymers in Planar Shear and Pressure-Driven Channel Flows," Ph.D thesis, University of California in Santa Barbara, 2007. |
[6] |
D. H. Klein, C. J. Garcia-Cervera, H. D. Ceniceros and L. G. Leal, Three-dimensional shear driven dynamics of polydomain textures and disclination loops in liquid crystalline polymers, J. Rheol., 52 (2008), 837-863.
doi: 10.1122/1.2890779. |
[7] |
R. G. Larson and D. W. Mead, Development of orientation and texture during shearing of liquid-crystalline polymers, Liq. Cryst., 12 (1992), 751-768.
doi: 10.1080/02678299208029120. |
[8] |
R. G. Larson and D. W. Mead, The Ericksen number and Deborah number casades in sheared polymeric nematics, Liq. Cryst., 15 (1993), 151-169.
doi: 10.1080/02678299308031947. |
[9] |
G. de Luca and A. D. Rey, Dynamic interactions between nematic point defects in the extrusion duct of spiders, Virtual Journal of Biological Physics Research, 124 (2006), 144904/1-8. |
[10] |
J. Shen, Efficient spectral-Galerkin method I. Direct solvers for second and fourth-order equations using Legendre polynomials, SIAM J. Sci. Comput., 15 (1994), 1489-1505.
doi: 10.1137/0915089. |
[11] |
T. Tsuji and A. D. Rey, Effect of long range order on sheared liquid crystalline materials : Flow regimes, transitions, and rheological diagrams, Phys. Rev. E, 62 (2000), 8141-8151.
doi: 10.1103/PhysRevE.62.8141. |
[12] |
X. Yang, M. G. Forest, Q. Wang and W. M. Mullins, Dynamic defect morphology and hydrodynamics of sheared nematic polymers in two space dimensions, J. Rheology, 53 (2009), 589-614.
doi: 10.1122/1.3089622. |
[13] |
X. Yang, M.G. Forest, Q. Wang and W. M. Mullins, 2-D Lid-driven cavity flow of nematic polymers: an unsteady sea of defects, Soft Matter, 6 (2010), 1138-1156.
doi: 10.1039/b908502e. |
[14] |
M. G. Forest and Q. Wang, Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows, Rheologica Acta, 42 (2003), 20-46.
doi: 10.1007/s00397-002-0252-0. |
[15] |
M. G. Forest, Q. Wang and R. Zhou, The weak shear kinetic phase diagram for nematic polymers, Rheol. Acta, 43 (2004), 17-37.
doi: 10.1007/s00397-003-0317-8. |
[16] |
M.G. Forest, S. Heidenreich, S. Hess, X. Yang and R. Zhou, Robustness of pulsating jet-like layers in sheared nano-rod dispersions, J. Non-Newtonian Fluid Mech., 155 (2008), 130-145.
doi: 10.1016/j.jnnfm.2008.06.003. |
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