Shear-flow and material instabilities in particulate suspensions and granular media

Particulate Science and Technology

Volumn 17, Issue 1-2, 1999, Pages 69-96

  Goddard, Joe D ^a   Alam, Meheboob ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLOW OF SOLIDS; GRANULAR MATERIALS; SUSPENSIONS (FLUIDS); THREE DIMENSIONAL; TWO DIMENSIONAL;

GRANULAR MEDIA; MATERIAL INSTABILITIES; NEWTONIAN FLUIDS; PARTICULATE SUSPENSIONS;

SHEAR FLOW;

ARTICLE; FLOW KINETICS; FLOW MEASUREMENT; GRAVITY; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PRIORITY JOURNAL; SHEAR RATE; SHEAR STRESS; SUSPENDED PARTICULATE MATTER; TEMPERATURE SENSITIVITY;

EID: 0032823997     PISSN: 02726351     EISSN: 15480046     Source Type: Journal    
DOI: 10.1080/02726359908906806     Document Type: Article

References (86)

1. ABBOTT, J. R., TETLOW, N., GRAHAM, A. L., ALTOBELLI, S. A., FUKUSHIMA, E., MONDY, L. A. & STEPHENS, T. S. 1991 Experimental observations of particle migration in concentrated suspensions: Couette flow. J. Rheol. 35, 773.
2. ACRIVOS, A., BATCHELOR, G. K., HINCH, E. J., KOCH, D. L. & MOURI, R. 1992 Longitudinal shear-induced diffusion of spheres in a dilute suspension. J. Fluid Much. 24, G51.
3. AKBAY, U., BECKER, E., KROGER, S. & SPONAGEL, S. 1980 Instability of slow viseoinetric flow. Mech. Res. Comm. 7, 199.
4. ALAM, M. 1998 Stability of unbounded and bounded granular shear flows. Ph.D. thesis. Indian Institute of Science, Bangalore, India.
5. ALAM, M. & NOTT, P. R. 1997 The influence of Friction on the stability of unbounded granular shear flow. J. Fluid Mech. 343, 2G7.
6. ALAM, M. & NOTT, P. R. 1998 Stability of plane Couette flow of a granular material. J. Fluid Mech. 377, 99.
7. ANDERSON, K., SUNDARESAN, S. & JACKSON, R. 1995 Instabilities and the formation of bubbles in fluidized beds. J. Fluid Mech. 303, 327.
8. BAOIĆ, M. 1993 On the stability of rapid granular flows. J. Fluid Mech. 254, 127.
9. BAGNOLD, R. A. 1D54 Experiments on a gravity-free dispersion of large solid spheres ill Newtonian fluid under shear, Proc. R. Soc. London A 225, 49.
10. BARDET, J. P. 1991 Orientation of shear bands in frictional soils. ASCE J. Engg. Mech. 117, 1466.
11. BEHRINGER, R. P. & BAXTER, G. W. 1991 Pattern formation and complexity in granular flows. In Granular Matter: An Interdisciplinary Approach (ed. Anita Mehta), pp. 85–119. Springer-Verlag.
12. BHATTACHARJEE, S. M., FREDERICKSON, G. H. & HELFAND, E. 1989 Large fluctuations in polj'mer solutions under shear. J. Chem. Phys. 90, 3305.
13. Bossis, G. & BRADY, J. F. 1987 Self diffusion of brownian particles in concentrated suspensions under shear. J. Chem. Phys. 20, 111.
14. Chen, W-F. & SALEEB, A. F. 1994 Constitutive Equations for Engineering Materials. Elsevier.
15. COLEMAN, B. D. 1983 Necking and drawing of polymeric fibers under tension. Arch. Rat. Mcch. Anal. 83, 155.
16. COLEMAN, B. D. & HodgDON, M. L. 1985 On shear bands in ductile materials. Arch. R.at. Mech. Anal. 90, 219.
17. COLEMAN, B. D. & NEWMAN, D. C. 1992 On the rheology of cold drawing. II. Viscoelastic materials./. Polymer Sei. 30, 25.
18. Davis, S.H., Kriegsmann, G.A., Laurence, R.L. and Rosenblat, S. 1983 Multiple solutions and hysteresis in steady parallel viscous flows. Phys. Flnids 26, 1177.
19. DENG, H. & NEMAT-NASSER, S. 1994 Dynamic damage evolution of soilds in compression: microcracking, plastic flow and brittle-ductile transition. ASME J. Engg. Mat. and Tech. 116, 226.
20. Doi, M, & EDWARDS, S. F. 1986 The Theory of Polymer Dynamics. Oxford.
21. Doi, M. & Onuki, A. 1992 Dynamic coupling between stress and composition in polymer solutions and blends. J. de Phys. U 2, 1631.
22. DESRUES, J., LANIER, J. & STUTZ, P. 1983 Localization of the deformation in tests oil sand samples. Engg. Frac. Mcch. 21, 909.
23. EGMOND, J. W. & FULLER, G. G. 1993 Concentration fluctuation enhancement in polymer solutions by extensional flow. Macromolecules. 26, 7182.
24. Ericksen, J. L. 1975 Equilibrium of bars. J. Elasticity 5, 191.
25. Ericksen, J. L. 1998 Introduction to the Thermodynamics of Solids. Springer.
26. Gadala-Maria, F. & Acrivos, A. 1980 Shear-induced structure in a concentrated suspensions of solid spheres. J. Rheol. 24, 799.
