1932

Abstract

Suspensions of non-Brownian particles are commonly encountered in applications in a large number of industries. These suspensions exhibit nonlinear flow behavior, even in Newtonian suspending fluids under conditions where inertial effects can be ignored and linearity would normally be expected. We review the observed rheological behavior, emphasizing concentrated suspensions of spheres in Newtonian fluids, and we examine both particle-level and continuum approaches to describing the nonlinear behavior. Particle-particle nonhydrodynamic interactions appear to be important in concentrated suspensions. Continuum descriptions are not yet adequate to describe the observed behavior.

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2014-06-07
2024-04-16
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Literature Cited

  1. Guazzelli E, Morris JF. 1.  2012. A Physical Introduction to Suspension Dynamics New York: Cambridge Univ. Press
  2. Mewis J, Wagner NJ. 2.  2012. Colloidal Suspension Rheology New York: Cambridge Univ. Press
  3. Denn MM. 3.  2008. Polymer Melt Processing: Foundations in Fluid Mechanics and Heat Transfer New York: Cambridge Univ. Press
  4. Einstein A. 4.  1906. Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 19:289–305 [Google Scholar]
  5. Einstein A. 5.  1911. Berichtigung zu meiner Arbeit: Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 34:591–92 [Google Scholar]
  6. Happel J, Brenner H. 6.  1965. Low Reynolds Number Hydrodynamics Englewood Cliffs, NJ: Prentice-Hall
  7. Lewis TB, Nielsen LE. 7.  1968. Viscosity of dispersed and aggregated suspensions of spheres. Trans. Soc. Rheol. 12:421–33 [Google Scholar]
  8. Roscoe R. 8.  1952. The viscosity of suspensions of rigid spheres. Br. J. Appl. Phys. 3:267–69 [Google Scholar]
  9. Zarraga IE, Hill DA, Leighton DT Jr. 9.  2000. The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44:185–220 [Google Scholar]
  10. Dai S-C, Bertevas E, Qi F, Tanner RI. 10.  2013. Viscometric functions for non-colloidal sphere suspensions with Newtonian matrices. J. Rheol. 57:493–510 [Google Scholar]
  11. Fall A, Bertrand F, Lemaître A, Bonn D, Overlez G. 11.  2010. Shear thickening and migration in granular suspensions. Phys. Rev. Lett. 105:268303 [Google Scholar]
  12. Fall A, Denn MM, Bonn D. 12.  2013. Why Is (Wet) Granular Rheology So Complicated? Amsterdam: Inst. Phys., Univ. Amsterdam (unpublished manuscript)
  13. Metzner AB. 13.  1985. Rheology of suspensions in polymeric liquids. J. Rheol. 29:739–75 [Google Scholar]
  14. Chong JS, Christiansen EB, Baer AD. 14.  1971. Rheology of concentrated suspensions. J. Appl. Polym. Sci. 15:2007–21 [Google Scholar]
  15. Farris RJ. 15.  1968. Prediction of the viscosity of multimodal suspensions from unimodal data. Trans. Soc. Rheol. 12:281–301 [Google Scholar]
  16. Chang C, Powell RL. 16.  1993. Dynamic simulation of bimodal suspensions of hydrodynamically interacting spherical particles. J. Fluid Mech. 253:1–25 [Google Scholar]
  17. Tanner RI, Qi F, Housiadad KD. 17.  2010. A differential approach to suspensions with power-law matrices. J. Non-Newton. Fluid Mech. 165:1677–81 [Google Scholar]
  18. Ohl N, Gleissle W. 18.  1993. The characterization of the steady-state shear and normal stress functions of highly concentrated suspensions formulated with viscoelastic liquids. J. Rheol. 37:381–406 [Google Scholar]
  19. Gleissle W, Baloch MK. 19.  1984. Reduced flow functions of suspensions based on Newtonian and non-Newtonian liquids. Proc. IX Int. Congr. Rheol. 2:549–56 [Google Scholar]
  20. Mall-Gleissle SE, Gleissle W, McKinley GH, Buggisch H. 20.  2002. The normal stress behavior of suspensions with viscoelastic matrix fluids. Rheol. Acta 41:61–76 [Google Scholar]
