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Complex microstructures of liquid-crystalline polymers in nonhomogenous shear flow are studied by element free Galerkin (EFG) method based on the micro-macro dualscale model. The dualscale model combines the orientational diffusion equation in microscale with the flow governing equations in macroscale. The EFG method which has the merits of high accuracy and good stability can ensure the reliability of the simulation results. One simple and five composite structures of liquid-crystalline polymers in nonhomogenous shear flow are predicted by studying the influences of Deborah number on microstructures of liquid-crystalline polymers in plane Poiseuille flow. It shows that the instabilities in the transition region of the composite structures can cause some defects.
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Keywords:
- liquid-crystaline /
- microstructure /
- dualscale /
- EFG
[1] Larson R G 1999 The structure and Rheology of Complex Fluids (Oxford: Oxford University Press) 64—69
[2] Marrucci G, Greco F 1991 Mol. Cryst. Liq. Cryst. 206 17
[3] (in Chinese)[苏 进、欧阳洁、王晓东 2010 物理学报 59 3362]
[4] Doi M, Edwards S F 1986 The Theory of Polymer Dynamics (Oxford: Oxford University Press) 289—322
[5] Helzel C, Otto F 2006 J. Comput. Phys. 216 52
[6] Yu H, Zhang P W 2007 J. Non-Newtonian Fluid Mech. 114 116
[7] Green M J, Brown R A, Armstrong R C 2009 J. Non-Newtonian Fluid Mech. 157 34
[8] Zhang H P, Ouyang, Ruan CH L 2009 Acta Phys. Sin. 58 619 (in Chinese) [张红平、 欧阳洁、 阮春蕾 2009 物理学报58 619]
[9] Yu H, Ji G, Zhang P W 2010 Commun. Comput. Phys. 7 383
[10] Su J, Ouyang J, Wang X D 2010 Acta Phys. Sin. 59 3362
[11] Liu G R, Gu Y T 2005 An Introduction to Meshfree Methods and their Programming (Netherlands: Springer)
[12] Nguyen V P, Rabczuk T, Bordas S, Duflot M 2008 Math. Comput. Simulat. 79 763
[13] Belytschko T, Lu Y Y, Gu L 1994 Int. J. Numer. Meth. Eng. 37 229
[14] Zhang Z, Zhao P, Liew K M 2009 Eng. Anal. Bound. Elem. 33 547
[15] Zhou N 2005 MS Thesis (Beijing: Peking University) (in Chinese) [周 娜 2005 硕士论文 (北京: 北京大学)]
[16] Lozomski A 2003 Ph. D. Dissertation (Lausanne: Ecole Polytechnique Fédérale de Lausanne)
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[1] Larson R G 1999 The structure and Rheology of Complex Fluids (Oxford: Oxford University Press) 64—69
[2] Marrucci G, Greco F 1991 Mol. Cryst. Liq. Cryst. 206 17
[3] (in Chinese)[苏 进、欧阳洁、王晓东 2010 物理学报 59 3362]
[4] Doi M, Edwards S F 1986 The Theory of Polymer Dynamics (Oxford: Oxford University Press) 289—322
[5] Helzel C, Otto F 2006 J. Comput. Phys. 216 52
[6] Yu H, Zhang P W 2007 J. Non-Newtonian Fluid Mech. 114 116
[7] Green M J, Brown R A, Armstrong R C 2009 J. Non-Newtonian Fluid Mech. 157 34
[8] Zhang H P, Ouyang, Ruan CH L 2009 Acta Phys. Sin. 58 619 (in Chinese) [张红平、 欧阳洁、 阮春蕾 2009 物理学报58 619]
[9] Yu H, Ji G, Zhang P W 2010 Commun. Comput. Phys. 7 383
[10] Su J, Ouyang J, Wang X D 2010 Acta Phys. Sin. 59 3362
[11] Liu G R, Gu Y T 2005 An Introduction to Meshfree Methods and their Programming (Netherlands: Springer)
[12] Nguyen V P, Rabczuk T, Bordas S, Duflot M 2008 Math. Comput. Simulat. 79 763
[13] Belytschko T, Lu Y Y, Gu L 1994 Int. J. Numer. Meth. Eng. 37 229
[14] Zhang Z, Zhao P, Liew K M 2009 Eng. Anal. Bound. Elem. 33 547
[15] Zhou N 2005 MS Thesis (Beijing: Peking University) (in Chinese) [周 娜 2005 硕士论文 (北京: 北京大学)]
[16] Lozomski A 2003 Ph. D. Dissertation (Lausanne: Ecole Polytechnique Fédérale de Lausanne)
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