Inhomogeneous distribution of a rigid fibre undergoing rectilinear flow between parallel walls at high Péclet numbers

Journal of Fluid Mechanics

Volumn 630, Issue , 2009, Pages 267-298

  Park, Joontaek ^a   Butler, Jason E ^a  

^a University of Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FIBERS; HYDRODYNAMICS; PARALLEL FLOW; REYNOLDS NUMBER; SUSPENSIONS (FLUIDS);

EFFECTIVE STRESS; HYDRODYNAMIC INTERACTION; HYDRODYNAMIC LIFT FORCES; INHOMOGENEOUS DISTRIBUTION; RECTILINEAR FLOW; SIMPLE SHEAR FLOW; SLENDER-BODY THEORY; STEADY AND TRANSIENT;

SHEAR FLOW;

COMPUTER SIMULATION; HYDRODYNAMICS; PREDICTION; REYNOLDS NUMBER; SHEAR FLOW; THEORETICAL STUDY; TRANSIENT FLOW;

EID: 67651062142     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009006545     Document Type: Article

References (72)

1. AGARWAL, U. S., DUTTA, A. & MASHELKAR, R. A. 1994 Migration of macromolecules under flow: The physical origin and engineering implications. Chem. Engng Sci. 49, 1693-1717.
2. ASOKAN, K., RAMAMOHAN, T. R. & KUMARA, V. 2002 A novel approach to computing the orientation moments of spheroids in simple shear flow at arbitrary Péclet number. Phys. Fluids 14, 75-84.
3. ATTANSIO, A., BERNINI, U., GALLOPO, P. & SEGRE, G. 1972 Significance of viscosity measurements in macroscopic suspensions of elongated particles. Trans. Soc. Rheol. 16, 147-154.
4. AUSSERRE, D., EDWARDS, J., LECOURTIER, J., HERVET, H. & RONDELEX, F. 1991 Hydro-dynamic thickening of depletion layers in colloidal solutions. Europhys. Lett. 14, 33-38.
5. BATCHELOR, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419-440.
6. BATCHELOR, G. K. 1971 The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J. Fluid Mech. 46, 813-829.
7. BEENAKKER, C. W. J. 1986 Ewald sum of the Rotne-Prager tensor. J. Chem. Phys. 85, 1581-1582.
8. BLAKE, J. R. 1971 A note on the image system for a Stokeslet in a no-slip boundary. Proc. Cambridge Phil. Soc. 70, 303-310.
9. BRENNER, H. 1974 Rheology of a dilute suspension of axisymmetric Brownian particles. Intl J. Multiphase Flow 1, 195-341.
10. BRICKER, J. M. & BUTLER, J. E. 2007 Correlation between structures and microstructures in concentrated suspensions of non-Brownian spherical particles subject to unsteady shear flows. J. Rheol. 51, 735-759.
11. BRICKER, J. M., PARK, H.-O. & BUTLER, J. E. 2008 Rheology of semidilute suspensions of rigid polystyrene ellipsoids at high Péclet numbers. J. Rheol. 52, 941-955.
12. BUTLER, J. E. & SHAQFEH, E. S. G. 2002 Dynamic simulations of the inhomogeneous sedimentation of rigid fibers. J. Fluid Mech. 468 205-237.
13. BUTLER, J. E. & SHAQFEH, E. S. G. 2005 Brownian dynamics simulations of a flexible polymer chain which includes continuous resistance and multibody hydrodynamic interactions. J. Chem. Phys. 122, 01491.
14. BUTLER, J. E., USTA, O. B., KEKRE, R. & LADD, A. J. C. 2007 Kinetic theory of a confined polymer driven by an external force and pressure-driven flow. Phys. Fluids 19, 113101.
15. CHAOUCHE, M. & KOCH, D. L. 2001 Rheology of non-Brownian rigid fiber suspensions with adhesive contacts. J. Rheol. 45, 369-382.
16. CHEN, S. B. & JIANG, L. 1999 Orientation distribution in a dilute suspension of fibers subject to simple shear flow. Phys. Fluids 11, 2878-2890.
17. CHEN, S. B. & KOCHh, D. L. 1996 Rheology of dilute suspensions of charged fibers. Phys. Fluids 8, 2792-2807.
18. CLAEYS, I. L. & BRADY, J. F. 1989 Lubrication singularites of the grand resistance tensor for two arbitrary particles. Physico-Chem. Hydrodyn. 11, 261-293.
19. COBB, P. D. & BUTLER, J. E. 2005 Simulations of concentrated suspensions of rigid fibers: Relationship between short-time diffusivities and the long-time rotational diffusion. J. Chem. Phys. 123, 054908.
