On flows of granular materials

Continuum Mechanics and Thermodynamics - Tập 6 Số 2 - Trang 81-139 - 1994
Kolumban Hutter1, Κ. R. Rajagopal2
1Institute für Mechanik (AG III), Technische Hochschule Darmstadt, Darmstadt, Germany
2Departments of Mechanical Engineering and Mathematics & Statistics, University of Pittsburgh, Pittsburgh, USA

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Ahmadi, G., 1982: A continuum theory of smectic a liquid crystals.J. Rheology,26, 535?566

Ahmadi, G., 1983: A generalized continuum theory for flow of granular materials. InAdvances in the mechanics and the flow of granular materials,2. (ed. M. Shahinpoor). II Gulf Publishing Co., 497?527

Ahmadi, G.; Ma, D. N., 1986.Int. J. Bulk Solid Storage in Silos, 2, p. 8

Ahmadi, G.; Shahinpoor, M., 1983: Towards a turbulent modeling of rapid flow of granular materials.Powder Tech., 35, 241?248

Ahn, H., 1989: Experimental and analytical investigation of granular materials.Ph. D. Thesis. Caltech

Ahn, H.; Brennen, C. E.; Sabersky, R. H., 1992: Analysis of the fully developed chute flow of granular materials.J. App. Mech. 59, 109?119

Augenstein, D. A.; Hogg R., 1978: An experimental study of the flow of dry powders over inclined surfaces.Powder Techn., 19, 205?15

Babic, M., 1993: On the stability of rapid granular flows.J. Fluid Mech., 254, 127?150

Bagnold, R. A., 1954: Experiments on a gravity free dispersion of large solid spheres in a Newtonian fluid under shear.Proc. R. Soc. London, Ser. A 225, 49?63

Bagnold, R. A., 1966: The shearing and dilatation of dry sand and the singing mechanism.Proc. R. Soc. London, A 295, 219?232

Bailard, J., 1978: An experimental study of granular-fluid flow.Ph. D. Thesis, Univ. of Calif., San Diego, 172 pp

Bashir, Y. M.; Goddard, J. D., 1990: Experiments on the conductivity of suspensions of ionically-conductive spheres.Ai. Ch. Engng. J., 36, 387?396

Batchelor, G. K.; O'Brien, R. W., 1977: Thermal or electrical conduction through a granular material.Proc. R. Soc., London., A 355, 313?333

Bhatnagar, P. L.; Gross, P.; Krook, M., 1954: A model for collision processes in gases I: small amplitude processes in charged and in neutral one component systems.Physical Reviews, 94, 5511?5536

Blinowski, A., 1978: On the dynamic flow of granular media.Arch. of Mech., Arch. Mech. Stoso., 30, Nr. 1, pp. 27?34

Boyle, E. J.; Massoudi, M., 1989: Kinetic theories of granular materials with applications to fluidized beds.U. S. Department of Energy, Technical Note, DOE/METC-89-4088.

Boyle, E. J.; Massoudi, M., 1990: A theory for granular materials exhibiting normal stress effects based on Enskog's dense gas theory.Int. J. Engng. Sci. 28, 1261?1275

Bridgewater, J., 1972: Stress-velocity relationships for particulate solids.ASME paper 72-MH-21, 7 pp

Buggisch, H.; Stadtler, R., 1986: On the relation between shear rate and stresses in one-dimensional steady flow of moist bulk solids.Proc. World Congress Particle Technolgy, Part III, Mechanics of Pneumatic and Hydraulic Conveying and Mixing, Nürnberg, 16?18 April, 187?202

Campbell, C. S., 1986: Computer simulation of rapid granular flows.Proc. 10th National Congr. on Appl. Mech. Austin, Texas, 327?338, New York, ASME

Campbell, C. S., 1990: Rapid granular flows.Ann. Rev. Fluid Mech. 22, 57?92

Carnahan, N. F.; Starling, K. E., 1969: Equations of state for non-attracting rigid spheres.J. Chem. Phys., 51, pp. 635?636

Criminale, W. O.; Jr., Ericksen, J. L.; Filbey, G. L., 1958: Steady shear flow of non-Newtonian Fluids.Arch. Rational Mech. Anal., 1, 410?417