  21. Le Meins J-F, Moldenaers P, Mewis J. 21.  2002. Suspensions in polymer melts. 1. Effect of particle size on the shear flow behavior. Ind. Eng. Chem. Res. 41:6297–304 [Google Scholar]
  22. Marrucci G. 22.  1972. The free energy constitutive equation for polymer solutions from the dumbbell model. Trans. Soc. Rheol. 16:321–30 [Google Scholar]
  23. Yurkovetsky Y, Morris JF. 23.  2008. Particle pressure in a sheared Brownian suspension. J. Rheol. 52:141–64 [Google Scholar]
  24. Macosko CW. 24.  1995. Rheology: Principles, Measurements, and Applications New York: VCH
  25. Morrison FA. 25.  2001. Understanding Rheology New York: Oxford Univ. Press
  26. Leong YK, Boger DV, Christie GB, Mainwairing DE. 26.  1993. Rheology of low-viscosity, high-concentration brown-coal suspensions. Rheol. Acta 32:277–85 [Google Scholar]
  27. Bousmina M, Ait-Kadi A, Faisant JB. 27.  1999. Determination of shear rate and viscosity from batch mixer data. J. Rheol. 43:415–33 [Google Scholar]
  28. Estellé P, Lanos C. 28.  2008. Shear flow curve in mixing systems—a simplified approach. Chem. Eng. Sci. 63:5887–90 [Google Scholar]
  29. Guillemin JP, Menard Y, Brunet L, Bonefoy O, Thomas G. 29.  2008. Development of a new mixing rheometer for studying rheological behaviour of concentrated energetic suspensions. J. Non-Newton. Fluid Mech. 151:136–44 [Google Scholar]
  30. Anna SL, McKinley GH, Nguyen DA, Sridhar T, Muller SJ. 30.  et al. 2001. An interlaboratory comparison of measurements from filament-stretching rheometers using common test fluids. J. Rheol. 45:83–114 [Google Scholar]
  31. Bischoff White EE, Chellamuthu M, Rothstein JP. 31.  2010. Extensional rheology of a shear-thickening cornstarch and water suspension. Rheol. Acta 49:119–29 [Google Scholar]
  32. Roché M, Kellay H, Stone HA. 32.  2011. Heterogeneity and the role of normal stresses during the extension thinning of non-Brownian shear-thickening fluids. Phys. Rev. Lett. 107:134503 [Google Scholar]
  33. Walberger JA, McHugh AJ. 33.  2000. A comparison of the rheology of reactive filled systems using lubricated squeezing flow. J. Rheol. 44:743–58 [Google Scholar]
  34. Kalyon DM, Tang H, Karuv B. 34.  2006. Squeeze flow rheometry for rheological characterization of energetic formulations. J. Energy Mat. 24:195–212 [Google Scholar]
  35. Denn MM. 35.  2001. Extrusion instabilities and wall slip. Annu. Rev. Fluid Mech. 33:265–87 [Google Scholar]
  36. Kalyon DM, Aktaş A. 36.  2014. Factors affecting the rheology and processability of highly filled suspensions. Annu. Rev. Chem. Biomol. Eng. 5:229–54 [Google Scholar]
  37. Jana S, Kapoor B, Acrivos A. 37.  1995. Apparent wall-slip velocity coefficients in concentrated suspensions of noncolloidal particles. J. Rheol. 39:1123–32 [Google Scholar]
  38. Kalyon DM. 38.  2005. Apparent slip and viscoplasticity of concentrated suspensions. J. Rheol. 49:621–40 [Google Scholar]
  39. Tanner RI, Keentok M. 39.  1983. Shear fracture in cone-plate rheometry. J. Rheol. 27:47–57 [Google Scholar]
  40. Gadala-Maria F. 40.  1979. The rheology of concentrated suspensions PhD Diss., Stanford Univ., Stanford, CA
  41. Aral BK, Kalyon DM. 41.  1997. Viscoelastic material functions of noncolloidal suspensions with spherical particles. J. Rheol. 41:599–620 [Google Scholar]
  42. Singh A, Nott PR. 42.  2003. Experimental measurements of the normal stresses in sheared Stokesian suspensions. J. Fluid Mech. 490:293–320 [Google Scholar]
  43. Boyer F, Pouliquen Guazzelli O. 43.  2011. Dense suspensions in rotating-rod flows: normal stresses and particle migration. J. Fluid Mech. 686:5–25 [Google Scholar]
  44. Couturier É, Boyer F, Pouliquen O, Guazzelli É. 44.  2011. Suspensions in a tilted trough: second normal stress difference. J. Fluid Mech. 686:26–39 [Google Scholar]
