Sedimentation

"SEDIMENTATION"
INTRODUCTION - THE PHENOMENON OF SEDIMENTATION

Sedimentation is the physical process whereby solid particles, of greater density than their suspending medium, will tend to separate into regions of higher concentration under the influence of gravity. As a solids/liquids separation technique it therefore possesses the great advantage of utilizing a natural, and therefore costless, driving force. This section of the suspension processing Guide is Intended to provide an Introduction to the science of the subject, and the means to judge where and how best to exploit sedimentation as a separation (or other processing) technique.

As a scientific discipline the subject of sedimentation is vast with perspectives ranging from the field of chemical engineering through to theoretical physics being covered In the literature [1-11]. Good reviews of the subject, with a bias towards the engineering aspects, have been written by Fitch and Koz [12, 13]. A short summary of some of the more relevant contributions from the literature is also provided in GBHE-SPG-PEG-302 “Basic Principles & Test Methods”, of the Suspensions Processing Guides.
.
The sedimentation process is traditionally divided into ..."

1. u CATALYST, PROCESS TECHNOLOGY

CONSULTANCY

Process Engineering Guide:
GBHE-PEG-SPG-304

SEDIMENTATION

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2. 1.2 Clarification
1.3Centrfugal - sedimentation

ENCE OF SEDIMENTATION - STATE OF THE LITERATURE
Clarification - Setting in Fairly Dilute Suspensions

The Zone Settling Regime - Kynch Theory
22.1 Construction of Curve APBO from a Particle Setting Model

22.2 Analysis of Sedimentation Curve to Yield Particle Settling

Function
Zone Settling and Compression - The Sediment
Structure

TESTS, CHARACTERISATION PROCEDURES AND DESIGN
METHODS
Batch Setting Tests
‘Suspension Characterization - Prediction of Sedimentation
Behavior
32.1 Equilibrium Degree of Concentration

3. a

6 FIGUAI
Figure 1
gure 2

Figure 3

Figure 4

The Different Sedimentation Regimes (Schematic)
Parameters used in the Kynch Theory of Sedimentation

Kynch Model for Sedimentation Showing Propagation of Constant
centration "Characteristics

‘Sedimentation behavior of a weakly flocculated suspension
(polystyrene latex + so llulose) under variou
entrfugal fields. Points are experimental data, continuous curv

Sedimentation (supernatant
suspension and n-sediment) as proposed by Tiller
(schematic)

Concentration Dependence of Uniaxial Modulus, K, for a Model
Suspension (polystyrene latex coagulated with Fi

4. gram of Proce
and Hence Depth of Compression Zone in Thickener (after Fitch in
(3)

dure from Batch Setting Data

itical Flux, Ge, Based on the Coe and
Clevenger Equation

The Yoshioka Construction for Thickeners based on the Batch Flux
rsus Concentration Graph (after reference [49])

Influence of Floceulants on Batch Flux Curve (Schematic)

Effects of Various Flocculant Types on Setting Velocity of Partic
during Brine Clarification (Schematic)

5. pros

As a scientific discipline the subject of
ranging from the field of chemical engi

being covered In the literature [1-11]. Good reviews of the subject,

towards the engineering aspects, have been written by Fitch and Koz (12, 1
short summary of some of the more relevant contributions from the literature
also provided in GBHE-SPG-PEG-302 “Basic Principles & Test Methods”, of
the Suspensions Processing Guides.

The sedimentation process is traditionally divided into setting within four regime:
which are schematically depicted In Figure 1. At very
solids, and in the absence of interparticle forces, ea

pendently ofall others at a limiting velocity giv

ided that the fluid flow is laminar. That is,

rave their conventional meanings. The above limiting velocity
found for particles sedimenting under conditions where the Reynolds Number,
defined as

6. s substantially
ym equations (1) to (3) are observed. This is
etting entity is buoyed” by the rising stream of fluid generated by
the others. That is, the particles or flocs interact through hydrodynamic
mechanisms although direct interparticle forces have negligible effect at such
jerage separations. This concentration regime is normally described as that
corresponding to clarification; depending upon the degree of interparticle
cohesion (during collisions) the clarification may be of primary or flocculated
paricles. At a phenomenological level the clarification mechanism may be
distinguished in a suspension by a “thinning out” of the upper regions of the
sample and by the deposition of a solid sediment at the base of the containing
vessel. A detailed discussion of clarification is provided in GBHE SPG PEG 304
| Centrifugation, of "Suspensions Processing Guides”

