Rheologica Acta

, Volume 44, Issue 5, pp 495–501 | Cite as

A correlation for yield stress fluid flow through packed beds

Original Contribution


Relatively few correlations are available for non-Newtonian fluid flows through packed beds, even though such fluids are frequently used in industry. In this paper, a correlation is presented for yield stress fluid flow through packed beds. The correlation is developed by introducing the yield stress model in place of the Newtonian model used in deriving Ergun’s equation. The resulting model has three parameters that are functions of the geometry and roughness of the particle surfaces. Two of the parameters can be deduced in the limit as the yield stress becomes negligible and the model reduces to Ergun’s equation for Newtonian fluids. The third model parameter is determined from experimental data. The correlation relates a defined friction factor to the dimensionless Reynolds and Hedstrom numbers and can be used to predict pressure drop for flow of a yield stress fluid through a packed bed of spherical particles. Conditions for flow or no-flow are also determined in the correlation. Comparison of model calculations, between a Newtonian and a yield stress fluid for flow penetration into a packed bed of spheres, shows the yield stress fluid initially performs similar to the Newtonian fluid, at large Reynolds numbers. At lower Reynolds numbers the yield stress effect becomes important and the flow rate significantly decreases when compared to the Newtonian fluid.


Bingham plastic Yield stress Packed bed Ergun’s equation 

List of symbols

a, b, c

Constants in Eq. 14

C1, C2, C3

Constants in Eq. 6


Spherical particle diameter (m), diameter of equivalent sphere having the same surface-to-volume ratio as the particle


friction factor


Hedstrom number for packed bed


Bed length (m), depth of penetration of fluid into bed (m)


Pressure at inlet to bed (kPa)


Pressure at exit of bed (kPa)


Tube radius (m)


Reynolds number for packed bed


Average velocity in a tube (m/s)


Empty vessel or superficial velocity (m/s)


Newtonian viscosity (kg/m/s)


Yield stress modulus (viscosity) (kg/m/s)


Yield stress (N/m2)


Shear stress at a tube wall (N/m2)




Density (kg/m3)



This work was supported by the Department of Chemical Engineering at The University of Akron and The University of Akron Faculty Research Grant FRG 1566. The Carbopol 941 was provided by the B.F. Goodrich Company.


  1. Al-Fariss TF (1989) Comput Chem Eng 13(4–5):475–482Google Scholar
  2. Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena, 2nd edn. Wiley, New YorkGoogle Scholar
  3. Christopher RH, Middleman S (1965) Ind Eng Chem Fundam 4(4):422–426Google Scholar
  4. Dachavijit P (2003) Study of electrorheology flow through a packed bed, PhD Dissertation, The University of Akron, AkronGoogle Scholar
  5. Dharmadhikar RV, Kale DD (1985) Chem Eng Sci 40(3):527–529Google Scholar
  6. Ergun S (1952) Chem Eng Prog 48:89–94Google Scholar
  7. Foust AS, Leonard AW, Clump CX, Maus L, Andersen LB (1960) Principles of unit operations. Wiley, New YorkGoogle Scholar
  8. Gaitonde NY, Middleman S (1967) IEC Fundam 6(1):145–147Google Scholar
  9. Hayes RE, Afacan A, Boulanger B, Shenoy AV (1996) Transport Porous Media 23(2):175–196Google Scholar
  10. Kececioglu I, Jiang Y (1994) J Fluids Eng 116 (1):164–170Google Scholar
  11. Kemblowski Z, Michniewicz M (1979) Rheol Acta 18(6):730–739Google Scholar
  12. Macdonald IF, El-Sayed MS, Mow K, Dullien FAL (1979) Ind Chem Fundam 18(3):199–207Google Scholar
  13. Park HC, Hawley MC, Blanks RF (1975) Polym Eng Sci 15(11):761–773Google Scholar
  14. Shirato M, Aragaki T, Iritani E, Funahashi T (1980) J Chem Eng Japan 13(6):473–478Google Scholar
  15. Wuensch O (1990) Rheol Acta 29(2):163–169Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Microscale Physiochemical Engineering CenterThe University of AkronAkronUSA

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