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PIERO M. ARMENANTE
NJIT
Centrifugation When a solid-liquid suspension is rotated in a
cylindrical container (bowl) the suspension issubject to a centrifugal force in the radialdirection.
Centrifugation is a process by which solidparticles are sedimented and separated from aliquid using centrifugal force as a driving force.
Depending on the rotational speed and distance
from the axis of rotation, the centrifugal forcecan be many times greater than the force ofgravity, allowing even very small particles orparticles slightly denser than the fluid to settle.
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Sludge Thickening and Dewatering
In wastewater treatment, sludge is producedfrom a number of operations such as primarysettling, coagulation and flocculation, andbiological activated sludge processes.
The sludge produced in these processes mayvary greatly in concentration, but it is typicallyof the order of 1%.
Sludge concentration, typically conducted in
stages, is a common way to reduce the amountof sludge to be eventually disposed of.Thickening and dewatering are commonoperations to concentrate sludges.
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Sludge Thickening
Sludge thickening consists of increasing theconcentration of a sludge from its originalvalue (typically about 1%) to between 2 and10%.
Physical methods are typically used, includingsedimentation, flotation, centrifugation andcake filtration.
The thickened sludge still contains a
significant amount of water and can bepumped.
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Sludge Dewatering
Thickened sludge still contains too muchwater to be economically transported anddisposed of.
Sludge dewatering is an operation throughwhich a significant portion of the sludgemoisture is removed to produce a semidrycake typically containing solids inconcentration ranging between 10 and 40%.
Operations such as cake filtration,centrifugation, and bed drying are commonlyemployed for this purpose.
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Application of Centrifugation toWaste and Wastewater TreatmentCentrifugation has two main applications, namely:
Thickening of sludges and especially activated
sludges and chemical slurries. In these casesthe sludge produced during primary orsecondary treatments is concentrated in itssolids content (typically up to 2-10%).
Dewatering of sludges from primary andsecondary treatments. In these applicationswater is removed from sludges that have beenalready thickened, producing cakes having 15-20% (or even higher) solids concentration.
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Thickening and Dewatering of Sludgesvia Centrifugation
Most centrifugation processes for wastewatertreatment operate in a continuous mode.
The performance of centrifuges as sludgethickeners (in which both the clarified liquidand the thickened sludge are fluids) is moreeasily predicted and quantified than whencentrifuges are used as sludge dewatering
devices (in which a moist solid or cake mustbe effectively moved out of the centrifuge as itis formed).
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NJIT
Centrifuges
Centrifuges are sedimentation devices inwhich suspended solids are separated from aliquid under the action of centrifugal forcesgenerated by spinning the internal bowl of the
centrifuge.
The resulting settling velocities of the solidscan be significantly higher than thosegenerated by gravity forces.
Centrifuges can be thought of assedimentation vessels operating under highgravitational forces.
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Types of Centrifuges Used inWastewater and Sludge Applications
Solid bowl centrifuges (decanters)
Basket centrifuges
- Perforated basket centrifuges
- Imperforated basket centrifuges
Disk bowl centrifuges
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Solid Bowl Decanter
Motor
Liquid DischargeSolid Discharge
SolidsLiquidHelicalScroll
RotatingBowl
Feed
Cover
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NJIT
Solid Bowl Centrifuge (or Decanter) A solid bowl centrifuge (or decanter) consists
of an elongated cylindrical rotating bowlhaving a tapered conical end
The bowl length-to-diameter ratio is typically in
the range 2.5:1 to 4:1
The suspension is continuously introduced atone end of the bowl and travels parallel to thebowl axis. The clarified liquid is collected at
the end of the cylindrical section of the bowl
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NJIT
Solid Bowl Centrifuge (or Decanter)(continued)
The solids are collected at the end of thetapered section of the centrifuge where thecentrifuge forms a dewatering beach.
The solids move typically countercurrent to theliquid. Co-current centrifuges are also used.