20. COX, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44, 791-810.
21. DHONT, J. K. G. & BRIELS, W. J. 2003 Inhomogeneous suspensions of rigid rods in flow. J. Chem. Phys. 118, 1466.
22. DOI, M. & EDWARDS, S. F. 1986 The Theory of Polymer Dynamics Oxford University Press.
23. FANG, L., HU, H. & LARSON, R. 2005 DNA configuration and concentration in shearing flow near a glass surface in a microchannel. J. Rheol. 49, 127.
24. FIXMAN, M. 1978 Simulation of polymer dynamics. Part 1. General theory. J. Chem. Phys. 69, 1527-1537.
25. GANANI, E. & POWLL, R. L. 1985 Suspensions of rodlike particles: literature review and data correlations. J. Composite Mater. 19 194-215.
26. GRASSIA, P. S., HINCH, E. J. & NITSCHE, L. C. 1995 Computer simulations of Brownian motion of complex systems. J. Fluid Mech. 282, 373-403.
27. HAPPEL, J. & BRENNER, H. 1965 Low Reynolds Number Hydrodynamics Prentice Hall.
28. HARLEN, O. G., SUNDARARAJAKUMAR, R. R. & KOCH, D. L. 1999 Numerical simulation of a sphere settling through a suspension of neutrally buoyant fibers. J. Fluid Mech. 388, 355-388.
29. HASIMOTO, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317-328.
30. HERNÁNDEZ-ORTIZ, J. P., DE PABLO, J. J. & GRAHAM, M. D. 2006 Cross-stream-line migration in confined flowing polymer solutions: theory and simulation. Phys. Fluids 18, 123101.
31. HIJAZI, A. & KHATER, A. 2001 Brownian dynamics simulations of rigid rod-like macromolecular particles flowing in bounded channels. Comput. Mater. Sci. 22, 279-290.
32. HIJAZI, A. & ZOAETER, M. 2002 Brownian dynamics simulations of rigid rod-like particlesin dilute flowing solution. Eur. Polym. J. 38, 2207-2211.
33. HINCH, E. J. & LEAL, L. G. 1972 The effect of Brownian motion on the rheological properties of suspension of non-spherical particles. J. Fluid Mech. 52, 683-712.
34. HINCH, E. J. & LEAL, L. G. 1976 Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations. J. Fluid Mech. 76, 187-208.
35. HODA, N. & KUMAR, S. 2007a Brownian dynamics simulations of polyelectrolyte adsorption in shear flow with hydrodynamic. J. Chem. Phys. 127, 234902.
36. HODA, N. & KUMAR, S. 2007b Kinetic theory of polyelectrolyte adsorption in shear flow. J. Rheol. 51, 799-820.
37. HODA, N. & KUMAR, S. 2008 Brownian dynamics simulations of polyelectrolyte adsorption in shear flow: Effects of solvent quality and charge patterning. J. Chem. Phys. 128, 164907.
38. HOLM, R. & SÖDERBERG, D. 2007 Shear influence on fibre orientation: Dilute suspension in the near wall region. Rheol. Acta 46, 721-729.
39. HSU, R. & GANATOS, P. 1976 Gravitational and zero-drag motion of a spheroid adjacent to an inclined plane at low Reynolds number. J. Fluid Mech. 268, 267.
40. JENDREJACK, R. M., SCHWARTZ, D. C., DE PABLO, J. J. & GRAHAM, M. D. 2004 Shear-induced migration in flowing polymer solutions: Simulation of long-chain DNA in microchannels. J. Chem. Phys. 120, 2513-2519.
41. LEAL, L. G. & HINCH, E. J. 1971 The effect of weak Brownian rotation on particles in shear flow. J. Fluid Mech. 46, 685-703.
42. LIRON, N. & MOCHON, S. 1976 Stokes flow for a Stokeslet between two parallel flat plates. J. Engng Math. 10, 287-303.
43. MA, H. & GRAHAM, M. 2005 Theory of shear-induced migration in dilute polymer solutions near solid boundaries. Phys. Fluids 17 083103.
44. MODY, N. A. & KING, M. R. 2005 Three-dimensional simulations of a platelet-shaped spheroid near a wall in shear flow. Phys. Fluids 17, 113302.
45. MORSE, D. C. 2004 Theory of constrained Brownian motion. Adv. Chem. Phys. 128, 65-189.
46. MOSES, K. B., ADVANI, S. G. & REINHARDTt, A. 2001 Investigation of fiber motion near solid boundaries in simple shear flow. Rheol. Acta 40, 296-306.
47. NITSCHE, L. C. & HINCH, E. J. 1997 Shear-induced lateral migration of Brownian rigid rods in parabolic channel flow. J. Fluid Mech. 332, 1-21.