  45. Dbouk T, Lobry L, Lemaire E. 45.  2013. Normal stresses in concentrated non-Brownian suspensions. J. Fluid Mech. 715:239–72 [Google Scholar]
  46. Seto R, Mauri R, Morris JF, Denn MM. 46.  2013. Discontinuous shear thickening of frictional hard-sphere suspensions. Phys. Rev. Lett. 111:218301 [Google Scholar]
  47. Lootens D, van Damme H, Hémar Y, Hébraud P. 47.  2005. Dilatant flow of concentrated suspensions of rough particles. Phys. Rev. Lett. 95:268302 [Google Scholar]
  48. Mewis J, de Blyser R. 48.  1975. Concentration effects in viscoelastic dispersions. Rheol. Acta 14:721–28 [Google Scholar]
  49. Sirocco R, Vermant J, Mewis J. 49.  2005. Shear thickening in filled Boger fluids. J. Rheol. 49:551–67 [Google Scholar]
  50. Ponche A, Dupuis D. 50.  2005. On instabilities and migration phenomena in cone and plate geometry. J. Non-Newton. Fluid Mech. 127:123–29 [Google Scholar]
  51. Sirocco R, Vermant J, Mewis J. 51.  2004. Effect of the viscoelasticity of the suspending fluid on structure formation in suspensions. J. Non-Newton. Fluid Mech. 117:183–92 [Google Scholar]
  52. Hwang WR, Hulsen MA, Meier HEH. 52.  2004. Direct simulation of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames. J. Non-Newton. Fluid Mech. 121:15–33 [Google Scholar]
  53. Choi YJ, Hulsen MA, Meier HEH. 53.  2010. An extended finite element method for the simulation of particulate viscoelastic flows. J. Non-Newton. Fluid Mech. 165:607–24 [Google Scholar]
  54. Hwang WR, Hulsen MA. 54.  2011. Structure formation of non-colloidal particles in viscoelastic fluids subjected to simple shear flow. Macromol. Mater. Eng. 296:321–30 [Google Scholar]
  55. Gadala-Maria F, Acrivos A. 55.  1980. Shear-induced structure in a concentrated suspension of solid spheres. J. Rheol. 24:799–814 [Google Scholar]
  56. Kolli VG, Pollauf EJ, Gadala-Maria F. 56.  2002. Transient normal stress response in a concentrated suspension of spherical particles. J. Rheol. 46:321–34 [Google Scholar]
  57. Leighton DT, Acrivos A. 57.  1987. The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181:415–39 [Google Scholar]
  58. Abbott JR, Tetlow N, Graham AL, Altobelli SA, Fukushima E. 58.  et al. 1991. Experimental observations of particle migration in concentrated suspensions: Couette flow. J. Rheol. 35:773–95 [Google Scholar]
  59. Koh CJ, Hookham P, Leal LG. 59.  1994. An experimental investigation of concentrated suspension flows in a rectangular channel. J. Fluid Mech. 266:1–32 [Google Scholar]
  60. Hampton RE, Mammoli AA, Graham AL, Tetlow N, Altobelli SA. 60.  1997. Migration of particles undergoing pressure-driven flow in a circular conduit. J. Rheol. 41:621–40 [Google Scholar]
  61. Overlez G, Bertrand F, Rodts S. 61.  2006. Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging. J. Rheol. 50:259–92 [Google Scholar]
  62. Chapman BK. 62.  1990. Shear-induced migration phenomena in concentrated suspensions PhD Diss., Univ. Notre Dame, IN
  63. Chow AW, Sinton SW, Iwamiya JH, Stephens TS. 63.  1994. Shear-induced particle migration in Couette and parallel-plate viscometers: NMR imaging and stress measurements. Phys. Fluids 6:2561–76 [Google Scholar]
  64. Merhi D, Lemaire E, Bossis G, Moukalled F. 64.  2005. Particle migration in a concentrated suspension flowing between rotating parallel plates: investigation of diffusion flux coefficients. J. Rheol. 49:1429–48 [Google Scholar]
  65. Chow AW, Iwayima JH, Sinton SW, Leighton DT. 65.  1995. Particle migration of non-Brownian, concentrated suspensions in a truncated cone-and-plate Presented at Soc. Rheol. Annu. Meet., Sacramento, CA
  66. MacDonald MJ, Muller SJ. 66.  1996. Experimental study of shear-induced migration of polymers in dilute solutions. J. Rheol. 40:259–83 [Google Scholar]