27. Glasser, B. J., Sundaresan, S. & Kevrekidis, I. G. 1998 From bubbles to clusters in flmdized beds. Phys. Rev. Lett. 81, 1849.
28. Goddard, J. D. 1988 Dissipative materials as constitutive models Tor granular media. Acta Mechanica, 63, 1.
29. Goddard, J. D. 1995 Material Instabilities. Report No. 95-20. Institute for Mechanics and Materials, University or California, San Diego.
30. Goddard, J. D. 1997 Migrational instabilities in particle suspensions. In Annual AIChE Meeting, Los Angeles, November 16–20.
31. Goddard, J. D. 1998 Continuum modeling of granular assemblies-quasistatic dilatancy and yield, In Physics of Dry Granular Media, (ed. H. Hermann, J.-P. Hovi fc S. Luding) pp. 1–24. Kluwer Academic.
32. Goddard, J. D. 1998a Migrational instabilities in particle suspensions. In Dynamics of Complex Fluids (ed. M.J. Adams), pp. 281–289. Imperial College Press-Loudon.
33. GODDARD, J. D. 1998b Migrational instabilities in shear-thinning suspensions. In IUTAM Symposium on Lubricated lYansport of Viscous Materials (ed. H. Ramkisson), pp. 193–190. Kluwer Academic Publishers.
34. Goddard, J. D. 1998c Migrational instabilities in particulate systems. In Annual AIChE Meeting, Miami, November 16–20.
35. Goddard, J. D. & Bashir, Y. B. 1990 On Reynolds dilatancy. In Recent Developemcnts in Structural Continua, vol. II, Res. Notes in Math., No. 229, (ed. D. DeDee Iz Kaloni, P. N.) pp. 23–35. Longman/John Wiley.
36. Goddard, L. D. & DidwaNIA, A. K. 1998 Computations of dilatancy and yield surfaces for assemblies of rigid frictional spheres. Q. J. Mech. Appl. Math, 51, 15.
37. GOLDIIIRSCH, I, & ZANETTI, G 1993 Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619.
38. Haff, P. K. 1983 Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401.
39. Helfand, E. & Frederickson, G. H. 1989 Large fluctuations in polymer solutions under shear. Phys. Rev. Lett. 62, 2468.
40. HILL, R. 1952 On discontinuous plastic states with localized necking in thin sheets. J. Mech. and Phys. Solids 1, 52.
41. Hill, R. & Hutchinson, J. W, 1975 On discontinuous plastic states with localized necking in thin sheets. J. Mech. and Phys. Solids 23, 239.
42. Hopkins, M. A. & Louge, M. Y. 1991 Inelastic rnicrostructure in rapid granular flows of smooth disks. Phys. Fluids A 3, 47.
43. Hunter, J. K. Sc Slemrod, M. 1983 Viscoelastic fluid flow exhibiting hysteretic phase changes. Phys. Fluids 26, 2345.
44. HUTCHINSON, J. W. & RICE, J. R,. 1975 Conditions for the localization of deformation in pressure-sensitive dilatant materials. J. Mech. and Phys. Solids 23, 371.
45. Hutter, K. & Rajagopal, K. R. 1994 On flows of granular materials. C'tmm. Mech. Thermodynamics 6, 81.
46. Ianniruberto, G. & Marucci, G. 1994 Falling spheres in polymeric solutions. Limiting results of the two-fluid theory of migration. J. Non-Newtonian Fluid Mcch. 54,231.
47. JACKSON, R. 1983 Some mathematical and physical aspects of continuum models for the motion of granular materials. In Theory of Dispersed Multiphase Flow (ed. R. Meyer), pp. 291–337. Academic Press.
48. JENKINS, J. T. & MCTIGUE, D. F. 1990 Transport processes in concentrated suspensions: the role of particle fluctuations. In Two-Phase Flows and Waves (ed. D. D. Joseph & D. G. Schaeffer), pp. 70–79. Springer.
49. JENKINS, J. T. & RICHMAN, M. W. 1985 Kinetic theory for plane shear flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28, 3485.
50. JENKINS, J. T. & RICHMAN, M. W. 1988 Plane simple shear of smooth inelastic circular disks: the anisotrophy of the second moment in the dilute and dense limit. J. Fluid Mech. 192, 313.
51. JOHNSON, P. C. & JACKSON, R. 1987 Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176, 67.
52. JOHNSON, P. C., NOTT, P. R. & JACKSON, R. 1990 Frictional-collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 210, 501.
53. Joseph, D. D. 1964 Variable viscosity effects on the flow and stability of the flow in channels and pipes. Phys, Fluids 7,1761.
54. Joseph, D. D. 1990 Fluid Dynamics of Viscoelastic Liquids. Springer.
55. JOSEPH, D. D. & Saut, J. C. 1986 Change of type and loss of evolution in the flow of viscoelastic fluids. J, Non-Newtonian Fluid Mech. 20, 117.
