-
Previous Article
Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays
- DCDS-B Home
- This Issue
-
Next Article
A nonlocal and fully nonlinear degenerate parabolic system from strain-gradient plasticity
Permeation flows in cholesteric liquid crystal polymers under oscillatory shear
1. | Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville, NC 28301, United States |
2. | Department of Mathematics & NanoCenter, University of South Carolina, Columbia, SC 29208, United States |
References:
[1] |
B. Bird, R. C. Armstrong and O. Hassager, "Dynamics of Polymeric Liquids," Vol 1, John Wiley and Sons, New York, 1987. |
[2] |
W. R. Burghardt, Oscillatory shear flow of nematic liquid crystals, J. Rheol., 35 (1991), 49-62.
doi: doi:10.1122/1.550208. |
[3] |
E. Choate, Z. Cui and M. G. Forest, Effects of strong anchoring on the dynamics moduli of heterogeneous nematic polymers, Rheological Acta., 47 (2008), 223-236.
doi: doi:10.1007/s00397-007-0235-2. |
[4] |
Chandrasekhar, "Liquid Crystals," 2nd ed., Cambridge University Press, Cambridge, 1992. |
[5] |
Z. Cui, Small amplitude oscillatory shear permeation flow of cholesteric liquid crystal polymers, Communications in Mathematical Sciences, 8 (2010), 943-963. |
[6] |
Z. Cui, M. C. Calderer and Q. Wang, Mesostructures in flows of weakly sheared chiral liquid crystalline polymers, Discrete and Continuous Dynamical Systems-Series B, 6 (2006), 291-310. |
[7] |
Z. Cui, et al., On weak plane shear and Poiseuille flows of rigid rod and platelet ensembles, SIAM J. Appl. Math., 66 (2006), 1227-1260.
doi: doi:10.1137/04061934x. |
[8] |
Z. Cui and Q. Wang, A continuum model for flows of chiral liquid crystal polymers and permeation flows, J. Non-Newtonian Fluid Mech., 138 (2006), 44-61.
doi: doi:10.1016/j.jnnfm.2006.04.005. |
[9] |
L. R. P. de Andrade Lima and A. D. Rey, Superposition and universality in the linear viscoelasticity of Leslie-Ericken liquid crystals, J Rheol., 48 (2004), 1067-1084.
doi: doi:10.1122/1.1773784. |
[10] |
L. R. P. de Andrade Lima and A. D. Rey, Assessing flow alignment of nematic liquid crystals through linear viscoelasticity, Phys. Rev. E, 70 (2004), 011701.
doi: doi:10.1103/PhysRevE.70.011701. |
[11] |
L. R. P. de Andrade Lima and A. D. Rey, Superposition principles for small amplitude oscillatory shearing of nematic mesophases, Rheol. Acta., 45 (2006), 591-600. |
[12] |
P. G. de Gennes and J. Prost, "The Physics of Liquid Crystals," Oxford University Press, 1993. |
[13] |
G. Derfel, Shear flow induced cholesteric-nematic transition, Mol. Cryst. Liq. Cryst., 92 (1983), 41-47.
doi: doi:10.1080/01406568308084517. |
[14] |
W. Helfrich, Capillary flow of cholesteric and semctic liquid crystals, Phys. Rev. Lett., 23 (1969), 372.
doi: doi:10.1103/PhysRevLett.23.372. |
[15] |
W. Helfrich, Capillary viscometry of cholesteric liquid crystals, in "Proceedings Am. Chem. Soc.," 2nd ed., (1970), 405-418. |
[16] |
U. D. Kini, G. S. Ranganath and S. Chandrasekhar, Flow of cholesteric liquid crystals-I: Flow along the helical axis, Pramana, 5 (1975), 101-106.
doi: doi:10.1007/BF02846036. |
[17] |
U. D. Kini, Shear flow of cholesterics normal to the helical axis, J. Phys. (France), 40 (1979), 62-65. |
[18] |
R. G. Larson, "The Structure and Rheology of Complex Fluids," Oxford University Press (1999). |
[19] |
F. M. Leslie, Continuum theory of cholesteric liquid crystals, Mol. Cryst. Liq. Cryst., 7 (1969), 407-420.
doi: doi:10.1080/15421406908084887. |
[20] |
F. M. Leslie, The theory of flow phenomena in liquid crystals, Adv. Liq. Cryst. 4 (1979), 1-81. |
[21] |
T. Lubenski, Hydrodynamics of cholesteric liquid crystals, Phys. Rev. A, 6 (1969), 452-461.
doi: doi:10.1103/PhysRevA.6.452. |
[22] |
D. Marenduzzo, E. Orlandini and J. M. Yeomans, Permeative flows in cholesteric liquid crystals, Physical Review Letters, 92 (2004), 188301.