If the proportion of solids in the suspension is increased further the zone
sedimentation regime results. Within this range of concentrations the suspension
has structure (though it may be very wea sequence of Ihe dire
interparticle forces [24-27]. As a result of this structure the particles sediment en

their relative height in the

lateral position. This zone setting (someti

line setting) is normally easy to distinguish from the clarification regime for it
exhibits a clear faling zone boundary between concentrating suspension and

7. ‘THE IMPORTANCE OF SEDIMENTATION TO SUSPENSION
PROCESSING

ready been stated, the principal application of sedimentation to
sing is In the field of solids/iquids separation,
Three main sorts of separation operation may be distinguished:

1.1 Gravity Thickening

a suspension
initially at a

of scientific tests to measure
tering operation are

8. [processing 0
the phenomena and theory are rel

(The theory of fluidized beds [17-19]

Settling of dust/other solid particles from smo

lethods for determining the density of particulates, and/or the viscosity of
a suspending medium.

2 THESCIENCE OF SEDIMENTATION - STATE OF THE LITERATURE

The object part of the section on sedimentation is to provid
outine ofthe state ofthe scientific (as opposed to chemical engineering)
erature on the subject For purposes of convenience the subject matter is

9. at
moderate 10 most useful of these is that
mplo s Jodwin and Ottewil [291 amongst others.
For suspensions of 1.55 um polystyrene latices the settling rate
ind to be of the form:
0

ich the par pack and

kis a numerical constant determined by Buscall et al to be equal to
5.4. (Note that under the artificial conditions where p = 1, this
well known Richardson and Zaki equation,

10. a

131]. For these, slow speed centrifuge exp

Theological measurements Indicated, a ck

between the stress dependence of the viscosi

dependence of the collective fiction coefficient on the ambient
gravitational field. Thus, in principle, with this result established it
should be possible to snake accurate predictions of sedimentation
rates, for weakly flocculated suspensions, from shear rheological
measurements,

The influence of floc structure and container dimensions on sett

rate was in d thoroughly by Michaels and Bolger [32] in a
the sedimentation properties of flocculated kaolin
By controling the pH of the suspending medium
orkers were able to control the degree of “openness” of the
¢ structure and correlate this with the setting properties.
Furthermore, they found that the flow conditions under which the
flocs were formed were also an important factor. In fact the
Influence of floc structure and the kinetics determining it are often
main variables in a claifcation context. For more details of the
that control them, the reader
“Suspensions Processing Guides”, particularly the folk
Centrifugation, Selection of Flocculants, Clarification,

11. its local concentrations only; that i

vo

where c is the particle number concentration at that point. It was
further assumed that al the setting entitles were of the same size
and shape. By considering the particle flux, S = c.u, through a
horizontal element of thickness dx, Figure 2, in the settling column,
he derived the basic continuity equation:

‘where x is the vertical height of the element within the column. This
may be re-expressed In the form

+ vor. de

12. hemati en
that all the concentration zones are propagated upwards at the
constant velocity, V, which is a simple function of that

‘concentration. Provided that the concentration function is
continuous, no two characteristics wil cross

The equation of these characteristics is then:

xo + Wet

Xabeing the Intercept of the characteristic on the height axis.

Two other relations enable Kynch theory to be exploited in ord
to understand the fall of the zone boundary, ABC. At any general
point P, the speed of fal

lax/ati

13. (14) sti hold provided that x = O inthis region. Alter C,
sedimentation ceases since the whole bed has reached the
uniform, maximum concentration, Cm. (As wil be seen later, these

umplions are erroneous since they do not allow for
‘consolidation

Having outlined the basis of the theory and presented the salient
equations, we now describe how to apply itn two important
situation:

Construction of Curve APBC from a Particle Settling Mode!

In order to construct a zone boundary decay curve as a function of
time, two additional pieces of information are required:

The initial concentration profile; c(xo) at t = 0.

ion for the settling rate as a function of concentration,
nstitutes the settling ‘model

ied pairs of (xt)

14. (6) The time, Y, is now evaluated from equation (14) th

od

only to apply the characteristic equation, as in (iv), and the
height x corresponding to time t's obtainec

(7) Anew, incremented value of Xo or e ls chosen.

(8) Go back to (1)

NB As soon as c reaches the value at the bottom of the bed, Xo is set to zero in
equations (12) and (14).