  67. Rangel-Nafaile C, Metzner AB, Wissbrun KF. 67.  1984. Analysis of stress-induced phase separation in polymer solutions. Macromolecules 17:1187–95 [Google Scholar]
  68. Osaki K, Doi M. 68.  1991. On the concentration gradient of polymer solution in a rotating rheometer. J. Rheol. 35:89–92 [Google Scholar]
  69. Morris JF, Boulay F. 69.  1999. Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43:1213–37 [Google Scholar]
  70. Nott PR, Brady JF. 70.  1994. Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275:157–99 [Google Scholar]
  71. Jenkins JT, McTigue DF. 71.  1990. Transport process in concentrated suspensions: the role of particle fluctuations. Two Phase Flows and Waves DD Joseph, DG Schaeffer New York: Springer [Google Scholar]
  72. Furbank RJ, Morris JF. 72.  2004. An experimental study of particle effects on drop formation. Phys. Fluids. 16:1777–90 [Google Scholar]
  73. Furbank RJ, Morris JF. 73.  2007. Pendant drop thread dynamics of particle-laden liquids. Int. J. Multiph. Flow 33:448–68 [Google Scholar]
  74. Bonnoit C, Bertrand T, Clement E, Lindner A. 74.  2012. Accelerated drop detachment in granular suspensions. Phys. Fluids 24:043304 [Google Scholar]
  75. Bertrand T, Bonnoit C, Clement E, Lindner A. 75.  2012. Dynamics of drop formation in granular suspensions: the role of volume fraction. Granul. Matter 14:169–74 [Google Scholar]
  76. Miskin MZ, Jaeger HM. 76.  2012. Droplet formation and scaling in dense suspensions. Proc. Natl. Acad. Sci. USA 109:4389–94 [Google Scholar]
  77. Le Meins J-F, Moldenaers P, Mewis J. 77.  2003. Suspensions of monodisperse spheres in polymer melts: particle size effects in extensional flow. Rheol. Acta 42:184–90 [Google Scholar]
  78. Batchelor GK. 78.  1971. The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J. Fluid Mech. 46:813–29 [Google Scholar]
  79. Mewis J, Metzner AB. 79.  1974. The rheological properties of suspensions of fibres in Newtonian fluids subjected to extensional deformations. J. Fluid Mech. 62:593–600 [Google Scholar]
  80. Weinberger CB, Goddard JD. 80.  1974. Extensional flow behavior of polymer solutions and particle suspensions in a spinning motion. Int. J. Multiph. Flow 1:465–86 [Google Scholar]
  81. Ooi YW, Sridhar T. 81.  2004. Resistance to uniform extensional flow of fiber suspensions. Rheol. Acta 43:223–31 [Google Scholar]
  82. Petrie CJS. 82.  1999. The rheology of fibre suspensions. J. Non-Newton. Fluid Mech. 87:369–402 [Google Scholar]
  83. Eberle ARP, Baird DG, Wapperom P. 83.  2008. Rheology of non-Newtonian fluids containing glass fibers: a review of the literature. Ind. Eng. Chem. Res. 47:3470–88 [Google Scholar]
  84. Férec J, Heuzey M-C, Pérez-González J, de Vargas L, Ausias G, Carreau PJ. 84.  2009. Investigation of the rheological properties of short glass fiber-filled polypropylene in extensional flow. Rheol. Acta 48:59–72 [Google Scholar]
  85. Drazer G, Koplik J, Khusid B, Acrivos A. 85.  2002. Deterministic and stochastic behavior of non-Brownian spheres in suspensions. J. Fluid Mech. 460:307–35 [Google Scholar]
  86. Dasan J, Ramamohan TR, Singh A, Nott PR. 86.  2002. Stress fluctuations in sheared Stokesian suspensions. Phys. Rev. E 66:021409 [Google Scholar]
  87. Metzger B, Butler JE. 87.  2010. Irreversibility and chaos: role of long-range hydrodynamic interactions in sheared suspensions. Phys. Rev. E 82:051406 [Google Scholar]
  88. Batchelor GK, Green JT. 88.  1972. The hydrodynamic interactions of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 56:375–400 [Google Scholar]
  89. Brady JF, Morris JF. 89.  1997. Microstructure in a strongly-sheared suspension and its impact on rheology and diffusion. J. Fluid Mech. 348:103–9 [Google Scholar]
  90. Wilson HJ. 90.  2005. An analytic form for the pair distribution function and rheology of a dilute suspension of rough spheres in plane strain flow. J. Fluid Mech. 534:97–114 [Google Scholar]
