Download Stoke`s Law of Settling

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SOLID-FLUID SEPARATION
Program Studi Teknik Lingkungan ITB
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Mixtures Types of Mixtures
Heterogeneous
Homogeneous
Coffee
Sea Water
Heterogeneous or Homogenous?
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Heterogeneous or Homogeneous?
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Heterogeneous or Homogeneous?
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Solid
• Floating & Settleable solid/materials
• Total Solid:
• Total Dissolved Solid (TDS):
• Fixed Dissolved Solid (FDS)
• Volatile Dissolved Solid (VDS)
• Total Suspended Solid (TSS):
• Fixed Suspended Solid (FSS)
• Volatile Suspended Solid (VSS)
• Colloidal solid: categorized as Suspended Solid but in the
laboratory classified as Dissolved Solid (size: 0.001 to 1.0 μm)
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Colloidal Solids
Medium
Material
Name
Example
Liquid
Solid
Sol
Clay turbidity
Liquid
Liquid
Emulsi
Oil
Liquid
Gas
Foam
Foam/Cream
Gas
Solid
Aerosol
Dust, smoke
Gas
Liquid
Aerosol
Mist, fog
Solid
Liquid
Gel
Jelly
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Solid-Fluids Separation
• Physical Separation: Suspended Solids
• Sedimentation
• Filtration
• Floatation
Mostly applied in Pollution Prevention
• Mechanical Separation
• Centrifugation
• Distillation
• Crystallization
• Chromatography
• Chemical Separation: Colloidal & Dissolved Solids
• Coagulation
• Precipitation
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Solid-Fluids Separation
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Sedimentation (Applied to Settling Chamber)
• Sedimentation, or clarification, is the process of letting
suspended material settle by gravity.
• Suspended material may be particles, such as clay or
silts, originally present in the source water.
• More commonly, suspended material or floc is created
from material in the water and the
chemical used in coagulation or in other treatment
processes, such as lime softening.
• Sedimentation is accomplished by decreasing the velocity
of the water being treated to a point below which the
particles will no longer remain in suspension.
• When the velocity no longer supports the transport of the
particles, gravity will remove them from the flow.
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Settling Velocity
Settling velocity can be calculated using a wide variety of formulae
that have been developed theoretically and/or experimentally.
Stoke’s Law of Settling is a very simple formula to calculate the settling
velocity of a sphere of known density, passing through a still fluid.
Stoke’s Law is based on a simple balance of forces that act on a particle
as it falls through a fluid.
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FG, the force of gravity acting to make the
particle settle downward through the fluid.
FB, the buoyant force which opposes the
gravity force, acting upwards.
FD, the “drag force” or “viscous force”,
the fluid’s resistance to the particles
passage through the fluid; also acting
upwards.
Force (F) = mass (m) X acceleration (A)
DISCRETE (TYPE I) SETTLING
DISCRETE (TYPE I) SETTLING
DISCRETE (TYPE I) SETTLING
DISCRETE (TYPE I) SETTLING
DISCRETE (TYPE I) SETTLING
DISCRETE (TYPE I) SETTLING
DISCRETE (TYPE I) SETTLING
DISCRETE (TYPE I) SETTLING
DISCRETE (TYPE I) SETTLING
DISCRETE (TYPE I) SETTLING
DISCRETE (TYPE I) SETTLING
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FG depends on the volume and density (rs) of the particle and is given by:
FG 

6
d  rs  g 
3

6
r s gd 3
FB is equal to the weight of fluid that is displaced by the particle:
FB 

6
d rg 
3

6
rgd 3
Where r is the density of the fluid.
FD is known experimentally to vary with the size of the particle, the
viscosity of the fluid and the speed at which the particle is traveling
through the fluid.
Viscosity is a measure of the fluid’s “resistance” to deformation as the
particle passes through it.
FD  3dU
Where  (the lower case Greek letter mu) is the fluid’s dynamic
viscosity and U is the velocity of the particle; 3d is proportional to the
area of the particle’s surface over which viscous resistance acts.
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Drag Coefficient on a Sphere
4 gd ( r p - r w )
Vt =
3 CD
rw
18
Stokes Law
100
10
1
laminar
Reynolds Number
turbulent
10
00
00
0
10
00
00
00
10
00
00
10
00
0
10
24
Re
10
00
Cd 
1
0.1
0.
1
Drag Coefficient
1000
10
0
Vt 
d 2 g r p  r w 
Re 
turbulent
boundary
Vt d r