Davies, T. R. H., 1986: Large debris flows: A macro-viscous phenomenon.Acta Mechanica, 63, 161?178

Davies, T. R. H., 1988: Debris flow surges-A laboratory investigation.Mitteilung No. 96 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie an der ETH Zürich, 122 pp

Eringen, A. C., 1969: Mechanics of micropolar continua.Contributions to Mechanics, (D. Abir, ed.) Pergamon Press, New York, 23?40

Faraday, M., 1831: On the peculiar class of accoustical figures assumed by groups of particles upon vibrating elastic surfaces.Phil. Trans, 299?340 (see alsoFaraday's Diary, 1 (T. Martin ed.), G. Bell and Sons Ltd., London, 324?359

Galdi, G.P.; Padula, M.; Rajagopal, K.R., 1991:Recent Advances in Mechanics of Structured Continua, AMD-117, ASME, New York

Goddard, J. D., 1986: Dissipative materials as constitutive models for granular media.Acta Mechanica, 63, 3?13

Goodman, M. A.; Cowin, S. C., 1971: Two problems in the gravity flow of granular materials.J. of Fluid Mechanics, 45, 321?339

Goodman, M. A.; Cowin, S. C., 1972: A continuum theory for granular materials,Arch. Rational Mech. Anal., 44, (4), 249?266

Grad, H., 1949: On the kinetic theory of rarified gases.Comm. Pure and Applied Math. 2, 331?407

Gudhe, R., 1993: A theoretical and numerical study of the flow of granular materials down an inclined plane.Ph. D. Thesis, University of Pittsburgh, Pittsburgh

Gudhe, R.; Rajagopal, K.R.; Massoudi, M., 1994: Fully developed flow of granular materials down an inclined plane.Acta Mechanica, 103, 63?78

Gudhe, R.; Yalamanchili, R. C.; Massoudi, M., 1993: The flow of granular materials in a pipe: numerical solutions.Rec. Adv. Mech. Strctd. Continua, AMD-160/MD-41, 41?53

Gupta, G., 1993: Flow of granular materials and non-newtonian fluids.Ph. D. Thesis, University of Pittsburgh, Pittsburgh

Haff, P. K., 1983: grain flow as a fluid-mechanical phenomenon.J. Fluid Mech., 134,401?430

Haff, P. K., 1986: A physical picture of kinetic granular flows.J. Rheology, 30.

Hanes, D. M.; Inman, D. L., 1985: Observation of rapidly flowing granular-fluid mixtures.J. Fluid Mech., 150, 357?380

Heim, A., 1882: Der Bergsturz von Elm.Deutsch. Geol. Gesell. Zeitschrift, 34, 74?115

Heim, A., 1932: Bergsturz und Menschenleben, Beiblatt zur Vierteljahresschrift derNatf. Ges. Zürich, 20, 1?218

Heisenberg, W., 1948: Zur statistischen Theorie der Turbulenz.Z. für Physik, 124, 628?657

Huber, A., 1980: Schwallwellen in Seen als Folge von Felsstürzen.Mitteilung No. 47 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie an der ETH Zürich, 1?122

Hui, K.; Haff, P. K.; Ungar, J. E.; Jackson, R., 1984, Boundary conditions for high-shear grain flows.J. Fluid Mech. 145, 223?233

Hungr, O.; Morgenstern, N. R. 1984: High velocity ring shear tests on sand.Gotechnique, 34, 415?421

Hutter, K., 1989: A continuum model for finite mass avalanches having shear-flow and plug-flow regime.Internal Report, Federal Institute of Snow and Avalanche Research, Weissfluhjoch, Ch-7620 Davos

Hutter, K., 1994: Avalanche dynamics, a review. In:Hydrology of Disasters (V. P. Singh, ed.) Kluwer Academic Publishers, Amsterdam. (in press)

Hutter, K.; Szidarovskiy, F.; Yakowitz, S., 1986a: Plane steady shear flow of a cohesionless granular material down an inclined plane: A model for flow avalanches, Part I: Theory.Acta Mechanica, 63, 87?112