A helical scroll rotating at a slightly differentspeed than the bowl is used to move the solidstoward the tapered end where they arecontinuously removed through ports.
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NJIT
Perforated Basket Centrifuge
Solids Liquid
Feed
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Perforated Basket Centrifuge This type of centrifuge is provided with a
rotating perforated basket, which allows acake of solids to build inside the basket whileallowing the liquid to pass through the
cylindrical wall of the basket (centrifugalfiltration)
The clarified liquid is continuously removed asit emerges from the basket
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Perforated Basket Centrifuge(continued)
The solid is intermittently removed with a knife(not rotating with the basket) placed inside thebasket, and collected in a vertical chute
Drier cakes are obtained with this type ofcentrifuge than with other types. Thereforethis type of centrifuge is used when therecovery of solids is desirable
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Imperforated Basket Centrifuge
Liquid
Cake
Feed
Knife
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Imperforated Basket Centrifuge This centrifuge consists of an imperforated
(solid) basket spinning vertically
The feed is continuously introduced into thecentrifuge while the liquid (centrate) is
continuously removed from an overflow weirinside the centrifuge
Solids build up during centrifugation forming acake that must be periodically discharged
After the basket becomes filled with solids thecentrifuge slows down and "skimming" (theremoval of the top semi-liquid soft cake layer)takes place
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NJIT
Imperforated Basket Centrifuge(continued)
Skimming typically removes 5 to 15% of thebowl solid volume
The bulk of the cake is discharged using aplowing knife moving into the slowly rotatingcake
The solid is discharged centrally at the bottomof the centrifuge
Solid accumulation is typically up to 60 to 85%of the maximum available depth
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Disk Bowl Centrifuge
Liquid
SolidsSolids
Feed
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Disk Bowl Centrifuge In order to leave the centrifuge the liquid must
pass between conical plates where the solidscan separate after impacting on the plates
The clarified liquid is continuously fed and
removed from the center of the centrifuge
The solid cake (thickened sludge) iscontinuously or intermittently removed fromthe side of the centrifuge
Only degritted suspension can be fed to thistype of centrifuge in order to minimizeproblems associated with plugging
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Chemical Additions DuringCentrifugation Operations
In sludge thickening operations chemicalconditioners (especially polyelectrolytes) areoften added to the sludge before feeding it tothe centrifuge or directly in the centrifuge.
The additives promote the ability of thesuspended particles to flocculate and settleinside the centrifuge, thus increasing solid
removal. Chemical additions promote the removal of
fine solids.
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NJIT
Chemical Additions DuringCentrifugation Operations
Chemical additives can also be used topromote sludge dewatering. However, this is amuch more difficult process to describe andpredict. Hence, the effectiveness of chemicaladdition in dewatering processes must betested in pilot plant experiments.
Cakes with a higher water content are obtained
if chemical additions are made duringdewatering processes.
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Typical Levels of Polymer Additionsfor Thickening of Sludges
Amount of Polymer Addition(lb dry polymer/ton dry solids)
Type of Sludge Dissolved
Air Flotation
Solid Bowl
Centrifuge
Basket
Centrifuge
Gravity Belt
Filter
WasteActivated
4-10 0-8 2-6 6-14
AnaerobicallyDigested
8-16
AerobicallyDigested
8-16
After Metcalf and Eddy, Wastewater Engineering, 1991, p. 262
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NJIT
Centrifuge Operations inWastewater and Sludge Applications
Batch
- Perforated basket centrifuge
- Imperforated basket centrifuges
Continuous
- Solid bowl centrifuges (decanters)
- Disk bowl centrifuges
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Centrifuges vs. Vacuum FiltersCentrifuges and vacuum filters are often used forthe same sludge treatment purposes.
Advantages of centrifuges over vacuum filters:
Lower capital costs; Lower space requirements;
Capability of treating suspension with poorfiltration capability.
Advantages of vacuum filters over centrifuges:
Higher solid concentration in the cake;
Lower solid concentration in the effluent.