 Regraph 

 CDsphere 


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Floc Drag
Flocs created in the
water treatment
process can have
Re exceeding 1 and
thus their terminal
velocity must be
modeled using
100
10
CDsphere
CDtransition Rek 
Stokes  Rek 
1
0.1
0.1
1
10
100
110
3
Regraph  Rek
110
4
110
5
110
6
110
7
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Example:
A spherical quartz particle with a diameter of 0.1 mm falling through
still, distilled water at 20°C
d = 0.0001m
rs= 2650kg/m3
 = 1.005 ´ 10-3 Ns/m2
g = 9.806 m/s2
r = 998.2kg/m3
2
r

r
gd


S

18
Under these conditions (i.e., with the values listed above) Stoke’s Law
reduces to:
   8.954 105   d 2
For a 0.0001 m particle:  = 8.954 ´ 103 m/s or  9 mm/s
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Effect of Temperature
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Flotation
• Flotation is an operation that removes not only oil and
grease but also suspended solids from wastewater
• The wastewater flow or a portion of clarified effluent is
pressurized in the presence of sufficient air to approach
saturation
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Waste flow is pressurized to approach saturation
released to the atmospheric pressure
Minute air bubbles are released from the solution
SS, oil & grease, sludge flocs are floated
attachment with air bubbles
Enmeshed in the floc particles
Air-solids mixture rises to the surface
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AIR SOLUBILITY AND RELEASE
• The saturation of air in water is directly proportional to
pressure and inversely proportional to temperature.
• The quantity of air that will theoretically be released from
solution when the pressure is reduced to 1 atm:
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AIR SOLUBILITY AND RELEASE
• The actual quantity of air released will depend
• upon the turbulent mixing conditions at the point pressure reduction
• on the degree of saturation obtained in the pressurizing system
• The performance of a flotation system depends upon
having sufficient air bubbles present to float substantially
all of the suspended solids
• An insufficient quantity of air will result in only partial
flotation of the solids, and excessive air will yield no
improvement
FLOTATION UNIT
• The performance of a flotation unit terms of
effluent quality and solids concentration in the
float can be related to an air/solids ratio:
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Air to Solid Ratio
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Filtration
• Conceptually, filtration is like sedimentation: solid-fluids
separation
• Filtration is configured mostly for solids that are small
enough to be removed in sedimentation or flotation
processes
• Filtration:
• Depth Filtration:
• Rapid sand filtration: 2 – 5 m3/m2/hr
• Slow sand filtration: 0.15 – 0.35 m3/m2/hr
• Surface Filtration:
• Filter cloth
• Membrane
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Depth Filtration Mechanisms
• Straining:
• Mechanical: solids larger than pore space
• Chance contact: solids smaller than pore size are trapped within
the filter
• Sedimentation: solids settling on the filtering medium
• Impaction: heavy solids will not follow the flow streamlines
• Interception: solids move along the flow streamline are
removed when they come in contact with the surface of
filtering medium
• Adhesion: solids become attached to the surface of
filtering medium as they pass by
• Flocculation: Solids growth
• Biological growth, especially in slow sand filtration
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Depth Filtration (Rapid Sand Filtration)
• Solids need a pre-treatment to destabilize the electrical
charge
• The most important things is not the straining process, but
the the removal of solids adhere to grains in the filter
medium
• Head loss in filter increases with time as filter clogs and
gets lower hydraulic conductivity
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Rapid Sand Filtration
• Medium
• Single: sand
• Dual: anthracite and sand
• Multi/Triple: anthracite, sand, and garnet
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• Porosity:
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Surface Filtration (Membrane Filtration)
• Solid-fluid separation by means of surface filtration:
• Disc Filter
• Membrane Process
• Membrane Filtration removes:
• Colloidal solid
• Dissolved Solid
• Membrane Selectivity be base on its porosity:
• Micro Filtration (MF)
: 0.02 – 10 um
• Ultra Filtration (UF)
: 0.01 – 0.02 um
• Nano Filtration (NF)
: 0.0001 – 0.001 um
• Reverse Osmosis (RO)
:  0.0001 um
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Chemical Solid-Fluid Separation