  91. Parsi F, Gadala-Maria F. 91.  1987. Fore-and-aft asymmetry in a concentrated suspension of solid spheres. J. Rheol. 31:725–32 [Google Scholar]
  92. Gao C, Kulkarni SD, Gilchrist JF, Morris JF. 92.  2010. Direct investigation of anisotropic suspension structure in pressure-driven flow. Phys. Rev. E 81:041403 [Google Scholar]
  93. Brady JF, Bossis G. 93.  1988. Stokesian dynamics. Annu. Rev. Fluid Mech. 20:111–57 [Google Scholar]
  94. Sierou A, Brady JF. 94.  2001. Accelerated Stokesian dynamics simulations. J. Fluid Mech. 448:115–46 [Google Scholar]
  95. Morris JF, Katyal B. 95.  2002. Microstructure from simulated Brownian suspension flows at large shear rate. Phys. Fluids 14:1920–37 [Google Scholar]
  96. Sierou A, Brady JF. 96.  2002. Rheology and microstructure in concentrated noncolloidal suspensions. J. Rheol. 46:1031–56 [Google Scholar]
  97. Bertevas E, Fan X, Tanner RI. 97.  2010. Simulation of the rheological properties of suspensions of oblate spheroidal particles in a Newtonian fluid. Rheol. Acta 49:53–73 [Google Scholar]
  98. Ladd AJC. 98.  1994. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271:285–309 [Google Scholar]
  99. Ladd AJC. 99.  1994. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271:311–39 [Google Scholar]
  100. Ladd AJC, Verberg R. 100.  2001. Lattice-Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104:1191–251 [Google Scholar]
  101. Yeo K, Maxey MR. 101.  2011. Numerical simulations of concentrated suspensions of monodisperse particles in Poiseuille flow. J. Fluid Mech. 682:491–518 [Google Scholar]
  102. Fernandez N, Mani R, Rinaldi D, Kadau D, Mosquet M. 102.  et al. 2013. Microscopic mechanism for shear thickening of non-Brownian suspensions. Phys. Rev. Lett. 111:108301 [Google Scholar]
  103. Heussinger C. 103.  2013. Shear thickening in granular suspensions: inter-particle friction and dynamically correlated clusters. Phys. Rev. E 88:050201 [Google Scholar]
  104. Maranzano BJ, Wagner NJ. 104.  2001. The effect of interparticle interactions and particle size on reversible shear thickening: hard-sphere colloidal dispersions. J. Rheol. 45:1205–22 [Google Scholar]
  105. Trulsson M, Andreotti B, Claudin P. 105.  2012. Transition from the viscous to inertial regime in dense suspensions. Phys. Rev. Lett. 109:118305 [Google Scholar]
  106. Woodcock LV. 106.  1981. Glass-transition in the hard-sphere model and Kauzmann paradox. Ann. N.Y. Acad. Sci. 371:274–98 [Google Scholar]
  107. Russel WB, Saville DA, Schowalter WR. 107.  1989. Colloidal Dispersions New York: Cambridge Univ. Press413
  108. Blanc F, Lemaire E, Meunier A, Peters F. 108.  2013. Microstructure in sheared non-Brownian concentrated suspensions. J. Rheol. 57:273–92 [Google Scholar]
  109. Yeo K, Maxey MR. 109.  2010. Dynamics of concentrated suspensions of non-colloidal particles in Couette flow. J. Fluid Mech. 649:205–31 [Google Scholar]
  110. Schunk PR, Scriven LE. 110.  1990. Constitutive equation for modeling mixed extension and shear in polymer solution processing. J. Rheol. 34:1085–119 [Google Scholar]
  111. Ryssel E, Brunn PO. 111.  1999. Flow of a quasi-Newtonian fluid through a planar contraction. J. Non-Newton. Fluid Mech. 85:11–27 [Google Scholar]
  112. Ryssel E, Brunn PO. 112.  1999. Comparison of a quasi-Newtonian fluid with a viscoelastic fluid in planar contraction flow. J. Non-Newton. Fluid Mech. 86:309–35 [Google Scholar]
  113. Jeffery GB. 113.  1922. The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102:161–79 [Google Scholar]
  114. Hinch EJ, Leal LG. 114.  1976. Constitutive equations in suspension mechanics. 2. Approximate forms for a suspension of rigid particles affected by Brownian motion. J. Fluid Mech. 76:187–208 [Google Scholar]
