Abstract
The influence of the contained wall on the drag of a sphere moving through a non-Newtonian fluid is analysed in this work separately for the low Reynolds number and the high Reynolds number regions. In the former, we make use of the two-concentric-sphere model. It is predicted that the wall effect will decrease with the increase of the shear-thinning anomaly and this is in a reasonable agreement with the available experimental data and correlations. The wall effect in the high Reynolds number region is analysed in this work using the cell model (used to study the motion of an assemblage of solid spheres) and the predictions are in satisfactory agreement with the available empirical correlation for non-Newtonian fluids.
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Abbreviations
- A 1,A 2,A 3,A 4 :
-
constants used in eq. (6)
- a :
-
radius of inner sphere
- B 1,B 2,B 3,B 4 :
-
constants used in eq. (7)
- b :
-
radius of outer sphere
- F D :
-
drag force
- K :
-
consistency index in power-law model
- K F :
-
drag factor
- K U :
-
velocity ratio
- n :
-
flow index in power-law model
- P :
-
pressure
- R :
-
radius of cylindrical tube
- Re * :
-
(2a)n U 2-n ρ/K, Reynolds number
- Re m :
-
(2a)n U 2-n ρ/3 n-1 K, Reynolds number
- r :
-
radial distance from the center of the sphere
- U :
-
terminal velocity of sphere
- u r :
-
radial velocity
- u θ :
-
tangential velocity
- W :
-
function defined by eq. (6)
- Δ ij :
-
rate of deformation tensor
- θ :
-
spherical coordinate
- λ :
-
b/a
- π :
-
second invariant of the rate of deformation tensor
- ρ :
-
density
- τ ij :
-
stress tensor
- ψ :
-
stream function
- ∞:
-
unbounded fluid
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Kawase, Y., Ulbrecht, J.J. The influence of walls on the motion of a sphere in non-Newtonian liquids. Rheol Acta 22, 27–33 (1983). https://doi.org/10.1007/BF01679826
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DOI: https://doi.org/10.1007/BF01679826