1932

Abstract

The dynamics and rheology of suspensions of rigid, non-Brownian fibers in Newtonian fluids are reviewed. Experiments, theories, and computer simulations are considered, with an emphasis on suspensions at semidilute and concentrated conditions. In these suspensions, interactions between the particles strongly influence the microstructure and rheological properties of the suspension. The interactions can arise from hydrodynamic disturbances, giving multibody interactions at long ranges and pairwise lubrication forces over short distances. For concentrated suspensions, additional interactions due to excluded volume (contacts) and adhesive forces are addressed. The relative importance of the various interactions as a function of fiber concentration is assessed.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-122316-045144
2018-01-05
2024-04-15
Loading full text...

Full text loading...

/deliver/fulltext/fluid/50/1/annurev-fluid-122316-045144.html?itemId=/content/journals/10.1146/annurev-fluid-122316-045144&mimeType=html&fmt=ahah

Literature Cited

  1. Advani SG, Tucker CLI. 1987. The use of tensors to describe and predict fiber orientation in short fiber composites. J. Rheol. 31:751–84 [Google Scholar]
  2. Batchelor GK. 1970a. Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44:419–40 [Google Scholar]
  3. Batchelor GK. 1970b. The stress system in a suspension of force-free particles. J. Fluid Mech. 41:545–70 [Google Scholar]
  4. Batchelor GK. 1971. The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J. Fluid Mech. 46:813–29 [Google Scholar]
  5. Batchelor GK, Green JT. 1972. The determination of the bulk stress in a suspension of spherical particles to order c2. J. Fluid Mech. 56:401–27 [Google Scholar]
  6. Bennington CPJ, Kerekes RJ, Grace JR. 1990. The yield stress of fibre suspensions. Can. J. Chem. Eng. 68:748–57 [Google Scholar]
  7. Bibbó MA. 1987. Rheology of semiconcentrated fiber suspensions PhD Thesis, Mass. Inst. Technol.
  8. Bibbó MA, Dinh SM, Armstrong RC. 1985. Shear flow properties of semiconcentrated fiber suspensions. J. Rheol. 29:905–29 [Google Scholar]
  9. Bivens CH, Boney C, Fredd C, Lassek J, Sullivan P. et al. 2005. New fibers for hydraulic fracturing. Oilfield Rev 17:34–43 [Google Scholar]
  10. Bounoua S, Kuzhir P, Lemaire É. 2016a. Normal stress differences in non-Brownian fiber suspensions. J. Rheol. 60:661–71 [Google Scholar]
  11. Bounoua S, Lemaire É, Férec J, Ausias G, Kuzhir P. 2016b. Shear-thinning in concentrated rigid fiber suspensions: aggregation induced by adhesive interactions. J. Rheol 60:1279–300 [Google Scholar]
  12. Brady JF. 2001. Computer simulation of viscous suspensions. Chem. Eng. Sci. 56:2921–26 [Google Scholar]
  13. Brenner H. 1974. Rheology of a dilute suspension of axisymmetric Brownian particles. Int. J. Multiph. Flow 1:195–341 [Google Scholar]
  14. Bretherton F. 1962. The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14:284–304 [Google Scholar]
  15. Chaouche M, Koch DL. 2001. Rheology of non-Brownian rigid fiber suspensions with adhesive contacts. J. Rheol. 45:369–82 [Google Scholar]
  16. Chung DH, Kwon TH. 2002. Fiber orientation in the processing of polymer composites. Korea-Aust. Rheol. J. 14:175–88 [Google Scholar]
  17. Chwang AT, Wu TY. 1975. Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows. J. Fluid Mech. 67:787–815 [Google Scholar]
  18. Claeys IL, Brady JF. 1993a. Suspensions of prolate spheroids in Stokes flow. Part 1. Dynamics of a finite number of particles in an unbounded fluid. J. Fluid Mech. 251:411–42 [Google Scholar]
  19. Claeys IL, Brady JF. 1993b. Suspensions of prolate spheroids in Stokes flow. Part 2. Statistically homogeneous dispersions. J. Fluid Mech. 251:443–77 [Google Scholar]
  20. Cox RG. 1970. The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44:791–810 [Google Scholar]
  21. Cox RG. 1971. The motion of long slender bodies in a viscous fluid. Part 2. Shear flow. J. Fluid Mech. 45:625–57 [Google Scholar]
