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, 2nd edition, 2008
Particle Settling Velocity
Put particle in a still fluid… what happens?
drag force
net
gravitational
force
Speed at which particle settles depends on:
particle properties: D, ρs, shape
fluid properties: ρf, μ, Re
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 D3 g(ρs- ρl) / 6 = 3 π D η U
Stokes drag force:
1/3 due to pressure, 2/3 due to shear stress
To obtain diameter from height and settling time:
D2 = 18 η H / (ρs- ρl) g t
Sedimentation parameters
D
g
ρs
ρl
η
U = H/t
diameter
gravitational constant
effective solid density
liquid density
liquid viscosity
settling velocity (height/time)
Stokes’ Law, assumptions & consequences 1
• Spherical particles, smooth and rigid
¾ Equivalent Stokes’ diameter
• Fluid has infinite extent
¾ Low particle concentration (< 0.2-1 % v/v)
¾ No wall effects (wall-wall > 5 mm)
• Terminal velocity reached
¾ Acceleration time neglected (< 1 s)
• Laminar flow
¾ Low settling velocity
¾ Reynolds number : Re = ρl.v.DSt/η < 0.2
(quartz in water, DSt< 60 µm)
Stokes’ Law, assumptions & consequences 2
• Insignificant Brownian motion
¾ DSt > ~ 1 µm
• No temperature influence
¾ liquid viscosity and convection
¾ fluctuations < 0.05 deg/min.
¾ overall < 1 deg. C
• Various
¾ vertical positioning
¾ no vibrations
Drag coefficient as a functions of Reynolds
Fdrag = CD π/4 D2 1/2 ρl U2
Settling of a suspension of particles
gravitational force = drag force
π D3 g (ρs- ρl)/6 = ¼ π D2 ½ ρave Urel2 CD
(3.4)
Settling of a suspension of particles
π D3 g (ρs- ρl)/6 = ¼ π D2 ½ ρave Urel2 CD
Batch settling
(3.18) & (3.19) Æ
hindered settling velocity of particles relative to vessel wall
(3.4)
Batch settling
Effective viscosity function (theoretical):
for particle vol. fraction C < 0.1
Richardson & Zaki (1954) by experiment: Up = Ut εn
n = 4.65 for Rep < 0.3; n = 2.4 for Rep >500
n for entire range of Re (Khan and Richardson, 1989):
Ar = x3 ρl (ρp –ρl)g/μ3
x = particle diameter; D = vessel diameter
Sharp interfaces in sedimentation
n=4.65