Rheologica Acta

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

A correlation for yield stress fluid flow through packed beds

Original Contribution

Abstract

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.

Keywords

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

dp

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

f

friction factor

Hep

Hedstrom number for packed bed

L

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

P0

Pressure at inlet to bed (kPa)

PL

Pressure at exit of bed (kPa)

R

Tube radius (m)

Rep

Reynolds number for packed bed

v

Average velocity in a tube (m/s)

V

Empty vessel or superficial velocity (m/s)

μ

Newtonian viscosity (kg/m/s)

μo

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

τo

Yield stress (N/m2)

τR

Shear stress at a tube wall (N/m2)

ɛ

Porosity

ρ

Density (kg/m3)

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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Microscale Physiochemical Engineering CenterThe University of AkronAkronUSA

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