Skip to main content
SpringerLink
Log in

Flow Relative to Assemblages of Particles

  • Chapter
Low Reynolds number hydrodynamics

Part of the book series: Mechanics of fluids and transport processes ((MFTP,volume 1))

  • 3231 Accesses

Abstract

Fluid flow relative to assemblages of particles represents an area of interest in many fields of science and technology16 as discussed in Chapter 1. An extremely wide range of problems is involved and, as would be expected, the number of possible variables is also large. A hydrodynamic treatment therefore constitutes a considerable idealization.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Adler, I. L. and J. Happel, Chem. Eng. Progr. Symposium Series 58 (1962), 98.

    Google Scholar 

  2. Andersson, K. E. B., Trans. Roy. Inst. Techn. (Stockholm) No. 131 (1959); No. 201 (1963); No. 202 (1963)

    Google Scholar 

  3. Andersson, K. E. B., Chem. Eng. Sci. 15 (1961), 276.

    Article  Google Scholar 

  4. Arnofsky, J. S., J. Appl. Phys. 25 (1954), 48.

    Article  ADS  Google Scholar 

  5. Bakhmeteff, B. A., and N. V. Feodoroff, J. Appl. Mech. 4 (1937), A 97

    Google Scholar 

  6. Ibid.5 (1938), A 86

    Google Scholar 

  7. Bakhmeteff, B. A., and N. V. Feodoroff Proc. 5th Intern. Congr. Appl. Mech. (1938), p. 555

    Google Scholar 

  8. Bakhmeteff, B. A., and N. V. Feodoroff Trans Amer. Geophys. Union 24 (1943), 545.

    Google Scholar 

  9. Baron, T., Chem. Eng. Progr. 48 (1952), 118.

    Google Scholar 

  10. Brenner, H., Phys. Fluids 1 (1958), 338.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. —, Eng. Sc. D. Thesis, New York University, 1957.

    Google Scholar 

  12. —, Chem. Eng. Sci. 19 (1964), 599.

    Article  Google Scholar 

  13. Bretherton, F. P., J. Fluid Mech. 14 (1962), 284.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Brinkman, H. C., Appl. Sci. Res. A1 (1947), 27

    Google Scholar 

  15. Brinkman, H. C., Appl. Sci. Res. A1 (1948), 81

    Google Scholar 

  16. Brinkman, H. C., Appl. Sci. Res. A2 (1949), 190.

    Google Scholar 

  17. Burgers, J. M., Proc. Koningl. Akad. Wetenschap. (Amsterdam) 44 (1941), 1045

    MathSciNet  Google Scholar 

  18. Burgers, J. M., Proc. Koningl. Akad. Wetenschap. (Amsterdam) 45 (1942), 9.

    Google Scholar 

  19. Carman, P. C., Flow of Gases through Porous Media. New York: Academic Press, 1956.

    MATH  Google Scholar 

  20. —, Trans. Inst. Chem. Engrs. (London) 15 (1937), 150.

    Google Scholar 

  21. Cheng, P. Y., and H. K. Schachman, J. Polymer Sci. 16 (1955), 19.

    Article  ADS  Google Scholar 

  22. Cunningham, E., Proc. Roy. Soc. (London) A83 (1910), 357.

    ADS  Google Scholar 

  23. DallaValle, J. M., Micromeritics—The Technology of Fine Particles, 2nd ed. New York: Pitman, 1948.

    Google Scholar 

  24. Darcy, H. P. G., Les Fontaines Publiques de la Ville de Dijon. Paris: Victor Dalmont, 1856.

    Google Scholar 

  25. Eagleson, P. S., R. G. Dean, and L. A. Peralta, Technical Memo No. 104, Beach Erosion Board, Dept. of the Army, Corps of Engineers, 1958.

    Google Scholar 

  26. Einstein, A., Ann. Phys. 17 (1905), 549

    Article  Google Scholar 

  27. Einstein, A., Ann. Phys. 19 (1906), 371

    Article  Google Scholar 

  28. Einstein, A., Ann. Phys. 22 (1907), 569. See also Investigations on the Theory of Brownian Movement. New York: Dover, 1956.

    Article  Google Scholar 

  29. Emersleben, O., Physik. Z. 26 (1925), 601.

    Google Scholar 

  30. Epstein, N., Eng. Sc. D. Thesis, New York University, 1954.

    Google Scholar 

  31. Epstein, P., Math. Ann. 60 (1903), 615

    Article  Google Scholar 

  32. Epstein, P., Math. Ann. 63 (1906), 205.

    Article  MathSciNet  Google Scholar 

  33. Fair, G. M., and L. P. Hatch, J. Amer. Water Works Assoc. 25 (1933), 1551.

    Google Scholar 

  34. Famularo, J., Eng. Sc. D. Thesis, New York University, 1962.

    Google Scholar 

  35. Faxen, H., Ark. Mat. Astron. Fys. 17, No. 27 (1923).

    Google Scholar 

    Google Scholar 

  36. —, Ark. Mat. Astron. Fys. 19A, No. 22 (1925).