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Colloidal Particles
• Colloid: small particles and disperse homogenously. Colloid particles
size around 10-6 mm – 10-3 mm (bigger than atom).
• In terms of their affinity In water, colloid particles are divided into:
• Hydrophylic: organic colloid particles because of polar side (OH, COOH,
NH2) on colloids surface. Characteristics: water soluble and having boundwater (water envelope).
• Hydrophobic: Inorganic colloid particles. Having no or very small affinity to
water: no bound water occurred
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Zeta Potensial
• Colloid stability is very much affected by “ionic charge” working on the
colloids surface
• Hydrophylic colloid: electric charge due to dissociation of polar group.
Example:
COOCOOH
COO
OH-
R
OHR
+
NH3
H+
R
H+
NH3+
Isoelectric point
NH3OH
pH
• Hydrophobic colloid: Adsorption of ionic molecule from the solution.
Ionic Charge of hydrophobic colloid is switchable by altering the
solution pH. It is suggested that the ionic charge of hydrophobic colloid
is formed from either hydroxyl or hydrogen ions
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Zeta Potential
• Colloid in medium attract opposite charge ions (counter ions) to form
double layer:
• Fixed or Stern layer
• Diffuse or Gouy layer
• Shear of plane: interface between solution as a part of particles and
•
•
•
•
solution
Shear of plane of hydrophobic colloid overlap and enclose fixed layer
Shear of plane of hydrophylic colloid overlap and working on the
surface bound water
Zeta potential: electrostatic force working on the surface of “shear of
plane”
Zeta potential: resultant between attraction force (van der Waals)
repulsion force
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Colloid Stability
• Colloid stability indicate by the magnitude of zeta potential. The
stronger the zeta potential, the more stable the colloid.
• Basically, zeta potential is the magnitude of ionic charge working on the
colloid
• Device: zeta meter
• Zeta Potential Equation:
 = 4qd/D
Where:
q = charge per unit area
d = thickness of “shear surface” interface
D = Dielectric constant
• Hydrophylic colloid stability is also affected by bound water that
behaves as elastic barrier
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Colloid Destabilization
• Zeta Potential Reduction:
• pH adjustment
• Counter ions addition
• Bivalent ions: 50x stronger than monovalent
• Trivalent ions: 1000x stronger than monovalent
• Hydrophylic colloids destabilization: not only zeta potential reduction,
but also to destroy bound-water: “salting out” (the addition of high
concentration salt: SO4, Cl-, NO3-, I-)
• Coagulation : colloid particles destabilization
• Solid-Fluid Separation by Chemical Process:
• Zeta potential reduction (electrokinetic): addition of coagulant agent
• Particles interaction and bounding (orthokinetic): flash mixing
• Floc formation: slow mixing (floculation)
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Coagulation Reaction - 1
• Al2(SO4)3xH2O:
• Sufficient alkalinity:
Al2(SO4)3xH2O + 6HCO3-
2Al(OH)3 + 3SO4- + 6CO2 + xH2O
reduction of bicarbonate and formation of CO2, causing the drop of pH
• No bicarbonate available, alkalinity should be added:
Al2(SO4)3xH2O + 6OH-
2Al(OH)3 + 3SO4- + xH2O
• Al(OH)3 is amphoteric compound and insoluble at pH between 5 – 7. At pH
below 5, this compound dissociates to form aluminium ion and at pH above 7
to form AlO2 ion
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Coagulation Reaction - 2
• Ferro sulphate (FeSO47H2O) :
• FeSO47H2O + 2OH-
Fe(OH)2 + SO4-2 + 7H2O
Fe(OH)2 is formed at high pH (above 9,5). To increase pH normally Ca(OH)2
is added
• If O2 available:
4Fe(OH)2 + O2 + 2H2O
Fe(OH)3
At neutral pH, Fe(OH)3 is more insoluble than Fe(OH)2.
• Fe(OH)3 is not an amphoteric compound
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Coagulation Reaction Pathway
• Dissociation of coagulant agent to form metallic ion
• Hydrolysis of metallic ion to form hidroxo-metallic ion complexes that
tend to polimerisize as Meq(OH)p+z:
• Al6(OH)15+3
• Al7(OH)17+4
• Al13(OH)34+5
• Fe2(OH)2+4
• Fe2(OH)4+5
• Those polyvalent ions interact and agregate with colloid as a result of
zeta pontetial reduction and the increase of van der Waals force
• Remaining coagulant continue to dissociate and polimerize to form
insoluble metallic hydroxide (Fe(OH)3 or Al(OH)3): sweep coagulation
(enmeshment process)
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Other Coagulant Agent
• Polymeric Coagulant as Coagulant aid:
• Cationic : behave as coagulant
• Anionic : to form floc
• Dosage: 1/100 of Inorganic Coagulant (Salt)
• Coagulant types and dose determination in laboratory :
• jar-test
• zeta potential measurement