  22. Derakhshandeh B, Kerekes RJ, Hatzikiriakos SG, Bennington CPJ. 2011. Rheology of pulp fibre suspensions: a critical review. Chem. Eng. Sci. 66:3460–70 [Google Scholar]
  23. Dhont JKG, Briels WJ. 2003. Viscoelasticity of suspensions of long, rigid rods. Colloids Surf. A 213:131–56 [Google Scholar]
  24. Dinh SM, Armstrong RC. 1984. A rheological equation of state for semiconcentrated fiber suspensions. J. Rheol. 28:207–27 [Google Scholar]
  25. Djalili-Moghaddam M, Ebrahimzadeh R, Toll S. 2004. Study of geometry effects in torsional rheometry of fibre suspensions. Rheol. Acta 44:29–37 [Google Scholar]
  26. Doi M, Edwards SF. 1978. Dynamics of rod-like macromolecules in concentrated solution. Part 1. J. Chem. Soc. Faraday Trans. 2 74:560–70 [Google Scholar]
  27. Doi M, Edwards SF. 1988. The Theory of Polymer Dynamics Oxford, UK: Oxford Univ. Press
  28. Elgaddafi R, Ahmed R, George M, Growcock F. 2012. Settling behavior of spherical particles in fiber-containing drilling fluids. J. Petrol. Sci. Eng. 84–85:20–28 [Google Scholar]
  29. Fan X, Phan-Thien N, Zheng R. 1998. A direct simulation of fibre suspensions. J. Non-Newton. Fluid Mech. 74:113–35 [Google Scholar]
  30. Fan XJ, Phan-Thien N, Zheng R. 2000. Simulation of fibre suspension flow with shear-induced migration. J. Non-Newton. Fluid Mech. 90:47–63 [Google Scholar]
  31. Folgar F, Tucker CLI. 1984. Orientation behavior of fibers in concentrated suspensions. J. Reinf. Plast. Compos. 3:98–119 [Google Scholar]
  32. Forgacs OL, Mason SG. 1959. Particle motions in sheared suspensions: IX. Spin and deformation of threadlike particles. J. Colloid Sci. 14:457–72 [Google Scholar]
  33. Franceschini A, Filippidi E, Guazzelli E, Pine DJ. 2011. Transverse alignment of fibers in a periodically sheared suspension: an absorbing phase transition with a slowly varying control parameter. Phys. Rev. Lett. 107:250603 [Google Scholar]
  34. Ganani E, Powell RL. 1985. Suspensions of rodlike particles: literature review and data correlations. J. Compos. Mater. 19:194–215 [Google Scholar]
  35. Harlen OG, Sundararajakumar RR, Koch DL. 1999. Numerical simulation of a sphere settling through a suspension of neutrally buoyant fibres. J. Fluid Mech. 388:355–88 [Google Scholar]
  36. Hassanpour M, Shafigh P, Mahmud HB. 2012. Lightweight aggregate concrete fiber reinforcement—a review. Constr. Build. Mater. 37:452–61 [Google Scholar]
  37. Hinch EJ. 2011. The measurement of suspension rheology. J. Fluid Mech. 686:1–4 [Google Scholar]
  38. Hinch EJ, Leal LG. 1972. The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech. 52:683–712 [Google Scholar]
  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. 268:267–92 [Google Scholar]
  40. Ivanov Y, van de Ven TGM, Mason SG. 1982. Damped oscillations in the viscosity of suspensions of rigid rods. I. Monomodal suspensions. J. Rheol. 26:213–30 [Google Scholar]
  41. Janosi IM, Tel T, Wolf DE, Gallas JAC. 1997. Chaotic particle dynamics in viscous flows: the three-particle Stokeslet problem. Phys. Rev. E 65:2858–68 [Google Scholar]
  42. Jeffery GB. 1922. The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. A 102:161–79 [Google Scholar]
  43. Keshtkar M, Heuzey M, Carreau P. 2009. Rheological behavior of fiber-filled model suspensions: effect of fiber flexibility. J. Rheol. 53:631–50 [Google Scholar]
  44. Kim S. 1985. A note on Faxen laws for non-spherical particles. Int. J. Multiph. Flow 11:713–19 [Google Scholar]
  45. Krochak PJ, Olson JA, Martinez DM. 2008. The orientation of semidilute rigid fiber suspensions in a linearly contracting channel. Phys. Fluids 20:073303 [Google Scholar]
  46. Ladd AJC, Verberg R. 2001. Lattice-Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104:1191–251 [Google Scholar]
  47. Lees A, Edwards S. 1972. The computer study of transport processes under extreme conditions. J. Phys. C 5:1921–29 [Google Scholar]