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Analysis of CentrifugePerformance
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Process Variables AffectingCentrifugation
Type of slurry and solid particles contained init:
- Liquid viscosity- Liquid density
- Solids concentration
- Particle size distribution
- Surface charge of particles
- Type and/or shape or particles
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Process Variables AffectingCentrifugation (continued)
Feed rate of slurry
Agitation speed
Size of centrifuge (distance from rotation axis) Height of cake
Allowable pressure drop across cake
Mode of operation (batch vs. continuous) Time at full speed
Depth of skimming
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Possible Cases to Be Examined Batch centrifugation (e.g., with imperforated
basket centrifuges)
Continuous centrifugation (e.g., with solidbowl centrifuges)*
Batch centrifugal filtration (e.g., withperforated basket centrifuges)*
(Semi-)Continuous centrifugal filtration (e.g.,with perforated basket centrifuges)
(*) Cases that will be examined here
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NJIT
Alternative Expression for theCentrifugal Force
The relationship between the rotational speed, N
expressed in rpm, and the angular velocity, , is:
=2
60N
If the rotational speed is expressed in rpm thenthe centrifugal force is:
F m a m r N e e= = 260
2
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Centrifugal AccelerationThe acceleration due to the centrifugal force isgiven by:
a re = 2
or
a r Ne =
2
60
2
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Relationship Between Centrifugal and
Gravity Accelerations: The g-FactorThe g factor is defined as the ratio of thecentrifugal force to the gravity force:
g ag
FF
rg
rg
Ne eg
= = = = factor 2 2
2
60
ga
g
F
Fr Ne e
g
= = =factor 0 001118 2. (SI units)
ga
g
F
Fr Ne e
g
= =factor = 0 000341 2. (English units)
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NJIT
Settling Velocity of Particles
Subject to Centrifugal ForceThe terminal velocity, vp, of a spherical particle of
diameter Dp and density s located in a rotatingfluid at a distance r from the rotation axis and
moving in laminar flow is:
( )v
r Dp
p s L=
2 2
18
where: = fluid viscosity
L = fluid density
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Analysis of Continuous Centrifugation
in a Solid Bowl Centrifuge
Liquid DischargeSolid Discharge
Feed
R r RL
Suspension
Solid Movement
Liquid Movement
b
w
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Nomenclature for Solid Bowl
Centrifugesb length of the cylindrical part of the centrifuge
r generic distance from the axis of rotation
RC radial distance from the axis of rotation tothe top layer of the cake
RL radial distance from the axis of rotation tothe liquid pool
RW radial distance from the axis of rotation tothe centrifuge wall
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Assumptions Made to Model Continuous
Centrifugation in a Solid Bowl Centrifuge The feed (suspension) enters at the end of the
cylindrical wall of the centrifuge bowl near thetapered end and travels across the centrifuge
If a particles reaches the bowl wall is consideredsettled
The settled solid particles and the cleared liquidmove countercurrent with respect to each other
The settled particles and the cleared liquid arecontinuously removed at opposite ends of thecentrifuge
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NJIT
Assumptions Made to Model Continuous
Centrifugation in a Solid Bowl Centrifuge The particles are assumed to settle
independently of each other (Type 1 settling)following Stokes law
Each liquid element remains in the centrifuge fora time equal to the residence time. Hence, theresidence time is the time available for theparticles to settle
All the particles that have not reached thecentrifuge wall within the residence time will exitwith the clarified liquid