    Google Scholar 

    Google Scholar 

  37. —, Z. Angew. Math. Mech. 7 (1927), 79.

    Article  MATH  Google Scholar 

  38. Fayon, A. M., and J. Happel, A.I.Ch.E. Jour. 6 (1960), 55.

    Google Scholar 

  39. Gardner, G. C., Chem. Eng. Sci. 7 (1957), 73.

    Article  Google Scholar 

  40. Gilliland, E. R., R. F. Baddour, and J. L. Russell, A.I.Ch.E. Jour. 4 (1958), 90.

    Google Scholar 

  41. Grace, H. P., Chem. Eng. Progr. 49 (1953), 303

    Google Scholar 

  42. Grace, H. P., Chem. Eng. Progr. 49 (1953), 367

    Google Scholar 

  43. Grace, H. P., Chem. Eng. Progr. 49 (1953), 427

    Google Scholar 

  44. Grace, H. P., A.I.Ch.E. Jour. 2 (1956), 307.

    Google Scholar 

  45. Green, H. L., and W. R. Lane. Particulate Clouds: Dusts, Smokes, and Mists. London: Spon, Ltd., 1957.

    Google Scholar 

  46. Haberman, W., and R. M. Sayre, “Motion of Rigid and Fluid Spheres in Stationary and Moving Liquids Inside Cylindrical Tubes,” Report 1143, David Taylor Model Basin, U.S. Navy Dept. Washington, D.C., October, 1958.

    Google Scholar 

  47. Hall, W. A., Trans. Amer. Geophys. Union 3 (1956), 185.

    Google Scholar 

  48. Happel, J., A.I.Ch.E. Jour. 4 (1958), 197.

    MathSciNet  Google Scholar 

  49. —, A.I.Ch.E. Jour. 5 (1959), 174.

    Google Scholar 

  50. —, Ind. Eng. Chem. 41 (1949), 1161.

    Article  Google Scholar 

  51. —, J. Appl. Phys 28 (1957), 1288.

    Article  ADS  MATH  Google Scholar 

  52. —, and P. A. Ast, Chem. Eng. Sci. 11 (1960), 286.

    Google Scholar 

  53. —, and H. Brenner, A.I.Ch.E. Jour. 3 (1957), 506.

    Google Scholar 

  54. —, and B. J. Byrne, Ind. Eng. Chem. 46 (1954), 1181.

    Article  Google Scholar 

  55. —, and N. Epstein, Chem. Eng. 57 (1950), 137.

    Google Scholar 

  56. —, and N. Epstein —, Ind. Eng. Chem. 46 (1954), 1161.

    Google Scholar 

  57. —, and N. Epstein —, Ind. Eng. Chem. 46 (1954), 1187.

    Article  Google Scholar 

  58. —, and R. Pfeffer, A.I.Ch.E. Jour. 6 (1960), 129.

    Google Scholar 

  59. Harris, C. C., Nature 183 (1959), 530

    Article  ADS  MATH  Google Scholar 

  60. Harris, C. C., Nature 184 (1959), 716.

    Article  ADS  MATH  Google Scholar 

  61. Hasimoto, H., J. Fluid Mech. 5 (1959), 317.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  62. —, J. Phys. Soc. Japan 13 (1958), 633.

    Article  MathSciNet  ADS  Google Scholar 

  63. Hubbert, M. K., Petrol. Trans. Amer. Inst. Min. Engrs. 207 (1956), 222.

    Google Scholar 

  64. Hutto, F. B., Chem. Eng. Progr. 53 (1957), 328.

    Google Scholar 

  65. Irmay, S., Trans. Amer. Geophys. Union 39 (1958), 702; see also discussion, Jour. Geophys. Res. 64 (1959), 485.

    Google Scholar 

  66. Kawaguchi, M., J. Phys. Soc. Japan 13 (1958), 209.

    Article  ADS  Google Scholar 

  67. Kaye, B. H., and R. P. Boardman, Proc. Symposium Interaction between Fluids and Particles. London: Brit. Inst. Chem. Engrs., 1962.