  48. Lindström SB, Uesaka T. 2008. Simulation of semidilute suspensions of non-Brownian fibers in shear flow. J. Chem. Phys. 128:024901 [Google Scholar]
  49. Lindström SB, Uesaka T. 2009. A numerical investigation of the rheology of sheared fiber suspensions. Phys. Fluids 21:083301 [Google Scholar]
  50. Liu D, Keaveny EE, Maxey MR, Karniadakis GE. 2009. Force-coupling method for flows with ellipsoidal particles. J. Comput. Phys. 228:3559–81 [Google Scholar]
  51. Lundell F, Söderberg LD, Alfredsson PH. 2011. Fluid mechanics of papermaking. Annu. Rev. Fluid Mech. 43:195–217 [Google Scholar]
  52. Ma WKA, Chinesta F, Ammar A, Mackley MR. 2008. Rheological modeling of carbon nanotube aggregate suspensions. J. Rheol. 52:1311–30 [Google Scholar]
  53. Mackaplow MB, Shaqfeh ESG. 1996. A numerical study of the rheological properties of suspensions of rigid, non-Brownian fibres. J. Fluid Mech. 329:155–86 [Google Scholar]
  54. Malamataris N, Papanastasiou TC. 1991. Closed-form material functions for semidilute fiber suspensions. J. Rheol. 35:449–64 [Google Scholar]
  55. Maschmeyer RO, Hill CT. 1977. Rheology of concentrated suspensions of fibers in tube flow. II. An exploratory study. Trans. Soc. Rheol. 21:183–95 [Google Scholar]
  56. Mason S, Manley R. 1956. Particle motions in sheared suspensions: orientations and interactions of rigid rods. Proc. R. Soc. A 238:117–31 [Google Scholar]
  57. Maxey M. 2017. Simulation methods for particulate flows and concentrated suspensions. Annu. Rev. Fluid Mech. 49:171–93 [Google Scholar]
  58. Maxey MR, Patel BK. 2001. Localized force representations for particles sedimenting in Stokes flow. Int. J. Multiph. Flow 27:1603–26 [Google Scholar]
  59. Mondy LA, Brenner H, Altobelli SA, Abbott JR, Graham AL. 1994. Shear-induced particle migration in suspensions of rods. J. Rheol. 38:444–52 [Google Scholar]
  60. Mongruel A, Cloitre M. 1995. Extensional flow of semidilute suspensions of rod-like particles through an orifice. Phys. Fluids 7:2546–52 [Google Scholar]
  61. Okagawa A, Cox RG, Mason SG. 1973. The kinetics of flowing dispersions. VI. Transient orientation and rheological phenomena of rods and discs in shear flow. J. Colloid Interface Sci. 45:303–29 [Google Scholar]
  62. Park J, Butler JE. 2009. Inhomogeneous distribution of a rigid fibre undergoing rectilinear flow between parallel walls at high Peclet numbers. J. Fluid Mech. 630:267–98 [Google Scholar]
  63. Park J, Butler JE. 2010. Analysis of the migration of rigid polymers and nanorods in a rotating viscometric flow. Macromolecules 43:2535–43 [Google Scholar]
  64. Petrich MP, Koch DL. 1998. Interactions between contacting fibers. Phys. Fluids 10:2111–13 [Google Scholar]
  65. Petrich MP, Koch DL, Cohen C. 2000. An experimental determination of the stress-microstructure relationship in semi-concentrated fiber suspensions. J. Non-Newton. Fluid Mech. 95:101–33 [Google Scholar]
  66. Petrie CJS. 1999. The rheology of fibre suspensions. J. Non-Newton. Fluid Mech. 87:369–402 [Google Scholar]
  67. Phelps JH, Tucker CLI. 2009. An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics. J. Non-Newton. Fluid Mech. 156:165–76 [Google Scholar]
  68. Powell RL. 1991. Rheology of suspensions of rodlike particles. J. Stat. Phys. 62:1073–94 [Google Scholar]
  69. Powell RL, Morrison TG, Milliken WJ. 2001. Apparent viscosity of suspensions of rods using falling ball rheometry. Phys. Fluids 13:588–93 [Google Scholar]
  70. Pozrikidis C. 2005. Orientation statistics and effective viscosity of suspensions of elongated particles in simple shear flow. Eur. J. Mech. B 24:125–36 [Google Scholar]
  71. Rahnama M, Koch DL, Iso Y, Cohen C. 1993. Hydrodynamic, translational diffusion in fiber suspensions subject to simple shear flow. Phys. Fluids 5:849–62 [Google Scholar]
  72. Salahuddin A. 2011. Orientation and rotational diffusion of fibers in semidilute suspension PhD Thesis, Ga. Inst. Technol.