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NJIT
Settling Velocity of a Particle Inside a
Continuous Solid Bowl CentrifugeA particle settling inside the bowl centrifuge willhave a settling (radial) velocity given by:
( ) ( )v r d rd t
r Dp
p s L= =
2 2
18
where RL
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Relationship Between Time and
Distance Traveled by a Particle Insidea Continuous Solid Bowl Centrifuge
The radial distance, dr, traveled by a particle
during an infinitesimal time interval, dt, is:
( )( )
dr v r dt r D
dtpp s L= =
2 2
18
This expression can be rearranged and integrated
to give:
( )18
2 2
1
2
1
2
r Dd r dt
p s Lr
r
t
t
=
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Relationship Between Time and
Distance Traveled by a Particle Insidea Continuous Solid Bowl Centrifuge
Upon integration it is:
( )18
2 2
2
1
2 1
Drr
t tp s L
= ln
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Residence Time of the Liquid Inside
the Continuous Solid Bowl CentrifugeThe residence time, to, of the liquid in the bowl isthe time an average element of fluid will spend inthe centrifuge at steady state conditions:
tV
Qo =
where: V = volume of centrifuge available toliquid
Q = volumetric flow rate of liquidthrough centrifuge
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Liquid Volume in a CentrifugeThe liquid volume in the centrifuge is determinedby the height of the weir over which the liquid isdischarged:
( )V b R R w L= 2 2
Hence:
( )t
b R R
Qo
w L= 2 2
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Critical Particle Diameter for Settling
in a Continuous Solid Bowl CentrifugeIn order for the particle to settle it will have totravel a distance (Rw- RL), i.e., the distancebetween the surface of the liquid (where the
suspension is added) and the bowl wall, and to doso in the time interval to.
Only particles having a diameter larger than acertain critical diameter will be able to cover this
distance during the time interval to.
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Critical Particle Diameter for Settling
in a Continuous Solid Bowl CentrifugeUpon substitution of:
t1 with 0 r1 with RL
t2with to r2with Rw
one gets:
( )
( )182 2
2 2
D
R
Rt
b R R
Qp s L
w
L
o
w L
= =
ln
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Critical Particle Diameter for Settling
in a Continuous Solid Bowl CentrifugeFrom the previous equation the critical particlediameter, Dpo, can be found to be:
( ) ( )D Q
b R RRR
po
w L s L
w
L
=
2 2 2
18 ln
Particles larger than Dpo will settle during to,particles smaller than Dpowill not.
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Generalized Design Equation for
Continuous Solid Bowl CentrifugesThe following equation can be derived from theprevious equations, and used as the main designequation for solid bowl centrifuges:
( ) ( )( )
QD b R R
R
p s L w L
L
=
2 2 2 2
18 ln Rw
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Simplified Design Equation for
Continuous Solid Bowl CentrifugesThe previous equation can be simplified if oneassumes that the distance traveled by the particlein order to settle (equal to the liquid radial height)
is small in comparison to the bowl radius, Rw, i.e.:R R R R w L L w
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Simplified Design Equation for
Continuous Solid Bowl CentrifugesAssuming that:
lnR
R
R R
Rw
L
w L
w
and R R Rw L w+ 2
the equation:
( ) ( )( )
QD b R R
R R
p s L w L
w L
=
2 2 2 2
18 ln
becomes:( )( )[ ]
( )Q
Db R R R
b R Dp s Lw w L
w p s L
+
2 2 2 2 2
18 9
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Centrifuge Scale-up: the Sigma ValueThe design equation:
( ) ( )( )
QD b R R
R R
p s L w L
w L
=
2 2 2 2
18 ln
can be rewritten as:
( ) ( )( )
QD g
g
b R R
R Rv
p s L w L
w L
p=
=218 2
2 2 2 2
ln
where the parameter (Sigma value), defined as:
( )( )
= 2 2 2
2gb R R
R R
w L
w L
ln
is independent of the particle type and size.
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Centrifuge Scale-up: the Sigma ValueFor two geometrically similar centrifuges ofdifferent sizes (1 and 2) separating the same solidparticles from the same fluid it will be:
Q v Q v p p1 1 2 2= = and
To scale up experimental results from alaboratory centrifuge one can use the followingscale-up rule:
Q
Q
v
v
p
p
1
2
1
2
1
2= =
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Simplified Expression for the
Sigma Value: Simplified Scale-upAssuming that:
lnR
R
R R
Rw
L
w L
w
and R R Rw L w+ 2
then the Sigma value can be rewritten as:
2 2b R
gw
i.e.:
Q
Q
b R
b Rw
w
1
2
1
2
1
2
1 1
2
2
2
2 2
2=
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Solid Movement Inside a Continuous
Solid Bowl Centrifuge In a continuous solid bowl centrifuge both
clarification of the suspension and removal ofsolids occur simultaneously.
If the settled solids are not transported out at asufficient rate the pool inside the bowl fills upwith solids and no separation occurs.
The settled solids are transported out of acontinuous solid bowl centrifuge by the actionof a helical screw (scroll) rotating at a slightlydifferent velocity than the bowl.
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Scale-up of Continuous Solid Bowl Centrifuges
Based on Solid Throughput: the Beta ValueIf two centrifuges (labeled 1 and 2) are comparedin terms of solids removal the followingrelationship between the mass flow rate of solidscan be obtained:
( )( )
W
W
R R R Z N
R R R Z N
s
s
w w L s s s
w w L s s s
2
1
2 2 2 2 2 2 2
1 1 1 1 1 1 1
2
2=
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Scale-up of Continuous Solid Bowl Centrifuges
Based on Solid Throughput: the Beta ValueAssuming that the fraction of solids is the same in
both centrifuges (i.e., s1 = s2) and that the solids
fraction is also equal (i.e., s1 = s2), then:
( )( )
WW
R R R Z N R R R Z N
s
s
w w L s
w w L s
c
c
2
1
2 2 2 2 2
1 1 1 1 1
2
1
=
=
This equation defines a second scale-up methodbased on the beta value, i.e., the ratio of solids
throughputs for two centrifuges of two differentsizes. This method is important to determine thesolids removal in full-scale centrifuges based onthe results of pilot tests.
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Effect of Bowl Diameter Size on Solids
Separation Larger bowl diameters (while maintaining the
same centrifugal force by slowing down themachine rotation) result in longer retention
time within the centrifuge.
This results in higher solids recovery and awetter cake (i.e., having a lower concentrationof solids).
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Effect of Pool Depth on Solids
Separation The pool depth is the height of the liquid
annulus in the centrifuge.
The pool depth can be adjusted in mostcentrifuges, even when the centrifuge is inoperation.
An increase in the pool depth will result inhigher solids recovery (because of the
increased residence time), and a wetter cake
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Effect of Feeding Point on Solids
Separation The incoming sludge can be fed (at least in
some centrifuges) at different points along theaxis of the centrifuge.
When the feeding point is closer to the beach awetter cake will be produced, but the solidscontent in the centrate will be lower (highersolids recovery) because of the longer timeavailable for solids separation.
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Performance of Solid Bowl CentrifugesType ofSludge
Concentrationof Solids in
Cake (%)
Solid Recovery[No ChemicalAddition] (%)
Solid Recovery[Chemical
Addition] (%)
Primary 20-40 70-90 75-98
Primary &Activated
15-30 50-80 75-98
Activated 5-15 65-90 85-95
DigestedActivated
15-25 70-90 85-95
LimeSoftening 35-60 70-90 85-95
After Sundstrom and Klei, Wastewater Treatment, 1979, p. 238
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Characteristics of
Solid Bowl Centrifuges Feed rate range: 1.5-12 L/s (25-200 gal/min). Specific flow rate range: 3.5-15 m3/(d KW) (0.5-
2 gal/(min hp)).
Rotational speed: 1000-6000 rpm. g factor (ratio of centrifugal force to gravity
force): 2000-3000.
Centrifuges with larger pool volumes are moreeffective at dewatering sludges.
Pool depth (radial height of liquid) can beadjusted in most centrifuges.
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Analysis of Semi-Batch Centrifugal
Filtration in a Perforated Centrifuge
Solids Liquid
Feed
R
RL
w
Cake Liquid
Rc
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Analysis of Semi-Batch Centrifugal
Filtration in a Perforated CentrifugeAssuming that the cake is not compressible (i.e.,
is independent of P) the pressure drop acrossthe cake at any given time is given by:
( )( )( )
( )P tX V t AR
AQ t
s F m
F=+
2
where XsVF(t) is the amount of solids that have
been deposited up to time t, and that have formedthe cake.
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Analysis of Semi-Batch Centrifugal
Filtration in a Perforated CentrifugeThe pressure drop across the cake has to beovercome by the hydraulic head of liquid abovethe cake. Similarly to the differential pressure
head in a gravitational field given by:
dP g d =
the differential pressure head in a centrifugal fieldis
dP r dr = 2
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Analysis of Semi-Batch Centrifugal
Filtration in a Perforated CentrifugeThe pressure head available to overcome thepressure drop can be obtained from integrationbetween the radial liquid height, RL and the
distance of the vessel wall from the rotation axis:
dP r dr P
LR
R
L
w
0
2
=
i.e.:
( )P
R RL
w L=
22 2
2
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Analysis of Semi-Batch Centrifugal
Filtration in a Perforated CentrifugeCombining the expressions for the pressure dropand the available pressure head one gets:
( ) ( ) ( )( ) ( )P t R R X V t AR AQ tL
w L s F mF= = + 2
2 2
22
i.e.:
( )
( )( )( )Q t
A R R
X V t AR F
L w L
s F m=
+
2 2 2 2
2
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Analysis of Semi-Batch Centrifugal
Filtration in a Perforated CentrifugeNote that the area A in:
( )( )
( )( )Q t
A R R
X V t AR F
L w L
s F m
=
+
2 2 2 2
2
is a function of the radii Rw, RL and Rc.
In addition, this equation is valid only for a givenmass of solids in the cake at a given time. This
equation is not in the integral form, i.e., it cannotbe used to describe the entire centrifugal filtrationprocess.
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Analysis of Semi-Batch Centrifugal
Filtration in a Perforated CentrifugeIf the filtration area A varies significantly with theradius then it can be shown that the flow rate Qcan be expressed as:
( ) ( )( )
Q tR R
X V t
A A
R
A
F
L w L
s F
L a
m
w
=
+
2 2 2
2
where: ( ) ( )[ ]( )
A b R R R R
A b R R
A b R
L w C w C
a w C
w w
=
= +
=
2
2
ln
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Additional Information and Examples on
CentrifugationAdditional information and examples on can be found in thefollowing references:
Corbitt, R. A. 1990, The Standard Handbook of EnvironmentalEngineering, McGraw-Hill, New York, pp. 5.138-5.139; 6.210-
6.211; 6.223-6.229; 9.32-9.34.
Droste, R. L., Theory and Practice of Water and WastewaterTreatment, John Wiley & Sons, New York, 1997, pp. 732-735.
Geankoplis, C. J., Transport Processes and Unit Operations,3rd Edition, 1993, Allyn and Bacon, Boston, pp. 828-838.
Haas, C. N. and Vamos, R. J., 1995, Hazardous and IndustrialWaste Treatment, Prentice Hall, Englewood Cliffs, NJ, pp. 67-69.
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PIERO M. ARMENANTE
Additional Information and Examples on
Centrifugation Metcalf & Eddy, 1991, Wastewater Engineering: Treatment,
Disposal, and Reuse, McGraw-Hill, New York, pp. 805-806; 860-864.
Sundstrom, D. W. and Klei, H. E., 1979, Wastewater Treatment,Prentice Hall, Englewood Cliffs, NJ, pp. 234-238.
Vesilind, P. A., 1979, Treatment and Disposal of WastewaterSludges, Ann Arbor Science, Ann Arbor, MI, pp. 161-200.
Wentz, C. W., 1995, Hazardous Waste Management, SecondEdition, McGraw-Hill, New York. pp. 193-194.