doi: doi:10.1103/PhysRevLett.92.188301. |
[23] |
D. Marenduzzo, E. Rlandini and J. M. Yeomans, Interplay between shear flow and elastic deformations in liquid crystals, J. Chem. Phys. 121 (2004), 582-591.
doi: doi:10.1063/1.1757441. |
[24] |
J. Prost, Y. Pomeau and E. Guyon, Stability of permeative flows in 1 dimensionally ordered systems, J. Phys. II, 1 (1991), 289-309.
doi: doi:10.1051/jp2:1991169. |
[25] |
A. D. Rey, Flow-alignment in the helix uncoiling of cholesteric liquid crystals, Phys. Rev. E, 53 (1986), 4198-4201.
doi: doi:10.1103/PhysRevE.53.4198. |
[26] |
A. D. Rey, Structural transformations and viscoelastic response of shear fingerprint cholesteric textures, J. Non-Newt. Fluid Mech., 64 (1996), 207-227.
doi: doi:10.1016/0377-0257(96)01434-6. |
[27] |
A. D. Rey, Helix uncoiling modes of sheared cholesteric liquid crystals, J. Chem. Phys., 104 (1996), 789-792.
doi: doi:10.1063/1.471184. |
[28] |
A. D. Rey, Theory of linear viscoelasticity for chiral liquid crystals, Rheol. Acta, 35 (1996), 400-409.
doi: doi:10.1007/BF00368991. |
[29] |
A. D. Rey, Theory of linear viscoelasticity in cholesteric liquid crystals, J. Rheol., 44 (2000), 855-869.
doi: doi:10.1122/1.551112. |
[30] |
A. D. Rey, Generalized cholesteric permeation flows, Phys. Rev. E, 65 (2002), 022701.
doi: doi:10.1103/PhysRevE.65.022701. |
[31] |
A. D. Rey, Simple shear and small amplitude oscillatory rectilinear shear permeation flows of cholesteric liquid crystals, J. Rheol., 46 (2002), 225-240.
doi: doi:10.1122/1.1428317. |
[32] |
N. Scaramuzza, F. Simoni and R. Bartolino, Permeative flow in cholesteric liquid crystals, Phys. Rev. Lett., 53 (1984), 2246-2249.
doi: doi:10.1103/PhysRevLett.53.2246. |
show all references
References:
[1] |
B. Bird, R. C. Armstrong and O. Hassager, "Dynamics of Polymeric Liquids," Vol 1, John Wiley and Sons, New York, 1987. |
[2] |
W. R. Burghardt, Oscillatory shear flow of nematic liquid crystals, J. Rheol., 35 (1991), 49-62.
doi: doi:10.1122/1.550208. |
[3] |
E. Choate, Z. Cui and M. G. Forest, Effects of strong anchoring on the dynamics moduli of heterogeneous nematic polymers, Rheological Acta., 47 (2008), 223-236.
doi: doi:10.1007/s00397-007-0235-2. |
[4] |
Chandrasekhar, "Liquid Crystals," 2nd ed., Cambridge University Press, Cambridge, 1992. |
[5] |
Z. Cui, Small amplitude oscillatory shear permeation flow of cholesteric liquid crystal polymers, Communications in Mathematical Sciences, 8 (2010), 943-963. |
[6] |
Z. Cui, M. C. Calderer and Q. Wang, Mesostructures in flows of weakly sheared chiral liquid crystalline polymers, Discrete and Continuous Dynamical Systems-Series B, 6 (2006), 291-310. |
[7] |
Z. Cui, et al., On weak plane shear and Poiseuille flows of rigid rod and platelet ensembles, SIAM J. Appl. Math., 66 (2006), 1227-1260.
doi: doi:10.1137/04061934x. |
[8] |
Z. Cui and Q. Wang, A continuum model for flows of chiral liquid crystal polymers and permeation flows, J. Non-Newtonian Fluid Mech., 138 (2006), 44-61.
doi: doi:10.1016/j.jnnfm.2006.04.005. |
[9] |
L. R. P. de Andrade Lima and A. D. Rey, Superposition and universality in the linear viscoelasticity of Leslie-Ericken liquid crystals, J Rheol., 48 (2004), 1067-1084.
doi: doi:10.1122/1.1773784. |
[10] |
L. R. P. de Andrade Lima and A. D. Rey, Assessing flow alignment of nematic liquid crystals through linear viscoelasticity, Phys. Rev. E, 70 (2004), 011701.