    Google Scholar 

  68. Kozeny, J., Hydraulik. Wien: Springer Verlag, 1953, p. 390

    Google Scholar 

  69. Kozeny, J., Sitz.-Ber. Wiener Akad., Abt. IIa, 136 (1927), 271.

    Google Scholar 

  70. Kuwabara, S., J. Phys. Soc. Japan (to be published).

    Google Scholar 

  71. —, J. Phys. Soc. Japan 14 (1959), 527.

    Article  MathSciNet  ADS  Google Scholar 

  72. Kynch, G. J., J. Fluid Mech. 5 (1959), 193.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  73. —, Trans. Farad. Soc. 48 (1952), 166.

    Article  Google Scholar 

  74. Lamb, Hydrodynamics, 6th ed. Cambridge: Cambridge Univ. Press, 1932.

    MATH  Google Scholar 

  75. Lanneau, K. P., Paper presented at the meeting of the Institution of Chemical Engineers, Oct. 21, 1959.

    Google Scholar 

  76. Lapple, C. E., in Chemical Engineers Handbook, ed. J. H. Perry. New York: McGraw-Hill, 1950.

    Google Scholar 

  77. Leibenson, L. S., Complete Works (in Russian), Vol. 3. Moscow, 1955.

    Google Scholar 

  78. Leva, M., Fluidization. New York: McGraw-Hill, 1959.

    Google Scholar 

  79. Lin, P. N., Ph. D. Thesis, Iowa State University, 1951.

    Google Scholar 

  80. Maude, A. D., and R. L. Whitmore, Brit. J. Appl. Phys. 9 (1958), 477.

    Article  ADS  Google Scholar 

  81. McHenry, K. W., and R. H. Wilhelm, A.I.Ch.E. Jour. 3 (1957), 83.

    Google Scholar 

  82. McNown, J. S., and P. N. Lin, “Proc. Second Midwestern Conf. Fluid Mechanics,” Reprint in Eng. No. 109, Iowa State Univ., 1952.

    Google Scholar 

  83. Milne-Thomson, L. M., Theoretical Hydrodynamics, 3rd ed. New York: Macmillan, 1955, pp. 182

    MATH  Google Scholar 

  84. Milne-Thomson, L. M., Theoretical Hydrodynamics, 3rd ed. New York: Macmillan, 1955, 540.

    MATH  Google Scholar 

  85. Miyagi, T., J. Phys. Soc. Japan 13 (1958), 209.

    Article  MathSciNet  Google Scholar 

  86. Morse, P. M., and H. Feshbach, Methods of Theoretical Physics. New York: McGraw-Hill, 1953.

    MATH  Google Scholar 

  87. Muskat, M., The Flow of Homogeneous Fluids through Porous Media. New York: McGraw-Hill, 1937; 2nd printing, Ann Arbor: Edwards, 1946.

    Google Scholar 

  88. Noda, H., Bull. Chem. Soc. Japan 30 (1957), 495.

    Article  Google Scholar 

  89. Oliver, D. R., Nature 194 (1962), 1269.

    Article  ADS  Google Scholar 

  90. Oman, A. O., and K. M. Watson, Natl. Petroleum News 36 (1944), R795.

    Google Scholar 

  91. Polubarinova-Kochina, P. Ya., Theory of Ground-Water Movement. Princeton: Princeton Univ. Press, 1962.

    MATH  Google Scholar 

  92. Prager, S., Phys. Fluids 4 (1961), 1477.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  93. Reboux, P., Phenomenes de Fluidisation. Paris: Assoc. Francaise de Fluidization, 1954.

    Google Scholar 

  94. Richardson, J. F., and W. N. Zaki, Chem. Eng. Sci. 3 (1954), 65.

    Article  Google Scholar 

  95. Rubinow, S. I., and J. B. Keller, J. Fluid Mech. 11 (1961), 447.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  96. Rutgers, R., Nature 193 (1962), 465.

    Article  ADS  Google Scholar 

  97. Saffman, P. G., J. Fluid Mech. 1 (1956), 540

    Article  MathSciNet  ADS  MATH  Google Scholar 

  98. Ibid. 6 (1959), 321.

    Article  MathSciNet  ADS  Google Scholar 

  99. —, and G. I. Taylor, Proc. Roy. Soc. (London) A 245 (1958), 312.

    MathSciNet  ADS  Google Scholar 

  100. Scheidegger, A. E., J. Appl. Phys. 25 (1954), 994.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  101. —, The Physics of Flow through Porous Media, 2nd ed. New York: Macmillan, 1960.

    MATH  Google Scholar 

  102. —, Phys. Fluids 3 (1960), 94.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  103. Schytil, F., Wirbelschttechnik. Berlin: Springer Verlag, 1961.