Hutter, K.; Szidarovskiy, F.; Yakowitz, S., 1986b: Plane steady shear flow of a cohesionless granular material down an inclined plane: A model for flow avalanches, Part II: Numerical results.Acta Mechanica, 65, 239?261

Ishida, M.; Shirai, T., 1979: Velocity, distributions in the flow of solid particles in an inclined open channel.J. Chem. Eng. of Japan, 12, 46?50

Ishida, M.; Hatano, H.; Shirai, T., 1980: The flow of solid particles in an aerated inclined channel.Powder Techn., 27, 7?12

Iverson, R. M.; Denlinger, R. P., 1987: The physics of debris flows-A conceptual assessment. In:Erosion and Sedimentation in the Pacific Rim (Proceedings of the Corvallis Symposium), IAHS Publ. No 165, 155?165

Jenkins, J. T. 1975: Static equilibrium of granular materials.J. of Appl. Mech. 42, 603?606

Jenkins, J. T., 1987: Balance laws and constitutive relations for rapid flows of granular materials. In:Proc. Army Research Office Workshop on Constitutive Relations (Chandra, J. and Srivastava, R., eds.), Philadelphia

Jenkins, J. T.; Cowin, S. C., 1979: Theories for flowing granular materials.The Joint ASME-CSME Appl. Mech. Fluid Engng. and Bioengng. Conf., AMD-Vol. 31, pp. 79?89

Jenkins, J.T.; Richman, M.W., 1985a: Grad's 13-moment system for a dense gas of inelastic spheres.Arch. Rat. Mech. and Anal., 87, 355?377

Jenkins, J.T.; Richman, M.W., 1985b: Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks.Physics of Fluids, 28, 3485?3494

Jenkins, J.T.; Richman, M.W., 19886. Boundary conditions for plane flows of smooth, nearly elastic, circular disks.J. Fluid Mech. 171, 53?69

Jenkins, J. T.; Savage, S. B., 1981: The mean stress resulting from interparticle collisions in a rapid granular shear flow. In:Proceedings of the Fourth International Conference on Continuum Models of Discrete Systems (O. Bruhin and R. K. T. Hsien, eds.), North Holland

Jenkins, J. T.; Savage, S. B., 1983: A theory for the rapid flow of identical, smooth, nearly elastic spherical particles.J. Fluid Mech., 130, 187?202

Johnson, G.; Massoudi, M.; Rajagopal, K. R., 1991a: Flow of a fluid-solid mixture between flat plates.Chem. Engng. Sci., 46, 1713?1723

Johnson, G.; Massoudi, M.; Rajagopal, K. R., 1991b: Flow of a fluid infused with solid particles through a pipe.Int. J. Engng. Sci., 29, 649?661

Johnson, G.; Massoudi, M., Rajagopal, K. R., 1991c: Couette flow of a fluid with entrained solid particles.Rec. Adv. Mech. Strctd. Cont., AMD- 117, 97?105

Johnson, P. C.; Jackson, R., 1987: Frictional-collisional constitutive relations for granular materials, with application to plane shearing.J. Fluid Mech., 176, 67?93

Johnson, P. C.; Nott, P.; Jackson, R., 1990: Frictional-collisional equations of motion for particulate flows and their application to chutes.J. Fluid Mech., 210, 501?535

Kadambi, J.R.; Chen, R.C.; Bunia, S., 1989: Laser velocimeter measurements of multiphase flow of solids.Technical Report, U.S. Department of Energy, DOE/ PETC-90961-T9

Kanatani, K. I., 1979: A micropolar continuum theory for the flow of granular materials.Int. J. Engng. Sci., 17, 419?432

Kolmogoroff, A., 1941: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers.Comptes rend. de l'Acad. de Sci. de l'USSR, 30, 301?305

Liu Ko-fei; Mei, C. C., 1991: Rapid flow of a Bingham-plastic fluid down a gentle slope.J. Fluid Mechanics (submitted)

Lun, C. K. K.; Savage, S. B.; Jeffrey, D. J.; Chepurniy, N., 1984: Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field.J. Fluid Mech., 140, 223?256

Ma, D.; Ahmadi, G., 1985: A turbulence model for rapid flows of granular materials, Part II. Simple Shear Flows.Powder Tech., 44, p. 269?279