doi: doi:10.1103/PhysRevE.70.011701. |
[11] |
L. R. P. de Andrade Lima and A. D. Rey, Superposition principles for small amplitude oscillatory shearing of nematic mesophases, Rheol. Acta., 45 (2006), 591-600. |
[12] |
P. G. de Gennes and J. Prost, "The Physics of Liquid Crystals," Oxford University Press, 1993. |
[13] |
G. Derfel, Shear flow induced cholesteric-nematic transition, Mol. Cryst. Liq. Cryst., 92 (1983), 41-47.
doi: doi:10.1080/01406568308084517. |
[14] |
W. Helfrich, Capillary flow of cholesteric and semctic liquid crystals, Phys. Rev. Lett., 23 (1969), 372.
doi: doi:10.1103/PhysRevLett.23.372. |
[15] |
W. Helfrich, Capillary viscometry of cholesteric liquid crystals, in "Proceedings Am. Chem. Soc.," 2nd ed., (1970), 405-418. |
[16] |
U. D. Kini, G. S. Ranganath and S. Chandrasekhar, Flow of cholesteric liquid crystals-I: Flow along the helical axis, Pramana, 5 (1975), 101-106.
doi: doi:10.1007/BF02846036. |
[17] |
U. D. Kini, Shear flow of cholesterics normal to the helical axis, J. Phys. (France), 40 (1979), 62-65. |
[18] |
R. G. Larson, "The Structure and Rheology of Complex Fluids," Oxford University Press (1999). |
[19] |
F. M. Leslie, Continuum theory of cholesteric liquid crystals, Mol. Cryst. Liq. Cryst., 7 (1969), 407-420.
doi: doi:10.1080/15421406908084887. |
[20] |
F. M. Leslie, The theory of flow phenomena in liquid crystals, Adv. Liq. Cryst. 4 (1979), 1-81. |
[21] |
T. Lubenski, Hydrodynamics of cholesteric liquid crystals, Phys. Rev. A, 6 (1969), 452-461.
doi: doi:10.1103/PhysRevA.6.452. |
[22] |
D. Marenduzzo, E. Orlandini and J. M. Yeomans, Permeative flows in cholesteric liquid crystals, Physical Review Letters, 92 (2004), 188301.
doi: doi:10.1103/PhysRevLett.92.188301. |
[23] |
D. Marenduzzo, E. Rlandini and J. M. Yeomans, Interplay between shear flow and elastic deformations in liquid crystals, J. Chem. Phys. 121 (2004), 582-591.
doi: doi:10.1063/1.1757441. |
[24] |
J. Prost, Y. Pomeau and E. Guyon, Stability of permeative flows in 1 dimensionally ordered systems, J. Phys. II, 1 (1991), 289-309.
doi: doi:10.1051/jp2:1991169. |
[25] |
A. D. Rey, Flow-alignment in the helix uncoiling of cholesteric liquid crystals, Phys. Rev. E, 53 (1986), 4198-4201.
doi: doi:10.1103/PhysRevE.53.4198. |
[26] |
A. D. Rey, Structural transformations and viscoelastic response of shear fingerprint cholesteric textures, J. Non-Newt. Fluid Mech., 64 (1996), 207-227.
doi: doi:10.1016/0377-0257(96)01434-6. |
[27] |
A. D. Rey, Helix uncoiling modes of sheared cholesteric liquid crystals, J. Chem. Phys., 104 (1996), 789-792.
doi: doi:10.1063/1.471184. |
[28] |
A. D. Rey, Theory of linear viscoelasticity for chiral liquid crystals, Rheol. Acta, 35 (1996), 400-409.
doi: doi:10.1007/BF00368991. |
[29] |
A. D. Rey, Theory of linear viscoelasticity in cholesteric liquid crystals, J. Rheol., 44 (2000), 855-869.
doi: doi:10.1122/1.551112. |
[30] |
A. D. Rey, Generalized cholesteric permeation flows, Phys. Rev. E, 65 (2002), 022701.
doi: doi:10.1103/PhysRevE.65.022701. |
[31] |
A. D. Rey, Simple shear and small amplitude oscillatory rectilinear shear permeation flows of cholesteric liquid crystals, J. Rheol., 46 (2002), 225-240.
doi: doi:10.1122/1.1428317. |
[32] |
N. Scaramuzza, F. Simoni and R. Bartolino, Permeative flow in cholesteric liquid crystals, Phys. Rev. Lett., 53 (1984), 2246-2249.