15. mM y
wn = mr ef carte

(The subscript, p, indicates the local evaluation of the expression in
brackets.)

(4) Hence xo is obtained and thus the concentration of the characteristic from
the known distribution of starting concentrations

(5) Thus the functions u(c) or S be evaluated by taking further points
P.

À detailed discussion of the deficiencies of Kynch's theory will be deferred
Until the next where attempts by various authors to remedy them
are described. However, itis instructive to list Kynch's own assumptions.

and therefore limitations:

(Uniform panicle concentration across any horizontal layer.

(i) Initial concentration function e(xO)at t = 0, is uniform or inc
the bottom of the dispersion.

16. a

y coefficient n(c), had similar conce
dependencies. The experimental points and fitted s

cures from the paper of Buscall and McGowan is reproduced in
Figure 4.

Zone Settling and Compression - The Sediment
‘Structure

The most restraining assumption
which requires that setting velocity be

ie. ule), only. Unfortunately this means that the theory is
incomplete as soon as a sediment with any structural strength 1
formed. In an attempt to revise and clarity the theory, Tiller [40]
presented new argument Jay be interpreted in terms of
Figure 5. This diagram may be und

constant rate section analogous to the part of the curve of Kynch

Figure 3 denoted APB. At the height, HI, the characteristic

emanating from the origin intersects the Hit) curve and thereafter a
It

17. À subsequent paper by

Kynch Theory so as to make the numeric

straightforward. In particular he developed graphical constructions

in order to yield a setting function, u(c), forthe first falling rate
tion of a sedimentation curve. Unfortunately, in common wi

Tiller the construction requires a knowledge of L(t) and
Fitch conceded that this removed much of the practical advantage
ofthe ch. He suggested two means of extracting L(t)

st, originally developed by Gaudin and
Fuerstenau [16], uses an X-Ray absorption Instrument scanning up
and di

points” by a whole series of batch settling te
heights. Unfortunately the use of a battery of batch test
the advantage that the Kynch approach originally conveyed.

The above discussions are concemed either with zone settling or a
sombination of zone setting occurring simultaneously with
ompression. There are, however, many circumstances where an
understanding of the compression or consolidation process
at is required. This

18. (1) The final solids content, ©, (or conversely porosity) that results
‚hen the compressive Strength of the network can fully support its
represents the ultimate degree of dewatering that
can be achieved via sedimentation. In the parlanc ction 3.2
of the manual (Basic Principles and Test Methods, ths is the
Structurally-Limited S-L, regime),
(2) The rate at which the consolidation takes place up to that
ultimate limit, Le. the kinetics of the process, (the so-called
Kinetically-Limited, K-L, Regime).

The first aspect is fairly readily approached provided that a means of
quantifying and measuring the strength of a particulate suspension is
available. One fundamental parameter that can be used for this purp
the uniaxial compressional modulus, K, defined as [46]:

= dp/ding = - dp/dlav

here © and V are the volume fraction or network volume resulting f
dating pre: The advantage of using K

yoo = Sana

19. ing chapter and In s
xperimentally found to be a very strong function of
often following the sort of dependence:

where Bois the volume fraction at which a space-filing net
and the exponent, n, is typically 3 or larger. This sort of relationship is
ilustrated in Figure 6 where the influence of shear on the modulus is also

in the strength of flocculation of a particulate network
¡ce on the modulus curve and consequently on
weakiy flocculated systems, eg polymer

are more easl ly rearranged
and yield smaller sediment than the strong, open structures that
s coagulation of small part
mechanisms and

20. The terms represent respectively the viscous drag forces on the sedimenting
ment, Ihe structural pressure gradient resisting consolidation and the weight of

unit volume of suspension. The main thrust of the Buscall and Mite model for the

Kinetics may be summarized In the constitutive equation that they employed

Dp/Dt = Xp = Pyipl, for p ? Pyip) and

In this equation, DO/D! is the material derivative, N@) a dynamic drag coefficient
for the squeezing out of water from the collapsing network, p the applied
pressure and Py the "yield pressure”. The assumption implicit in (19) is that the
driving pressure for consolidation Is attenuated by the ful elastic strength of the
particle network. Once again (cf 3) the analogy between the concentra
dependence of sedimentation rate with shear rheology may be drawn

equation (19) may be cast into a form reminiscent of the Bingham plastic
constitutive equation.