Ma, D.; Ahmadi, G., 1988: A kinetic model for rapid granular flows of nearly elastic particles including interstitial fluid effects.Powder Tech., 56, p. 191

Massoudi, M., 1986: Application of mixture theory to fluidized beds.Ph. D. Thesis, University of Pittsburgh

Massoudi, M., 1988: Stability analysis of fluidized beds.Int. Journal of Engineering Science, 26, 765

Massoudi, M.; Boyle, E. J., 1991: A review of theories for flowing granular materials with applications to fluidized beds and solids transport.U.S. Department of energy Report, DOE/PETC/TR-91/8

Maxwell, B.; Chartoff, R.P., 1965: Studies of a polymer melt in an othogonal rheometer.Trans. Soc. Rheology, 9, 51

McQuarrie, V.V., 1976:Statistical mechanics, Haper and Row, New York

McTigue, D. F., 1982: A nonlinear continuum theory for flowing granular materials.Ph. D. Thesis, Dept. of Geol, Stanford University

McTigue, D. F., 1982: A nonlinear constitutive model for granular materials: application to gravity flow.J. of Appl. Mech., 49, 291?296

Middleton, G. V., 1970: Experimental studies related to problem of flysch sedimentation. In:Flysch Sedimentology in North America (Lajoie, J., ed.), Business and Economics Science Ltd., Toronto, 253?272

Middleton, G. V.; Hampton, M. A., 1976: Subaqueous sediment transport and deposition by sediment gravity flows. In:Marine Sediment Transport and Environmental Management (Stanley, D. J. and Swift D. J. P., eds.), Wiley, New York, 197?218

Naylor, M. A., 1980: The origin of inverse grading in muddy debris flow deposits-A review.J. Sedimentary Petrology, 50, 1111?1116

Nedderman, R. M.; Tuzun, U., Savage, S. B.; Houlsby, G. T., 1982: The flow of granular materials, I. Discharge rates from hoppers.Chem. Engng. Sci., 37, 1597?1609

Noll, W., 1962: Motions with constant stretch history.Arch. Rational Mech. Anal., 11, 97?105

Norem, H.; Irgens, F.; Schieldrop, B. A., 1987: A continuum model for calculating snow avalanches. In:Avalanche Formation. Movement and Effects, (Salm, B. and Gubler, H., eds.), IAHS Publ. No. 126, 363?379

Novosad, J., 1964: Studies on granular materials, II. Apparatus for measuring the dynamic angle of internal and external friction of granular materials.Collection Czechoslov. Chem. Commun., 29. No. 2697

Nunziato, J. W.; Passman, S. L.; Thomas Jr.; J. P., 1980: Gravitational flows of granular materials with incompressible grains.J. of Rheology, 24, 395?420

Ogawa, S., 1978: Multitemperature theory of granular materials. In:Proc. Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials, (S. C. Cowin and M. Satake, eds.) US-Japan Seminar, Sendai, Japan, pp. 208?217

Ogawa, S.; Umemura, A.; Oshima, N. 1980: On the equations of fully fluidized granular matrials.ZAMP, 31, pp. 483?493

Oppenheim, I., 1991: Statistical mechanical theory of inelastic granular systems.Joint NSF-DOE workshop on Flow of Particulates and Fluids, October 22?24, Worcester Polytechnic Institute, Worcester, 236?253

Oppenheim, I.; McBride, J.,1990: Transport equations for suspensions of inelastic particles.Physica A, 165, 279?302

Passman, S. L.; Nunziato, J. W.; Bailey, P. B.; Thomas Jr., J. P., 1980: Shearing flows of granular materials.J. Engg. Mech. Div., ASCE, 106, 773?783

Poynting, G. H., 1905: Radiation-pressure.Phil. Magazine, 9, 335?346

Rajagopal, K. R., 1982: On the flow of a simple fluid in an orthogonal rheometer.Arch. Rational Mech. Anal., 79, 29

Rajagopal, K. R.; Gudhe, R., 1992: Stability of the flow of granular materials down an inclined plane.Fourth NSF-DOE workshop on Flow of Particulates and Fluids, September 17?18, Gaithersburg, Maryland, 167?187