doi: doi:10.1103/PhysRevLett.53.2246. |
[1] |
Zhenlu Cui, M. Carme Calderer, Qi Wang. Mesoscale structures in flows of weakly sheared cholesteric liquid crystal polymers. Discrete and Continuous Dynamical Systems - B, 2006, 6 (2) : 291-310. doi: 10.3934/dcdsb.2006.6.291 |
[2] |
Junyu Lin. Uniqueness of harmonic map heat flows and liquid crystal flows. Discrete and Continuous Dynamical Systems, 2013, 33 (2) : 739-755. doi: 10.3934/dcds.2013.33.739 |
[3] |
Marissa Condon, Jing Gao, Arieh Iserles. On asymptotic expansion solvers for highly oscillatory semi-explicit DAEs. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4813-4837. doi: 10.3934/dcds.2016008 |
[4] |
Shanshan Guo, Zhong Tan. Energy dissipation for weak solutions of incompressible liquid crystal flows. Kinetic and Related Models, 2015, 8 (4) : 691-706. doi: 10.3934/krm.2015.8.691 |
[5] |
Jihong Zhao, Qiao Liu, Shangbin Cui. Global existence and stability for a hydrodynamic system in the nematic liquid crystal flows. Communications on Pure and Applied Analysis, 2013, 12 (1) : 341-357. doi: 10.3934/cpaa.2013.12.341 |
[6] |
Chun Liu, Huan Sun. On energetic variational approaches in modeling the nematic liquid crystal flows. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 455-475. doi: 10.3934/dcds.2009.23.455 |
[7] |
Chun Liu, Jie Shen. On liquid crystal flows with free-slip boundary conditions. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 307-318. doi: 10.3934/dcds.2001.7.307 |
[8] |
Xiaoli Li, Boling Guo. Well-posedness for the three-dimensional compressible liquid crystal flows. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 1913-1937. doi: 10.3934/dcdss.2016078 |
[9] |
Hong Zhou, M. Gregory Forest, Qi Wang. Anchoring-induced texture & shear banding of nematic polymers in shear cells. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : 707-733. doi: 10.3934/dcdsb.2007.8.707 |
[10] |
Yang Liu, Xin Zhong. On the Cauchy problem of 3D nonhomogeneous incompressible nematic liquid crystal flows with vacuum. Communications on Pure and Applied Analysis, 2020, 19 (11) : 5219-5238. doi: 10.3934/cpaa.2020234 |
[11] |
Francisco Guillén-González, Mouhamadou Samsidy Goudiaby. Stability and convergence at infinite time of several fully discrete schemes for a Ginzburg-Landau model for nematic liquid crystal flows. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4229-4246. doi: 10.3934/dcds.2012.32.4229 |
[12] |
Jishan Fan, Fei Jiang. Large-time behavior of liquid crystal flows with a trigonometric condition in two dimensions. Communications on Pure and Applied Analysis, 2016, 15 (1) : 73-90. doi: 10.3934/cpaa.2016.15.73 |
[13] |
Yang Liu, Sining Zheng, Huapeng Li, Shengquan Liu. Strong solutions to Cauchy problem of 2D compressible nematic liquid crystal flows. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 3921-3938. doi: 10.3934/dcds.2017165 |
[14] |
Yinxia Wang. A remark on blow up criterion of three-dimensional nematic liquid crystal flows. Evolution Equations and Control Theory, 2016, 5 (2) : 337-348. doi: 10.3934/eect.2016007 |
[15] |
Dongfen Bian, Yao Xiao. Global well-posedness of non-isothermal inhomogeneous nematic liquid crystal flows. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1243-1272. doi: 10.3934/dcdsb.2020161 |
[16] |
Hao Wu. Long-time behavior for nonlinear hydrodynamic system modeling the nematic liquid crystal flows. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 379-396. doi: 10.3934/dcds.2010.26.379 |
[17] |
Shengquan Liu, Jianwen Zhang. Global well-posedness for the two-dimensional equations of nonhomogeneous incompressible liquid crystal flows with nonnegative density. Discrete and Continuous Dynamical Systems - B, 2016, 21 (8) : 2631-2648. doi: 10.3934/dcdsb.2016065 |
[18] |
Stefano Bosia. Well-posedness and long term behavior of a simplified Ericksen-Leslie non-autonomous system for nematic liquid crystal flows. Communications on Pure and Applied Analysis, 2012, 11 (2) : 407-441. doi: 10.3934/cpaa.2012.11.407 |
[19] |
Eric S. Wright. Macrotransport in nonlinear, reactive, shear flows. Communications on Pure and Applied Analysis, 2012, 11 (5) : 2125-2146. doi: 10.3934/cpaa.2012.11.2125 |
[20] |
Zhaoyang Qiu, Yixuan Wang. Martingale solution for stochastic active liquid crystal system. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2227-2268. doi: 10.3934/dcds.2020360 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]