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In this paper the complex rheological behaviors of rod-like polymer solutions in plane Couette flow are studied using micro-macro simulation. The micro-macro model is described by Doi theory with local inhomogeneous fluid. The finite volume method is used to solve the conservation equation on the macroscopic level and the Smoluchowski equation on the microscopic level in the numerical simulation. The numerical results predict several plane flow modes including some typical plane modes and two new complicated modes. Furthermore, simulation results show that the rheological phase diagrams for solutions of rigid rod molecules are mainly dependent on the Deborah number, the concentration of solutions and molecular scale, and the varying Deborah number have great influence on some micro-properties of tumbling period and orientation angle of flow-aligning.
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Keywords:
- rod-like molecules /
- polymeric solutions /
- micro-macro simulation
[1] ［1］Keunings R 2001 Computational Fluid Dynamics Journal. 9(4) 449
[2] ［2］Zhang H P, Ouyang J,Ruan C L 2009 Acta Phys. Sin. 58 619（in Chinese） ［张红平、 欧阳洁、 阮春蕾 2009 58 619］
[3] ［3］Zhou R, Forest M G, Wang Q 2005 Multi-scale Model. Simul. 3(4) 853
[4] ［4］Forest M G, Zhou R, Wang Q 2005 Multi-scale Model. Simul. 4(4) 1280
[5] ［5］Green M J, Brown R, Armstrong R C 2009 J. Non-Newtonian Fluid Mech.157 34
[6] ［6］Doi M, Edwards S F 1986 The Theory of Polymer Dynamics (Oxford: Oxford University Press) p289
[7] ［7］Yu H J, Zhang P W 2007 J. Non-Newtonian Fluid Mech.141 116
[8] ［8］E W N, Zhang P W 2004 Phys. Rev. E 65 051504
[9] ［9］Zhou N. 2005 MS dissertation (Peking: Peking University) (in Chinese) ［周娜 2005 硕士论文 (北京: 北京大学)］
[10] ］Strang G 1968 SIAM J.Num. Anal.5 506
[11] ］Tao W Q 2004 Numerical Heat Transfer(Xian: Xian Jiaotong University Press) p176 (in Chinese) ［陶文铨 2004 数值传热学 (西安: 西安交通大学出版社) 第176页］［12］Rey A D, Tsuji T 1998 Phys. Rev. E 57 5610
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[1] ［1］Keunings R 2001 Computational Fluid Dynamics Journal. 9(4) 449
[2] ［2］Zhang H P, Ouyang J,Ruan C L 2009 Acta Phys. Sin. 58 619（in Chinese） ［张红平、 欧阳洁、 阮春蕾 2009 58 619］
[3] ［3］Zhou R, Forest M G, Wang Q 2005 Multi-scale Model. Simul. 3(4) 853
[4] ［4］Forest M G, Zhou R, Wang Q 2005 Multi-scale Model. Simul. 4(4) 1280
[5] ［5］Green M J, Brown R, Armstrong R C 2009 J. Non-Newtonian Fluid Mech.157 34
[6] ［6］Doi M, Edwards S F 1986 The Theory of Polymer Dynamics (Oxford: Oxford University Press) p289
[7] ［7］Yu H J, Zhang P W 2007 J. Non-Newtonian Fluid Mech.141 116
[8] ［8］E W N, Zhang P W 2004 Phys. Rev. E 65 051504
[9] ［9］Zhou N. 2005 MS dissertation (Peking: Peking University) (in Chinese) ［周娜 2005 硕士论文 (北京: 北京大学)］
[10] ］Strang G 1968 SIAM J.Num. Anal.5 506
[11] ］Tao W Q 2004 Numerical Heat Transfer(Xian: Xian Jiaotong University Press) p176 (in Chinese) ［陶文铨 2004 数值传热学 (西安: 西安交通大学出版社) 第176页］［12］Rey A D, Tsuji T 1998 Phys. Rev. E 57 5610
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