17
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

THE LOCAL VOLUME-AVERAGED EQUATIONS OF MOTION FOR A SUSPENSION OF NON-NEUTRALLY BUOYANT SPHERES

, , &
Pages 1-30 | Received 22 Oct 1985, Accepted 02 Jun 1986, Published online: 03 Apr 2007

REFERENCES

  • Aleman , M. , Ramamohan , T.R. , and Slattery , J.C. , “ A Statistical Model for Unsteady-State Displacement in Porous Media ,” currently being reviewed ( 1986 ).
  • Anderson , T.B. , and Jackson , R. , “ A Fluid Mechanical Description of Fluidized Beds ,” Ind. Eng. Chem. Fundam. , 6 , 527 ( 1967 ).
  • Bachmat , Y. , “ Spatial Macroscopization of Processes in Heterogeneous Systems , ” Isr. J. Tecknot. , 10 , 391 ( 1972 ).
  • Batchelor , G.K. , An Introduction to Fluid Dynamics , pp. 250 , 252 , Cambridge ( 1967 ) .
  • Batchelor , G.K. , “ The Stress System in a Suspension of Force-Free Particles ,” J. Fluid Mech. , 41 , 545 ( 1970 ).
  • Batchelor , G.K. , and Green , J.T. , “ The Determination of the Bulk Stress in a Suspension of Spherical Particles to Order c2 ,” J. Fluid. Meek. , 56 , 401 ( 1972 ).
  • Bear , J. , Dynamics of Fluids in Porous Media , American Elsevier , New York ( 1972 ) .
  • Brenner , H. , “ Dissipation of Energy due to Solid Particles Suspended in a Viscous Liquid ,” Pkys, Fluids , 1 , 338 ( 1958 ).
  • Einstein , A. , “ Ene neue Bestimmung der Molekiildimensionen ,” Ann. Phys. , 19 , 289 ( 1906 ).
  • Einstein , A. , Investigations of the Theory of the Brownian Movement , pp. 37 – 54 , Dover , New York ( 1956 ) .
  • Gray , W.G. , “ A Derivation of the Equations for Multiphase Transport ,” Chem. Eng. Sci. , 30 , 229 ( 1975 ).
  • Gray , W.G. , and O'Neill , K. , “ On the General Equations for Flow in Porous Media and their Reduction to Darcy's Law ,” Water Resour. Res. , 12 , 148 ( 1976 ).
  • Gray , W.G. , and Lee , P.C.Y. , “ On the Theorems for Local Volume Averaging of Multiphase Systems ,” Int. J. Multiphase Flow , 3 , 333 ( 1977 ).
  • Happel , J. , and Brenner , H. , Low Reynolds Number Hydrodynamics , second edition , pp. 65 , 436 , 441 , Noordhoff , Leyden ( 1973 ) .
  • Hassanizadeh , M. , and Gray , W.G. , “ General Conservation Equations for Multi-Phase Systems 1. Averaging Procedure ,” Adv. Water Resour. , 1 , 131 ( 1979 ).
  • Higginbotham , G.H. , Oliver , D. R. , and Ward , S. G. , “ Studies of the Viscosity and Sedimentation of Suspensions Part 4-Capillary Tube Viscometry Applied to Stable Suspensions of Spherical Particles ,” Brit. J. Appi Phys. , 9 , 372 ( 1958 ).
  • Hopke , S.W. , and Slattery , J.C. , “ Bounding Principles for Two-Phase Flow Systems ,” Int. J. Multiphase Flow , 1 , 111 ( 1975 ).
  • Jeffrey , D.J. , and Acrivos , A. , “ The Rheological Properties of Suspensions of Rigid Particles ,” AIChEJ. , 22 , 417 ( 1976 ).
  • Kim , M.H. , Jiang , T.S. , Kremesec Jr., V.J., and Slattery , J.C. , “ Flow of A Suspension Through A Vertical Tube ,” Chem. Eng. Commun . ( 1986 a ).
  • Kim , M.H. , VanderHeyden , W.B. , Jiang , T.S. , and Slatlery , J.C. , “ Flows of Neutrally Buoyant Suspensions in Several Viscometers ,” in preparation ( 1987 ).
  • Kremesec , V.J. Jr. , and Slattery , J.C. , “ The Apparent Stress-Deformation Behavior of a Dilute Suspension of Spheres in a Power Model Fluid ,” Trans. Soc. Rheology , 21 , 469 ( 1977 ).
