Sedimentation

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21 Φεβ 2014 (πριν από 3 χρόνια και 5 μήνες)

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Sedimentation
Ruud van Ommen
Department of Chemical Engineering
Delft University of Technology
JMBC+OSPT course Particle Technology 2010
Based on M. Rhodes, Introduction to
Particle Technology, 2
nd
edition, 2008
Particle Settling Velocity
Put particle in a still fluid…what happens?
Speed at which particle settles depends on:
particle properties: D, ρ
s
, shape
fluid properties: ρ
f
, μ, Re
drag force
net
gravitational
force
If needed, gravity force can be replaced by centrifugal force
Stokes’ law for terminal settling velocity
Gravity sedimentation (steady state):
net gravitational force = drag force
π D
3
g(ρ
s
- ρ
l
) / 6 = 3 π D η U
Stokes drag force:
1/3 due to pressure, 2/3 due to shear stress
To obtain diameter fromheight and settling time:
D
2
= 18 η H / (ρ
s
- ρ
l
) g t
Sedimentation parameters
D diameter
g gravitational constant
ρ
s
effective solid density
ρ
l
liquid density
η liquid viscosity
U = H/t settling velocity (height/time)
Stokes’ Law, assumptions & consequences 1
• Spherical particles, smooth and rigid
 Equivalent Stokes’ diameter
• Fluid has infinite extent
 Low particle concentration (< 0.2-1 % v/v)
 No wall effects (wall-wall > 5 mm)
• Terminal velocity reached
 Acceleration time neglected (< 1 s)
• Laminar flow
 Low settling velocity
 Reynolds number : Re = ρ
l
.v.D
St
/η < 0.2
(quartz in water, D
St
< 60 µm)
Stokes’ Law, assumptions & consequences 2
• Insignificant Brownian motion

D
St
> ~ 1 µm
• No temperature influence

liquid viscosity and convection
 fluctuations < 0.05 deg/min.
 overall < 1 deg. C
• Various

vertical positioning
 no vibrations
Drag coefficient as a functions of Reynolds
F
drag
= C
D
π/4 D
2
1/2 ρ
l
U
2
Settling of a suspension of particles
gravitational force = drag force
π D
3
g (ρ
s
- ρ
l
)/6 = ¼π D
2
½ρ
ave
U
rel
2
C
D
(3.4)
π D
3
g (ρ
s
- ρ
l
)/6 = ¼π D
2
½ρ
ave
U
rel
2
C
D
(3.4)
Settling of a suspension of particles
Batch settling
(3.18) & (3.19) 
hindered settling velocity of particles relative to vessel wall
Effective viscosity function (theoretical):
for particle vol. fraction C < 0.1
Richardson & Zaki (1954) by experiment: U
p
= U
t
ε
n
n = 4.65 for Re
p
< 0.3; n = 2.4 for Re
p
>500
n for entire range of Re (Khan and Richardson, 1989):
Ar = x
3
ρ
l

p
–ρ
l
)g/μ
3
x = particle diameter; D = vessel diameter
Batch settling
Sharp interfaces in sedimentation
n=4.65