  115. Öttinger HC. 115.  2009. On the stupendous beauty of closure. J. Rheol. 53:1285–304 [Google Scholar]
  116. Lipscomb GG II, Denn MM, Hur DU, Boger DV. 116.  1988. The flow of fiber suspensions in complex geometries. J. Non-Newton. Fluid Mech. 26:297–315 [Google Scholar]
  117. Folgar FP, Tucker CL III. 117.  1984. Orientation behavior of fibers in concentrated suspensions. J. Reinf. Plast. Compos. 3:98–119 [Google Scholar]
  118. Phan-Thien N, Fan XJ, Tanner RI, Zheng R. 118.  2002. Folgar-Tucker constant for a fibre suspension in a Newtonian fluid. J. Non-Newton. Fluid Mech. 103:251–60 [Google Scholar]
  119. Zheng R, Kennedy P, Phan-Thien N, Fan X-J. 119.  1999. Thermoviscoelastic simulation of thermally and pressure-induced stresses in injection moulding for the prediction of shrinkage and warpage for fibre-reinforced thermoplastics. J. Non-Newton. Fluid Mech. 84:159–90 [Google Scholar]
  120. Hand GL. 120.  1962. A theory of anisotropic fluids. J. Fluid Mech. 13:33–46 [Google Scholar]
  121. Phan-Thien N. 121.  1995. Constitutive equation for concentrated suspensions in Newtonian liquids. J. Rheol. 39:679–95 [Google Scholar]
  122. Goddard JD. 122.  2006. A dissipative anisotropic fluid model for non-colloidal particle dispersions. J. Fluid Mech. 568:1–17 [Google Scholar]
  123. Narumi T, See H, Honma Y, Hasegawa T, Takahashi T, Phan-Thien N. 123.  2002. Transient response of concentrated suspensions after shear reversal. J. Rheol. 46:295–305 [Google Scholar]
  124. Phan-Thien N, Fan X-J, Khoo BC. 124.  1999. A new constitutive model for monodisperse suspensions of spheres at high concentrations. Rheol. Acta 38:297–304 [Google Scholar]
  125. Phan-Thien N, Fan X-J, Zhong R. 125.  2000. A numerical simulation of suspension flow using a constitutive model based on anisotropic particle interactions. Rheol. Acta 39:122–30 [Google Scholar]
  126. Goddard JD. 126.  2008. A weakly nonlocal anisotropic fluid model for inhomogeneous Stokesian suspensions. Phys. Fluids 20:040601 [Google Scholar]
  127. Stickel JJ, Phillips RJ, Powell RL. 127.  2006. A constitutive equation for microstructure and total stress in particulate suspensions. J. Rheol. 50:379–413 [Google Scholar]
  128. Stickel JJ, Phillips RJ, Powell RL. 128.  2007. Application of a constitutive model for particulate suspensions: time-dependent viscometric flow. J. Rheol. 51:1271–302 [Google Scholar]
  129. Yapici K, Powell RL, Phillips RJ. 129.  2009. Particle migration and suspension structure in steady and oscillatory plane Poiseuille flow. Phys. Fluids 21:05302 [Google Scholar]
  130. Miller RM, Singh JPB, Morris JF. 130.  2009. Suspension flow modeling for general geometries. Chem. Eng. Sci. 64:4597–610 [Google Scholar]
  131. Altobelli SA, Fukushima E, Mondy LA. 131.  1997. Nuclear magnetic resonance imaging of particle migration in suspensions undergoing extrusion. J. Rheol. 41:1105–15 [Google Scholar]
  132. Moraczewski T, Tang H, Shapley NC. 132.  2005. Flow of a concentrated suspension through an abrupt axisymmetric expansion measured by nuclear magnetic resonance imaging. J. Rheol. 49:1409–28 [Google Scholar]
  133. Boyer F, Guazzelli E, Pouliquen O. 133.  2011. Unifying suspension and granular rheology. Phys. Rev. Lett. 107:188301 [Google Scholar]
  134. Walker DW, Tordesillas A, Thornton C, Behringer RP, Zhang J, Peters JF. 134.  2011. Percolating contact subnetworks on the edge of isostaticity. Granul. Matter 13:233–40 [Google Scholar]
  135. Tordesillas A, Lin Q, Zhang J, Behringer RP, Shi J. 135.  2011. Structural stability and jamming of self-organized cluster conformations in dense granular materials. J. Mech. Phys. Solids 59:265–96 [Google Scholar]
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