  • Lamb , H. , Hydrodynamics , sixth edition , pp. 595 – 597 , Dover , New York ( 1945 ) .
  • Landau , L. , and Lifshitz , E.M. , Mechanika Splosznych Sried, Moskva ( 1954 ); as referenced by R. Herczynski and I. Pienkowska , “ Effective Viscosity of Suspension ,” Arch. Mech. , 27 , 201 ( 1975 ).
  • Landau , L.D. , and Lifshitz , E.M. , Fluid Mechanics , Addison-Wesley ( 1959 ) .
  • Lin , C.Y. , and Slattery , J.C. , “ Three-Dimensional, Randomized, Network Model for Two-Phase Flow through Porous Media ,” AlChE J. , 28 , 311 ( 1982 ).
  • Lundgren , T.S. , “ Slow Flow Through Stationary Random Beds and Suspensions of Spheres ,” J. fluid Mech. , 51 , 273 ( 1972 ).
  • Maude , A. D. , “ The Viscosity of a Suspension of Spheres ,” J. Fluid Mech. , 7 , 230 ( 1960 ).
  • Mellema , J. , and Willemse , M.W.M. , “ Effective Viscosity of Dispersions Approached by a Statistical Continuum Method ,” Physica , 122A , 286 ( 1983 ).
  • Nagatani , T. , “ Statistical Theory of Effective Viscosity in a Random Suspension ,” J. Phys. Soc. Japan , 47 , 320 ( 1979 ).
  • Oliver , D.R. , and Ward , S.G. , “ Studies of the Viscosity and Sedimentation of Suspensions Part 5-the Viscosity of Settling Suspensions of Spherical Particles ,“ Brit. J. Appl. Phys. , 10 , 317 ( 1959 ).
  • Russel , W.B. , “ Low-Shear Limit of the Secondary Electroviscous Effects ,” J. Colloid Interface Sci. , 55 , 590 ( 1976 )
  • Rutgers , R. , “ Packing of Spheres ,” Nature , 193 , 465 ( 1962 ).
  • Scott , G.D. , “ Packing of Spheres ,” Nature , 188 , 908 (|1960|p).
  • Sha , W.T. , and Slattery , J.C. , “ Local Volume-Time Averaged Equations of Motion for Dispersed, Turbulent, Multiphase Flows ,” NUREG/CR-1491, ANL-80-51 , Argonne National Laboratory , Argonne , Illinois ( 1980 ) .
  • Slattery , J.C. , “ Flow of Viscoelastic Fluids through Porous Media ,” AIChEJ. , 13 , 1066 ( 1967 ).
  • Slattery , J.C. , “ Multiphase Viscoelastic Flow through Porous Media ,” AIChEJ. , 14 , 50 ( 1968 ).
  • Slattery , J.C. , “ Single-Phase Flow through Porous Media ,” AIChEJ. , 15 , 866 ( 1969 ).
  • Slattery , J.C. , “ Two-phase Flow through Porous Media ,“ AIChEJ. , 16 , 345 ( 1970 ).
  • Slattery , J.C. , “ A Fundamental Approach to Mass Transfer in Porous Media ,” in Workshop on Heat and Mass Transfer in Porous Media , edited by A. Dybbs , Department of Fluid, Thermal and Aerospace Science, Case Western Reserve University , Cleveland ( 1974 ) .
  • Slattery , J.C. , Momentum, Energy, and Mass Transfer in Continua , Second edition , pp. 12 – 17 , 37 , 38 , 51 , 193 – 199 , Robert E. Krieger , Malabar , FL ( 1981 ) .
  • Vand , V. , “ Viscosity of Solutions and Suspensions. 1. Theory ,” J. Phys. Coll. Chem. , 52 , 277 ( 1984 a).
  • Vand , V. , “ Viscosity of Solutions and Suspensions. II. Experimental Determination of the Viscosity-Concentration Function of Spherical Suspensions ,” J. Phys. Coll. Chem. , 52 , 300 ( 1948 b).
  • Whitaker , S. , “ Diffusion and Dispersion in Porous Media ,“ AIChEJ. , 13 , 420 ( 1967 ).
  • Whitaker , S. , “ Advances in Theory of Fluid Motion in Porous Media ,” Ind. Eng. Chem. , 61 ( 12 ), 14 ( 1969 ).
  • Whitaker , S. , “ The Transport Equations for Multiphase Systems ,” Chem. Eng. Sci. , 28 , 139 ( 1973 ).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.