Rajagopal, K. R.; Gudhe, R., 1993: Stability analysis for the flow of granular materials down an inclined plane using kinetic model.Fifth NSF-DOE workshop on Flow of Particulates and Fluids, Cornell

Rajagopal, K. R.; Massoudi, M., 1990: A method for measuring material moduli of granular materials: flow in an orthogonal rheometer. Topical Report U, Department of Energy. DOE/PETC/TR-90/3

Rajagopal, K. R.; Massoudi, M.; Ekmann, J.M., 1990: Mathematical modeling of fluid-solid mixtures.In Recent Developments in Structural Continua II, Longman

Rajagopal, K. R.; Troy, W. C.; Massoudi, M., 1992: Existence of solutions to the equations governing the flow of granular materials.Eur. J. Mech.,B/Fluids, 11, 265?276

Ratkai, G., 1976: Particle flow and mixing in vertically vibrated beds.Powder Tech., 15, 187?192

Reid, F., 1965: Fundamentals of statistical mechanics and thermal physics. McGraw Hill, New York

Reiner, M., 1945: A mathematical theory of dilatancy.Am. J. Math, 67, 350?362

Reynolds, O., 1885. On the dilatancy of media composed of rigid particles in contact.Phil. Mag. Ser. 5, 20, 469?481

Richman, M. W., 1988: Boundary conditions based upon a modified Maxwellian velocity distribution for flows of identical, smooth, nearly elastic spheres.Acta Mech. 75, 227?240.

Richman, M. W.; Marciniec, R. P., 1990: Gravity-driven granular flows of smooth, inelastic spheres down bumpy inclines.J. Appl. Mech. 57, 1036?1043

Sallenger, A. H., 1979: Inverse grading and hydraulic equivalence in grain-flow deposits.J. Sedimentary Petrology, 49, 553?562

Savage, S. B., 1979: Gravity flow of cohesionless granular materials in chutes and channels.J. Fluid Mech., 92, 53?96

Savage, S. B., 1983: Granular flows down rough inclines-Review and extension. In:Mechanics of Granular Materials: New Models and Constitutive Relations (Jenkins, J. T. and Satake, M., eds.), Elsevier, pp. 261?82

Savage, S. B., 1984: The mechanics of rapid granular flows. In:Advances in Applied Mechanics, 24 (Wu, T. Y. and Hutchinson, J., eds.), Academic, 289?366

Savage, S. B., 1987: Interparticle percolation and segregation in granular materials: A review. In:Developments in Engineering Mechanics (Selvadurai, A.P.S., ed.), Elsevier, Amsterdam, 347?363

Savage, S. B., 1988. Streaming motions in a bed of vibrationally fluidized dry granular material.J. Fluid Mech., 194, 457?478

Savage, S. B., 1989: Flow of granular materials. In:Theoretical and Applied Mechanics (P. Germain, M. Piau and D. Caillerie eds., Elsevier Science Publishers B. V., North-Holland. iutam, 241?266

Savage, S. B., 1993: Mechanics of granular flows. In:Continuum mechanics in environmental sciences and geophysics (K. Hutter, ed.) CISM Courses and Lectures No. 337, Springer Verlag, Vienna-New York

Savage, S. B.; Hutter, K., 1989: The motion of a finite mass of granular material down a rough incline.J. Fluid Mech., 199, 177?215.

Savage, S. B.; Hutter, K., 1991: The dynamics of avalanches of granular materials from initiation to runout. Part I. Analysis.Acta Mech., 86, 201?223

Savage, S. B.; Jeffrey, D. J., 1981: The stress tensor in a granular flow at high shear rates.J. Fluid Mech., 110, 255?272

Savage, S. B.; Lun, C. K. K., 1988: Particle size segregation in inclined chute flow of dry cohesionless granular solids.J. Fluid Mech., 189, 311?335

Savage, S. B.; McKeown, S., 1983: Shear stresses developed during rapid shear of dense concentrations of large spherical particles between concentric rotating cylinders.J. Fluid Mech., 127, 453?472

Savage, S. B.; Nohguchi, Y., 1988: Similartiy solutions for avalanches of granular materials down curved beds.Acta Mechanica, 75, 153?174

