Startseite Wall-retardation effects on particles settling through non-Newtonian fluids in parallel plates
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Wall-retardation effects on particles settling through non-Newtonian fluids in parallel plates

  • Guo-Dong Zhang EMAIL logo , Ming-Zhong Li EMAIL logo , Jian-Quan Xue , Lei Wang und Jin-Lin Tian
Veröffentlicht/Copyright: 25. Juni 2016
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Chemical Papers
Aus der Zeitschrift Chemical Papers Band 70 Heft 10

Abstract

Walls can exert a retardation effect on particles settling in bounded fluid media. In this work, the parallel plate retardation effect was studied for particles falling in non-Newtonian fluids along the centreline of parallel plate ducts. The eccentric effect was also investigated for those particles which approached the wall. For spheres settling in sodium carboxymethylcellulose (CMC) solutions, the variation in wall factors against the size ratio of the sphere’s diameter to the parallel plate wall spacing shows a non-linear trend; the particle settling velocity is independent at small size ratio, and then decreases quickly with increase in size ratio. A new correlation was presented covering a wider range of size ratios (0.02 < λ < 0.83) in the flow region of 0.0011 < Re < 9.75. When particles settle in polyacrylamide solutions, the fluid elasticity reduces the wall-retardation effect and it can be deduced that the drag reduction mechanism of some polyacrylamide solutions may weaken the wall retardation effect. As the spheres settling in the CMC solutions approach the wall, the neighbouring wall exerts no retardation effect at small size ratios (≤ 0.8). Then the settling velocity reduces sharply, while the effect is negligible for polyacrylamide solutions. In comparison with cylinders, the actuating range of the neighbouring wall is smaller for parallel plates.

Key words: wall factor; settling velocity; viscoelastic; Giesekus model; eccentric effect; parallel plate

Acknowledgements

This study received financial support from the Programme for Changjiang Scholars and Innovative Research Team in University (IRT1294).

Symbols

A, B

fitting parameters in Eq. (8)

b

distance from centreline of parallel plates

m

d

sphere diameter

m

f

wall factor

fi

parameter in Eq. (6)

f0

wall factor at low size ratio

f∞

wall factor at high size ratio

G′

elastic modulus

Pa

G″

viscous modulus

Pa

K

consistency index

Pa s"

m

mode numbers

N1

first normal stress difference

n

flow behaviour index

R

maximum eccentric distance,

R = (W − d)/2

m

Re

Reynolds number

V

particle settling velocity along the

centreline

m s−1

Vb

settling velocity of the particle at position

b

m s−1

Vœ

particle terminal settling velocity

m s−1

W

parallel plate width

m

Wi

Weissenberg number, Wi = N1/σ

Greek symbols

αi

the i-th anisotropy parameter

γ

shear rate

s−1

η

absolute fluid viscosity

Pa s

ηi

the i-th partial viscosity

Pa s

ηs

viscosity of the Newtonian solvent

Pa s

λ

size ratio of sphere diameter to wall spacing

λi

the i-th relaxation time

s

ρ1

fluid density

kg m−3

σ

shear stress

Pa

χi

parameter in Eq. (7)

ω

dynamic oscillatory frequency

rads−1

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Received: 2015-10-28
Revised: 2016-2-20
Accepted: 2016-3-1
Published Online: 2016-6-25
Published in Print: 2016-10-1

© 2016 Institute of Chemistry, Slovak Academy of Sciences

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https://doi.org/10.1515/chempap-2016-0082
Schlagwörter für diesen Artikel
wall factor; settling velocity; viscoelastic; Giesekus model; eccentric effect; parallel plate

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  3. Original Paper
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