Solution of three-dimensional fiber orientation in two-dimensional fiber suspension flows

Physics of Fluids

Volumn 19, Issue 11, 2007, Pages

  Zhou, Kun ^a   Lin, Jianzhong ^a,b   Chan, Tat Leung ^c  

^a ZHEJIANG UNIVERSITY   (China)

^b CHINA JILIANG UNIVERSITY   (China)

^c HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FLUID DYNAMICS; PECLET NUMBER; PERTURBATION TECHNIQUES; ROTATIONAL FLOW; SUSPENSIONS (FLUIDS);

FOKKER-PLANCK EQUATION; THREE-DIMENSIONAL FIBER ORIENTATION; TWO-DIMENSIONAL FIBER SUSPENSION FLOWS;

FIBER REINFORCED MATERIALS;

COMPUTER SIMULATION; FIBER REINFORCED MATERIALS; FLUID DYNAMICS; PECLET NUMBER; PERTURBATION TECHNIQUES; ROTATIONAL FLOW; SUSPENSIONS (FLUIDS);

EID: 36849000703     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2815718     Document Type: Article

References (50)

1. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1965).
2. S. B. Chen and L. Jiang, "Orientation distribution in a dilute suspension of fibers subject to simple shear flow," Phys. Fluids PHFLE61070-663110.1063/1.870146 11, 2878 (1999).
3. Z. H. Wan and J. Z. Lin, "Hydrodynamic instability of semi-concentration fiber suspensions between two rotating coaxial cylinders," Int. J. Nonlinear Sci. Numer. Simul. IJNS5F1565-1339 5, 211 (2004).
4. J. Z. Lin, X. Shi, and Z. S. Yu, "The motion of fibers in an evolving mixing layer," Int. J. Multiphase Flow IJMFBP0301-932210.1016/S0301-9322(03)00086-7 29, 1355 (2003).
5. J. Z. Lin, W. F. Zhang, and Z. S. Yu, "Numerical research on the orientation distribution of fibers immersed in laminar and turbulent pipe flows," J. Aerosol Sci. JALSB70021-850210.1016/ j.jaerosci.2004.05.007 35, 63 (2004).
6. T. Nishinura, K. Yasuda, and K. Nakamura, "Orientation behaviour of fibers in suspension flow through a branching channel," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/S0377-0257(97)00046-3 73, 279 (1997).
7. J. Z. Lin, X. Shi, and Z. J. You, "Effects of the aspect ratio on the sedimentation of a fiber in newtonian fluids," J. Aerosol Sci. JALSB70021-850210.1016/S0021-8502(03)00023-5 34, 909 (2003).
8. J. Z. Lin, K. Sun, and J. Lin, "Distribution of orientations in fiber suspension flowing in a turbulent boundary layer," Chin. Phys. Lett. CPLEEU0256-307X10.1088/0256-307X/22/12/036 22, 3111 (2005).
9. J. Z. Lin, S. L. Zhang, and J. A. Olson, "Effect of fibers on the flow property of turbulent fiber suspensions in a contraction," Fibers Polym. FPIOA61229-9197 18, 60 (2007).
10. J. A. Olson, I. Frigaard, C. Chan, and J. P. Hamalainen, "Modeling a turbulent fibre suspension flowing in a planar contraction: The one-dimensional headbox," Int. J. Multiphase Flow IJMFBP0301-932210.1016/j.ijmultiphaseflow.2003.10.006 30, 51 (2004).
11. M. Parsheh, M. L. Brown, and C. K. Aidun, "On the orientation of stiff fibres suspended in turbulent flow in a planar contraction," J. Fluid Mech. JFLSA70022-112010.1017/S0022112005006968 545, 245 (2005).
12. L. X. Zhang, J. Z. Lin, and T. L. Chan, "Orientation distribution of cylindrical particles suspended in a turbulent pipe flow," Phys. Fluids PHFLE61070-663110.1063/1.2046713 17, 093105 (2005).
13. S. L. Zhang, J. Z. Lin, and W. F. Zhang, "Numerical research on the fiber suspensions in a turbulent T-shaped branching channel flow," Chin. J. Chem. Eng. CJCEEB1004-9541 15, 30 (2007).
14. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, 2nd ed. (Wiley, New York, 1987), Vol. 1.
15. R. B. Bird, O. Hassager, R. C. Armstrong, and C. F. Curtiss, Dynamics of Polymeric Liquids, 2nd ed. (Wiley, New York, 1987), Vol. 2.
16. J. M. J. Dentoonder, M. A. Hulsen, G. D. C. Kuiken, and F. T. M. Nieuwstadt, "Drag reduction by polymer additives in a turbulent pipe flow: Numerical and laboratory experiments," J. Fluid Mech. JFLSA70022-112010.1017/S0022112097004850 337, 193 (1997).
17. J. S. Paschkewitz, Y. Dubief, C. D. Dimitropoulos, E. S. G. Shaqfeh, and P. Moin, "Numerical simulation of turbulent drag reduction using rigid fibres," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112004001144 518, 281 (2004).
18. M. Manhart, "Rheology of suspensions of rigid-rod like particles in turbulent channel flow," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/S0377-0257(03)00105-8 112, 269 (2003).
19. G. K. Batchelor, "The stress system in a suspension of force-free particles," J. Fluid Mech. JFLSA70022-112010.1017/S0022112070000745 41, 545 (1970).
20. G. K. Batchelor, "Slender-body theory for particles of arbitrary cross-section in Stokes flow," J. Fluid Mech. JFLSA70022-112010.1017/S002211207000191X 44, 419 (1970).
21. G. K. Batchelor, "The stress generated in a non-dilute suspension of elongated particles by pure straining motion," J. Fluid Mech. JFLSA70022-112010.1017/S0022112071000879 46, 813 (1971).
22. E. S. G. Shaqfeh and G. H. Fredrickson, "The hydrodynamic stress in a suspension of rods," Phys. Fluids A PFADEB0899-821310.1063/ 1.857683 2, 7 (1990).
23. E. J. Hinch and L. G. Leal, "Constitutive equations in suspension mechanics. Part 1. General formulation," J. Fluid Mech. JFLSA70022-112010.1017/S0022112075002698 71, 481 (1975).
24. E. J. Hinch and L. G. Leal, "Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations," J. Fluid Mech. JFLSA70022-112010.1017/S0022112076003200 76, 187 (1975).
25. S. G. Advani and C. L. Tucker III, "Closure approximations for three-dimensional structure tensors," J. Rheol. JORHD20148-605510.1122/1.550133 34, 367 (1990).
26. J. S. Cintra and C. L. Tucker III, "Orthotropic closure approximations for flow-induced fiber orientation," J. Rheol. JORHD20148-605510.1122/1.550630 39, 1095 (1995).
27. K. H. Han and Y. T. Im, "Modified hybrid closure approximation for prediction of flow-induced fiber orientation," J. Rheol. JORHD20148-605510.1122/1.551002 43, 569 (1999).
28. M. Parsheh, M. L. Brown, and C. K. Aidun, "Investigation of closure approximations for fiber orientation distribution in contracting turbulent flow," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/j.jnnfm.2006.03.001 136, 38 (2006).
29. M. C. Altan and B. N. Rao, "Closed-form solution for the orientation field in a center-gated disk," J. Rheol. JORHD20148-605510.1122/1.550714 39, 581 (1995).
30. L. Tang and M. C. Altan, "Entry flow of fiber suspension in a straight channel," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/0377-0257(94)01280-U 56, 183 (1995).
31. K. A. Ericsson, S. Toll, and J. A. E. Manson, "The two-way interaction between anisotropic flow and fiber orientation in squeeze flow," J. Rheol. JORHD20148-605510.1122/1.550833 41, 491 (1997).
32. G. B. Jeffery, "The motion of ellipsoidal particles immersed in a viscous fluid," Proc. R. Soc. London, Ser. A PRLAAZ1364-502110.1098/ rspa.1922.0078 102, 161 (1922).
33. D. Jackson, "The harmonic boundary value problem for an ellipse or an ellipsoid," Am. Math. Monthly AMMYAE10.2307/2304576 51, 555 (1944).
34. G. I. Taylor, "The motion of ellipsoidal particles in a viscous fluid," Proc. R. Soc. London, Ser. A PRLAAZ1364-502110.1098/ rspa.1923.0040 103, 58 (1923).
35. F. P. Bretherton, "The motion of rigid particles in a shear flow at low Reynolds number," J. Fluid Mech. JFLSA70022-112010.1017/ S002211206200124X 14, 284 (1962).
36. S. M. Dinh and R. C. Armstrong, "A rheological equation of state for semiconcentrated fiber suspensions," J. Rheol. JORHD20148-605510.1122/1.549748 28, 207 (1984).
37. F. Folgar and C. L. Tucker III, "Orientation behavior of fibers in concentrated suspensions," J. Reinf. Plast. Compos. JRPCDW0731-684410.1177/073168448400300201 3, 98 (1984).
38. C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed. (Springer-Verlag, New York, 1997).
39. H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications, 2nd ed. (Springer-Verlag, Berlin, 1989).
40. V. I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed. (Springer-Verlag, New York, 1989).
41. K. Zhou and J. Z. Lin, "Analytical research on 3D fiber orientation distribution in arbitrary planar flows," J. Zhejiang Univ., Sci. A JZUSFR1009-309510.1631/jzus.2007.A1021 8, 1021 (2007).
42. K. Chiba, K. Yasuda, and K. Nakamura, "Numerical solution of fiber suspension flow through a parallel plate channel by coupling flow field with fiber orientation distribution," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/S0377-0257(01)00118-5 99, 145 (2001).
43. A. J. Szeri and L. G. Leal, "A new computational method for the solution of flow problems of microstructured fluids. Part 2. Inhomogeneous shear flow of a suspension," J. Fluid Mech. JFLSA70022-112010.1017/S0022112094000479 262, 171 (1994).
44. J. P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd ed. (Dover, New York, 2000).
45. D. L. Koch, "A model for orientational diffusion in fiber suspensions," Phys. Fluids PHFLE61070-663110.1063/1.868455 7, 2086 (1995).
46. E. S. G. Shaqfeh and D. L. Koch, "Orientational dispersion of fibers in extensional flows," Phys. Fluids A PFADEB0899-821310.1063/ 1.857608 2, 1077 (1990).
47. R. Courant, Methods of Mathematical Physics (Interscience, New York, 1962), Vol. II.
48. A. J. Szeri and L. G. Leal, "A new computational method for the solution of flow problems of microstructured fluids. Part 1. Theory," J. Fluid Mech. JFLSA70022-112010.1017/S0022112092002490 242, 549 (1992).
49. W. Greiner, Classical Mechanics: System of Particles and Hamiltonian Dynamics (Springer-Verlag, New York, 2003).
50. L. G. Leal and E. J. Hinch, "The effect of weak Brownian rotation on particles in shear flow," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112071000788 46, 685 (1971).