48. NITSCHE, J. M. & ROY, P. 1996 Shear-induced alignment of nonspherical Brownian particles near walls. AIChE J. 42, 2729-2742.
49. NOTT, P. R. & BRADY, J. F. 1994 Pressure-driven flow of suspensions: Simulation and theory. J. Fluid Mech. 275, 157-199.
50. OLLA, P. 1999 Simplified model for red cell dynamics in small blood vessels. Phys. Rev. Lett. 82, 453-456.
51. DE PABLO, J. J., OTTINGER, H. C. & RABIN, Y. 1992 Hydrodynamic changes of the depletion layer of dilute polymer solutions near a wall. AIChE J. 38, 273-283.
52. PARK, J., BRICKER, J. M. & BUTLER, J. E. 2007 Cross-stream migration in dilute solutions of rigid polymers undergoing rectilinear flow near a wall. Phys. Rev. E 76, 040801.
53. PETRIE, C. J. S. 1999 The rheology of fibre suspensions. J. Non-Newton. Fluid Mech. 87, 369-402.
54. PRYAMITSYN, V. & GANESAN, V. 2008 Screening of hydrodynamic interactions in Brownian rod suspensions. J. Chem. Phys. 128 134901.
55. ROTNE, J. & PRAGER, S. 1969 Variational treatment of hydrodynamic interaction in polymers. J. Chem. Phys. 50, 4831-4837.
56. SAINTILLAN, D., SHAQFEH, E. S. G. & DARVE, E. 2006a Effect of flexibility on the shear-induced migration of short-chain polymers in parabolic channel flow. J. Fluid Mech. 557, 297-306.
57. SAINTILLAN, D., SHAQFEH, E. S. G. & DARVE, E. 2006b The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation. J. Fluid Mech. 553, 347-388.
58. SAINTILLAN, D., SHAQFEH, E. S. G. & DARVE, E. 2006c Hydrodynamic interactions in the induced-charge electrophoresis of colloidal rod dispersions. J. Fluid Mech. 563, 223-259.
59. SCHIEK, R. L. & SHAQFEH, E. S. G. 1995 A nonlocal theory for stress in bound, Brownian suspensions of slender, rigid fibers. J. Fluid Mech. 296, 271-324.
60. SCHIEK, R. L. & SHAQFEH, E. S. G. 1997 Cross-streamline migration of slender Brownian fibres in plane Poiseuille flow. J. Fluid Mech. 332, 23-39.
61. SHAQFEH, E. S. G. & FREDRICKSON, H. 1990 The hydrodynamic stress in a suspension of rods. Phys. Fluids A 2, 7-24.
62. SINGH, A. & NOTT, P. 2000 Normal stresses and microstructure in bounded sheared suspensions via Stokesian dynamics simulations. J. Fluid Mech. 412, 279-301.
63. STABEN, M. E., ZINCHENKO, A. Z. & DAVIS, R. H. 2003 Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Phys. Fluids 15, 1711-1733.
64. STONE, H. A., STROOCK, A. D. & AJDARI, A. 2004 Engineering flows in small devices: Microfluidics towards a lab-on-a-chip. Annu. Rev. Fluid Mech. 36, 381-411.
65. STOVER, C. A. & COHEN, C. 1990 The motion of rodlike particles in the pressure-driven flow between two flat plates. Rheol. Acta 29, 192-203.
66. STOVER, C. A., KOCH, D. L. & COHEN, C. 1992 Observations of fibre orientation in simple shear flow of semi-dilute suspensions. J. Fluid Mech. 238, 277-296.
67. SUNDARARAJAKUMAR, R. R. & KOCH, D. L. 1997 Structure and properties of sheared fiber suspensions with mechanical contacts. J. Non-Newton. Fluid Mech. 73, 205-239.
68. TORNBERG, A.-K. & GUSTAVSSON, K. 2006 A numerical method for simulations of rigid fiber suspensions. J. Comput. Phys. 215 172-196.
69. USTA, O. B., BUTLER, J. E. & LADD, A. J. C. 2006 Flow induced migration of polymers in dilute solution. Phys. Fluids 18, 031703.
70. USTA, O. B., BUTLER, J. E. & LADD, A. J. C. 2007 Transverse migration of a confined polymer driven by an external force. Phys. Rev. Lett. 98, 098301.
71. YANG, S. M. & LEAL, L. G. 1984 Particle motion in Stokes flow near a plane fluid-fluid interface. Part 2. Linear shear and axisymmetric straining flows. J. Fluid Mech. 149, 275-304.
72. ZURITA-GOTOR, M., BŁAWZDZIEWICZ, J. & WAJNRYB, E. 2007 Motion of a rod-like particle between parallel walls with application to suspension rheology. J. Rheol. 51, 71-97.