Savage, S. B.; Sayed, M., 1984: Stresses developed by dry cohesionless granular materials sheared in an annular shear cell.J. Fluid Mech., 142, 391?430

Savage, S. B.; Nedderman, R. M.; Tuzan, U.; Houlsby, G. T., 1983: The flow of granular materials, III. Rapid shear flows.Chem. Engng. Sci., 38, 189?195

Scheiwiller, T.; Hutter, K., 1982: Lawinendynamik, Übersicht über Experimente und theoretische Modelle von Fließ-und Staublawinen.Mitteilung No. 5 für Wasserbau, Hydrologie und Glaziologie an der ETH Zürich, 166 pp

Schofield, A. N.; Wroth, C. P., 1968:Critical State Soil Mechanics, McGraw-Hill, New York

Scott, R. F., 1963:Principles of Soil Mechanics, Addison Wesley, Reading

Shahinpoor, M.; Ahmadi, G., 1983: A kinetic theory for the rapid flow of rough inelastic spherical particles and the evolution of fluctuations. In:Advances in the mechanics and the flow of granular materials (M. Shahimpoor, ed.), Vol. II, 641?667.Gulf Publ. Comp. Houston

Shahinpoor, M.; Lin, S. P. 1982: Rapid Couette flow of cohesionless granular materials.Acta Mechanica. 42, 183?196

Spencer, A. J. M., 1964: A theory of the kinematics of ideal solids under plane strain conditions.J. Mech. Phys. Solids, 12, 337?351

Squire, H. B., 1933: On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls.Proc. Roy. Soc., A, 142, 621?628

Stadler, R., 1986: Stationäres, schnelles Fließen von dicht gepackten trockenen und feuchten Schüttgütern.Dr.-Ing. Dissertation, Univ. Karlsruhe, Karlsruhe, West Germany

Stadler, R.; Buggisch, H., 1985: Influence of the deformation rate on shear stress in bulk solids: Theoretical aspects and experimental results. In:Reliable Flow of Particulate Solids (EFCE Publication Series No. 49, Bergen, Norway), pp. 15

Szidarovszky, F.; Hutter, K.; Yakowitz, S., 1987: A numerical sudy of steady plane granular chute flows using the Jenkins-Savage model and its extension.Int. J. Num. Meth. Engng., 24, 1993?2015

Takahashi, T., 1981: Debris flow.Ann. Rev. Fluid Mech., 13, 57?77

Takahashi, T., 1983: Debris flow and debris flow deposition. In:Advances in the Mechanics and Flow of Granular Materials, (Shahinpoor, M., ed.), Vol. II,Gulf Publ. Company, Houston, 57?77

Thomson, W.; Tait, P.G., 1867:Treatise on Natural Philosophy, Part I, Cambridge

Truesdell, C.; Noll, W., 1965: The non-linear field theories of mechanics. In:Handbuch der Physik, III/3, ed. Flugge, Springer-Verlag

Tuzan, U.; Houlsby, G. T.; Nedderman, R. M.; Savage, S. B., 1982: The flow of granular materials, II. Velocity distributions in slow flows.Chem. Engng. Sci., 37, 1691?1709

Van Kampen, N.G.; Oppenheim, I. 1986: Brownian motion as a problem of eliminating fast variables.Physica A, 138, 231?248

Walker, J., 1982: The amateur scientist.Scientific American, 247, 206?216

Walton, O.R., 1991: Numerical simulation of inclined chute flows of nondisperse, inelastic, frictional spheres.Joint NSF-DOE workshop on Flow of Particulates and Fluids, October 1991, Worcester Polytechnic Institute, Worcester, 347?355

Walton, O. R.; Braun, R. L., 1986: Stress calculations for assemblies of inelastic spheres in uniform shear.Acta Mechanica, Vol. 63, p. 73

Yalamanchili, R.C.; Gudhe, R.; Rajagopal, K.R., Cohesionless granular materials flow in a vertical channel under the action of gravity.In Preparation

Yih, C.S., 1954: Stability of two-dimensional parallel flows for three-dimensional disturbances.Quaterly of Applied Math., 12