    Google Scholar 

  104. Segré, G., and A. Silberberg, J. Fluid Mech. 14 (1962), 115

    Article  ADS  MATH  Google Scholar 

  105. Segré, G., and A. Silberberg, J. Fluid Mech. 14 (1962), 136.

    Article  ADS  Google Scholar 

  106. Slezkin, N. A., Dokladi Akad. Nauk. SSSR 86 (1952), 235.

    MathSciNet  Google Scholar 

  107. —, Dynamics of Viscous Incompressible Fluids (in Russian). Moscow: Gos. Izdat. Tekh.-Teor. Lit., 1955.

    Google Scholar 

  108. —, and S. M. Shustov, Dokladi Akad. Nauk. SSSR 96 (1954), 933.

    MATH  Google Scholar 

  109. Smoluchowski, M., Bull. Acad. Sci. Cracow 1a (1911), 28.

    Google Scholar 

  110. —, Proc. 5th Intern. Congr. Math. 2 (1912), 192.

    Google Scholar 

  111. —, Phys. Z. 17 (1916), 557

    ADS  Google Scholar 

  112. —, Phys. Z. 17 (1916), 585

    Google Scholar 

  113. —, Z. Phys. Chem. 92 (1917), 129.

    Google Scholar 

  114. Sokolnikoff, I. S., and R. M. Redheffer, Mathematics of Physics and Modern Engineering. New York: McGraw-Hill, 1958.

    MATH  Google Scholar 

  115. Sparrow, E. M., and A. L. Loeffler, Jr., A.I.Ch.E. Jour. 5 (1959), 325.

    Google Scholar 

  116. Steinour, H. H., Ind. Eng. Chem. 36 (1944), 618

    Article  Google Scholar 

  117. Steinour, H. H., Ind. Eng. Chem. 36 (1944), 840

    Article  Google Scholar 

  118. Steinour, H. H., Ind. Eng. Chem. 36 (1944), 901.

    Article  Google Scholar 

  119. Streeter, V. L., Fluid Dynamics. New York: McGraw-Hill, 1948.

    Google Scholar 

  120. Sullivan, R. R., J. Appl. Phys. 13 (1942), 725.

    Article  ADS  Google Scholar 

  121. Talmadge, W. P., and E. B. Fitch, Ind. Eng. Chem. 47 (1955), 38.

    Article  Google Scholar 

  122. Tamada, K., and H. Fujikawa, Quart. J. Mech. Appl. Math. 10 (1957), 423.

    Article  MathSciNet  Google Scholar 

  123. Tesarik, J., Proudeni tekuting porovityn prostredim (Flow of Fluids in Porous Media) Prague: Artia, P.O.B. 790, 1961.

    Google Scholar 

  124. Theodore, L., Ph.D. Thesis, New York University, 1964.

    Google Scholar 

  125. Tiller, F. M., Chem. Eng. Progr. 49 (1953), 467

    Google Scholar 

  126. Tiller, F. M., Chem. Eng. Progr. 51 (1955), 282.

    Google Scholar 

  127. Uchida, S., Dept. Inst. Sci. Technol. Univ. Tokyo (in Japanese), 3 (1949), 97

    Google Scholar 

  128. Uchida, S., abstract, Ind. Eng. Chem. 46 (1954), 1194.

    Article  Google Scholar 

  129. Wilson, B. W., Austr. J. Appl. Sci. 4 (1953), 300.

    Google Scholar 

  130. Wilson, L. H., W. L. Sabbitt, and M. Jakob, J. Appl. Phys. 22 (1951), 8.

    Article  Google Scholar 

  131. Weissberg, H. L., and S. Prager, Phys. Fluids 5 (1962), 1390.

    Article  ADS  MATH  Google Scholar 

  132. Zenz, F. A., Ind. Eng. Chem. 41 (1949), 2801.

    Article  Google Scholar 

  133. Zenz, F. A., and D. Othmer, Fluidization and Fluid-Particle Systems. New York: Reinhold, 1960.

    Google Scholar 

  134. Zierep, J., Z. Flugwiss. 3 (1955), 22.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering and Applied Chemistry, Columbia University, New York, New York, USA

    John Happel

  2. Department of Chemical Engineering, Cambridge, Massachusetts, USA

    Howard Brenner

Authors
  1. John Happel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Howard Brenner
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Martinus Nijhoff Publishers, The Hague

About this chapter

Cite this chapter

Happel, J., Brenner, H. (1983). Flow Relative to Assemblages of Particles. In: Low Reynolds number hydrodynamics. Mechanics of fluids and transport processes, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8352-6_8

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-8352-6_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-247-2877-0

  • Online ISBN: 978-94-009-8352-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation