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Solid-Liquid
Separation in
Water Treatment
Settling and Flotation
J(Hans) van Leeuwen, DEE
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Introduction
The need to clarify water -
Aesthetic and health reasons
Technologies available
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Topics of Discussion
Separation by settling
Separation by flotation
Direct filtration
Softening
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Typical surface water
treatment process
Ferric/alum sludge
Ferric/
Alum
Screen
T
R
E
A
t
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Typical water treatment
process with lime softening
Lime sludge
Ca(OH)
2
Lime
OR
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Typical layout of a water treatment plant
Solid- liquid separation in water treatment
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Analysis of
Forces Acting
On a Settling
Particle
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Archimedess Principle
Examination of the nature of buoyancy shows that the
buoyant force on a volume of water and a submerged object
of the same volume is the same. Since it exactly supports
the volume of water, it follows that the buoyant force on any
submerged object is equal to the weight of the water
displaced. This is the essence of Archimedes principle.
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Terminal Velocity of a Particle
An expression for V
t
from the submerged weight of
the particle, W, and the fluid drag force, D.
The drag force on a particle is given by
D = C
D
l
A
p
V
t
2
/2
The submerged weight of the particle can be expressed as
W = ( -
l
)g
s
Since D = W, the above, after substituting A
p
and
p
for particle diameter d
_______________
V
t
= / 4 ( -
l
) gd
3
l
C
D
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Stokess Law
R
e
< 1, C
D
= 24 /Re
Substitute in the equation for v
t
V
t
=
g ( -
l
) d
2
18
V
t
=
2 ( -
l
)gr
2
9
The upflow velocity in a settling tank needs to be < V
t
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(20-40 m
3
m
-2
d
-1
)
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Activated Sludge Mass Balance over Settler
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Weir Details
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LAMELLA SETTLING TANKS:
Shortening the settling distance
Pipe
bundles
also used
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(20 40 m
3
m
-2
d
-1
or 0.8 1.7 m/h)
(2.5 mm/s) limits weir loading rate to
100 200 m
3
m
-1
d
-1
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Sludge Thickening Design
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FLOTATION
Separation of low density flocs
If flocs have a density very close
to that of water, it may be
necessary to decrease their
density by adding gas bubbles
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FLOTATION
Separation of low density flocs
Methods of forming gas bubbles
Diffusion
Vacuum
Electrolysis
Dissolved air
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Surface Tension and Bubbles
The surface tension of water provides the wall tension
for the formation of bubbles. To minimize the wall tension
the bubble pulls into a spherical shape (LaPlace's law).
Pressure difference between the inside and outside of
a bubble depends upon the surface tension and the radius
of the bubble. Visualize the bubble as two hemispheres
Note the internal pressure which tends to push the
hemispheres apart is counteracted by the surface tension
acting around the circumference of the circle.
For a bubble with two surfaces providing tension, the
pressure relationship is:
P
i
P
o
= 4T/r
P
i
P
o
P
i
T
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La Place's Law
The larger the vessel radius, the larger the wall tension
required to withstand a given internal fluid pressure.
For a given vessel radius and internal pressure, a spherical
vessel will have half the wall tension of a cylindrical vessel.
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Wall Tension
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Why does wall tension increase with radius?
If the upward part of the fluid pressure remains the same, then the
downward component of the wall tension must remain the same.
If the curvature is less, then the total tension must be greater in
order to get that same downward component of tension.
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Bubble Pressure
Net upward force on the top hemisphere of the bubble:
F
upward
= (P
i
P
o
)r
2
The surface tension force downward around circle is
twice the surface tension times the circumference,
since two surfaces contribute to the force:
F
downward
= 2T(2r)
P
i
P
o
P
i
T
P
i
P
o
= 4T/r for a spherical bubble
P
i
P
o
= 2T/r for half a bubble
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Attachment to floc
Ratio of area/volume increases
with decreasing size
Forces acting on a gas bubble:
Internal pressure x area
= surface tension x circumference
Easier for bubble to form against
solid
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Stokess law for flotation
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Essential Elements in a Flotation Unit Process
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Dissolved Air Flotation
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Saturation tank for flotation
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Overview of solid-liquid separation alternatives in water
Direct
Filtration
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What you need to be able to do
Be able to size settling tanks on the basis
of particle settling rates and identify
important zones in the settling tank
Be able to do a mass balance over a
flotation unit to account for air usage
Be able to size a flotation unit based on
particle sizes and densities