  73. Salahuddin A, Wu J, Aidun CK. 2012. Numerical study of rotational diffusion in sheared semidilute fibre suspension. J. Fluid Mech. 692:153–82 [Google Scholar]
  74. Salahuddin A, Wu J, Aidun CK. 2013. Study of semidilute fibre suspension rheology with lattice-Boltzmann method. Rheol. Acta 52:891–902 [Google Scholar]
  75. Sepehr M, Carreau P, Moan M, Ausias G. 2004. Rheological properties of short fiber model suspensions. J. Rheol. 48:1023–48 [Google Scholar]
  76. Shaqfeh ESG, Fredrickson GH. 1990. The hydrodynamic stress in a suspension of rods. Phys. Fluids A 2:7–24 [Google Scholar]
  77. Sierou A, Brady JF. 2001. Accelerated Stokesian dynamics simulations. J. Fluid Mech. 448:115–46 [Google Scholar]
  78. Snabre P, Mills P. 1996. I. Rheology of weakly flocculated suspensions of rigid particles. J. Phys. III Fr. 6:1811–34 [Google Scholar]
  79. Snook B. 2015. The dynamics of the microstructure and the rheology in suspensions of rigid particles PhD Thesis, Univ. Fla.
  80. Snook B, Davidson LM, Butler JE, Pouliquen O, Guazzelli E. 2014. Normal stress differences in suspensions of rigid fibres. J. Fluid Mech. 758:486–507 [Google Scholar]
  81. Snook B, Guazzelli E, Butler JE. 2012. Vorticity alignment of rigid fibers in an oscillatory shear flow: role of confinement. Phys. Fluids 24:121702 [Google Scholar]
  82. Stover C, Koch D, Cohen C. 1992. Observations of fibre orientation in simple shear flow of semi-dilute suspensions. J. Fluid Mech. 238:277–96 [Google Scholar]
  83. Sundararajakumar R, Koch DL. 1997. Structure and properties of sheared fiber suspensions with mechanical contacts. J. Non-Newton. Fluid Mech. 73:205–39 [Google Scholar]
  84. Trevelyan B, Mason S. 1951. Particle motions in sheared suspensions. I. Rotations. J. Colloid Sci. 6:354–67 [Google Scholar]
  85. Vaccaro A, Marrucci G. 2000. A model for the nonlinear rheology of associating polymers. J. Non-Newton. Fluid Mech. 92:261–73 [Google Scholar]
  86. Wang J, O'Gara JF, Tucker CLI. 2008. An objective model for slow orientation kinetics in concentrated fiber suspensions: theory and rheological evidence. J. Rheol. 52:1179–200 [Google Scholar]
  87. Wierenga AM, Philipse AP. 1998. Low-shear viscosity of isotropic dispersions of (Brownian) rods and fibres; a review of theory and experiments. Colloids Surf. A 137:355–72 [Google Scholar]
  88. Williams SR, Philipse AP. 2003. Random packings of spheres and spherocylinders simulated by mechanical contraction. Phys. Rev. E 67:051301 [Google Scholar]
  89. Wu J, Aidun CK. 2010. A numerical study of the effect of fibre stiffness on the rheology of sheared flexible fibre suspensions. J. Fluid Mech. 662:123–33 [Google Scholar]
  90. Yamane Y, Kaneda Y, Dio M. 1994. Numerical simulation of semi-dilute suspensions of rodlike particles in shear flow. J. Non-Newton. Fluid Mech. 54:405–21 [Google Scholar]
/content/journals/10.1146/annurev-fluid-122316-045144
Loading
/content/journals/10.1146/annurev-fluid-122316-045144
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error