Summary
A model has been developed for the flow of a non-Newtonian fluid past a porous sphere. The drag force exerted on a porous sphere moving in a power-law fluid is obtained by an approximate solution of equations of motion in the creeping flow regime. It is predicted that the effect of the pseudoplastic anomaly on the drag force is more pronounced at large porosity parameters.
Zusammenfassung
Es wird ein Modell für die Strömung einer nichtnewtonschen Flüssigkeit längs einer porösen Kugel entwickelt. Die auf die in einer Ostwald-DeWaele-Flüssigkeit bewegte Kugel ausgeübte Reibungskraft wird durch eine Näherungslösung der Bewegungsgleichungen für schleichende Strömung gewonnen. Man findet, daß der Einfluß der Abweichung vom newtonschen Verhalten um so ausgeprägter wird, je größer die Porosität ist.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- A, B, C, D a, b, c, d :
-
coefficients in eqs. [10] and [18]
- F D :
-
drag force
- K :
-
consistency index in power-law model
- k 1 ,k 2 :
-
coefficients defined by eq. [18]
- m :
-
porosity parameter
- n :
-
flow index in power-law model
- P :
-
pressure
- P * :
-
dimensionless pressure defined by eq. [4]
- ΔP :
-
pressure difference
- R :
-
radius of porous sphere
- r :
-
radial distance from the center of the sphere
- U :
-
velocity of uniform stream
- u i :
-
velocity component
- u * i :
-
dimensionless velocity component defined by eq. [4]
- Y :
-
drag force correction factor defined by eq. [27]
- Δ ij :
-
rate of deformation tensor
- Δ * ij :
-
dimensionless rate of deformation tensor defined by eq. [4]
- θ, φ :
-
spherical coordinates
- ξ :
-
dimensionless radial distance defined by eq. [4]
- Π :
-
second invariant of rate of deformation tensor
- Π * :
-
dimensionless second invariant of rate of deformation tensor defined by eq. [4]
- τ ij :
-
stress tensor
- τ * ij :
-
dimensionless stress tensor defined by eq. [4]
- ψ :
-
stream function
- ψ * :
-
dimensionless stream function defined by eq. [4]
- i :
-
inside the surface of the sphere
- o :
-
outside the surface of the sphere
References
Acharya, A., R. A. Mashelkar, J. Ulbrecht, Rheol. Acta5, 454 (1976).
Bhavaraju, S. M., R. A. Mashelkar, H. W. Blanch, Amer. Inst. Chem. Engs. J.24, 1070 (1978).
Coleman, B. D., W. Noll, Arch. Rat. Mech. Anal.6, 355 (1960).
Hirose, T., M. Moo-Young, Can. J. Chem. Eng.67, 265 (1969).
Kawase, Y., J. J. Ulbrecht, Chem. Eng. Commun.8, 213 (1981).
Kawase, Y., J. J. Ulbrecht, Chem. Eng. Sci. (in print) (1981).
Leonov, A. I., Prikl. Mat. Mekh.26, 564 (1962).
Proudman, I., J. R. A. Pearson, J. Fluid Mech.2, 237 (1957).
Rajvanshi, S. C., Arch. Mech. Stos.21, 585 (1969).
Verma, P. D., N. C. Sacheti, J. Appl. Phys.46, 2065 (1975).
Author information
Authors and Affiliations
Additional information
With 1 figure and 1 table
Rights and permissions
About this article
Cite this article
Kawase, Y., Ulbrecht, J.J. A power-law fluid flow past a porous sphere. Rheol Acta 20, 128–132 (1981). https://doi.org/10.1007/BF01513055
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01513055