56. LAI, J. & FULLER, G.G. 1996 Dynamic response of a near-critical polymer blend solution under oscillatory shear flow. J. Rheol. 40, 153.
57. Leighton, D. T. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions, J. Fluid Mech, 181, 415.
58. Lun, C. K. K. 1991 Kinetic theory for granular (low of dense, slightly inelastic, slightly rough spheres. J. Fluid Mech. 233, 539.
59. Lun, C. K., Savage, S. B., Jeffrey, D. J. & Chepurniy, N 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic panicles in a general flow field. J. Fluid Mech. 140, 223.
60. LUTSKO, I. F. & Dufty, J. W. 1986 Possible instability for shear-induced orderdisorder transition. Phys. Rev. Lett. 57, 2275.
61. Miller, T. M., O'Hern, C. & Behringer, R. F. 1996 Stress fluctuations for continuously sheared granular materials. Phys. Rev. Lett. 77, 3110.
62. Nott, P. R. & Brady, J. F. 1994 Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275, 157.
63. NOTT, P. R., Alam, M., Agrawal, K., JAGKSON, R. & Sundaresan, S. 1998 The effects of boundaries on plane Couette flows of granular materials: a bifurcation analysis. Submitted to J. Fluid Mech.
64. Ogawa, S., Umemura, A. & Oshima, N. 1980 On the equations of fully fluidizerl granular materials. Z. Angew. Math. Phys. 31, 483.
65. Papoula, R. M. 1987 Possible shear instabilities for colloidal structures in a solvent. J. Phys. A: Math. Gen. 20, L649.
66. Pearson, J. R. A. 1994 Flow curves with a maximum. J. Rheot. 38, 309.
67. Phan-Thien, N. & Fang, Z. 1996 Entrance length and pulsatile flows of a model concentrated suspensions. J. Rheol. 40, 521.
68. Phan-Thien, N., Fang, Z. & Graham, A. L. 1995 Stability of some shear flows for concentrated suspensions. Rheol. Acta 35, 69.
69. Phillips, R. J., Armstrong, R. C., Brown, R. A., Graham, A. L. & Abbott, J. R. 1992 A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys. Fluids A 4, 30.
70. Quemada, D. 1981 Unstable flows of concentrated suspensions. In Stability of Thermodynamic Systems, (ed. J. Casas-Vazquez k Lebob, G.), pp. 201. Springer.
71. Regirer, S.A. 1958 Some thermo-hydrodynamics problems on steady uniform flow of a viscous liquid J. Appl. Math. Mech.22, 414 (translation of 1957 Piik. Mat. Afe/s.21,424).
72. Savage, S. B. 1992a Numerical simulations of CoueLte flow of granular materials: spatio-temporal coherence and 1/f noise. In Physics of Granular Media (ed. D. Bideau k.1. Dodds), pp. 343–362. New York: Nova Science.
73. Savage, S. B. 1992b Instability of unbounded uniform granular shear flow. J. Fluid Mech. 241, 109.
74. SCHAEFFER, D. G. 1992 A mathematical model for localization in granular flow. Proc. Roy. Soc. Lond. A 436, 217.
75. Schmid, P.I. & Kytomaa, H. K. 1994 Transient and asymptotic stability of granular shear flow. J. Fluid Mech. 264, 255.
76. Sela, N. & Goldhirsch, I. 1998 Hydrodynamic equations for rapid shear flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361, 41.
77. Tan, M-L. Goldhirsch, I. 1997 Intcrcluster interactions in rapid granular shear flows. Phys. Fluids A 9, 856.
78. Thomson, W. 1887 Stability of fluid motion: rectilineal motion of viscous fluid between two parallel plates. Phil. Mug. 24, 188.
79. Trefethen, L.N., Trefethen, A.E., Reddy, S.C. & Driscoll, T. 1993 Hydrodynamic stability without eigenvalues. Science 261,578.
80. Truesdell, C. 1954 Kinematics of Vorticity. Indiana Univ. Press.
81. VardOULakis, I. 1983 Rigid granular plasticity model and bifurcation in the triaxial test. Acta Mechanica 49, 57.
82. Walgraef, D. & Ghoniem, N.M. 1990 Patterns, Defects and Materials Instabilities. (Proc. NATO Advanced Study Institute, Cargése, France, 1989), Kluwcr Academic Publishers.
83. Wang, Y, Jackson, R. & Sundaresan, S. 1990 Stability of bounded rapid shear flows of a granular material. J. Fluid Mech. 308, 31.
84. Wang, C-H., Jackson, R, & Sundaresan, S. 1997 Instabilities of fully developed rapid flow of a granular material in a channel. J. Fluid Mech. 341, 161.
85. WANG, V., MAURI, R. & Acrivos, A. 1998 Transverse shear-induced gradient diffusion in a dilute suspension of spheres. J. Fluid Mech. 357, 279.
86. Wright, T. W. & BATRA, R. C. 1985 The initiation and growth of adiabatic shear bands. Int. J. Plasticity 1, 205.