By combining equations (18) and (19) with Kynch-ike continuity equations,
Buscall and White produced a rather complicated 2nd Order partial differential
equation. By considering just the t = 0, or initial rates solution, the problem was,

21. = poli = $0) 298
Ge?

Hol = $0) 098
ET

[Rue 160
Fol = 40)

and Xo repres
Py(@). Hence below Xo the bed
uniformly without compaction. A
the concentration dependence of the perm

Drawing upon approximations that demonstrate that À x Ha is very large
(10°- 10) equations
for the Initial consolidation rate:

MET rte tet = ew

22. a

31 Batch Settling Tests

The first and most basic application of a batch setting tes
suspension Is to Identity the class of sedimentation that pre
concentration, Thus If the upper regions of the sample are seen to “thin
out gradually with a visiby rising sediment, it may be safely assumed that
for at least the initial stages, the process may be regarded as clarification
If, on the other hand, a fairly distinct boundary develops

lear supematant above an opaque, falling sediment boundary then zone
settling is occurring. To distinguish between zone
consolidation the most riterion Is the rate offal of th

solidation is muc of course, the type of
rom the initial concentration

of the suspension, Figure 1

In the context of this chapter on dewatering, it will usually be a zone
1 regime which is being investigated. The setting up

the fall of the zone boundary with time. A number of
precautions are necessary, however, Ifthe results are to be free from
Perhaps the greatest danger in these tests isthe rs

23. ‘etc may be employed in the laboratory tests to gain at least a
qualitative idea of the Influence of "raking" on a large scale thickener. In all
these considerations the main feature isto e ucture of the

pension in the batch test is not perturbed by any factors other than th
controlled sedimentation process. Itis therefore wholly unsatisfactory to

sspension in order to carry out some further

experimentation. In some cases the re-suspended material will behave in
the same way as fresh suspension, but this should not be assumed for all

mples. Likewise good mixing (eg of a flocculant is relatively easil
accomplished on a laboratory scale but is often less satisfactory on the
plant.

As far as the actual application and analysis of batch settling tests to
specific problems Is concerned, It will already be clear from the section on
Kynch's theory and the subsequent modifications to It, that these
procedures enable the particle settling-concentration, u(c) relationship to
be evaluated. An outline of how these sors of tests and models are then
used for design purposes for thickeners is give 33.4(c). In

of applications, including both cariicaton and thickening, are
given in Purchas’ book "Sold Liquid Equipment Scale-Up', Centrifugation
[El

24. pt ie Sediment
degree of concentration b

Equilibrium Degree of Concentration

explained previously the guiding principle in his area is that
sedimentation, in the form of the consolidation process, will cease
when the sediment has acquired sufficient compressive strength to
‘completely resist the gravitational forces acting upon it. This w
‘correspond to:

Py Gs aus

here H Is the height of the consolidating sediment and
equilibrium degree of concentration. Variations in the degree of
densification down the bed will of course arise and, where the
‘consolidating pressure arises from a centrifugal gravitational field
(Section 3.4), “g” itself will vary through the sediment. Despite these|
problems the equilibrium degree of consolidation, ©", can usually
be calculated, or at least estimated as des tion 3.2. All

25. 3.2.7 Pulse Shearometry

This technique measures the propagation speed of a very small
ain sh through a small sample ("50 cm) of the
suspension of interest [46]. From this speed, u, and p, the
density of the sample, a quantity known as the wave rigidity
modulus, 6, may be derived!

= ap

Under circumstances where the shear wave propagation
time can be measured, G gives a good approximation to the
instantaneous (Le., high frequency limiting> shear modulus,
Gs Invoking the very close numerical agreement bet

&. and K [46] permits the yield pressure, Py(O), to be
deduced:

” ud

yan Jamas =f 600

26. ‘of any conditioning pro
flocculants, or physical pr 9
final sediment volume and solids concentration can be

sed very ef In addition, time dependent effects
such as “ageing” of the sediment can be readiy followed
‘over extended periods if necessary,

Slow-speed Centrifugation [44-46]

tion method measures the yield function,
y. The experiment consists of measuring the

equilibrium height of the sediment in a

function of he centrfuge speed and hence the applied

‘consolidating field, Figure 9. Two approaches may be used

to calculate the results. The old and original approach is

simple since it requires no numerical differentiation to
evaluate the function, Py, which is simply calculated from the
equilibrium and intial sediment heights (Hz, Ho), the relative
density (Ap), centrifuge angular velocity (w) and the

distance R from the axis of rotation to the bottom of the
centrifuge tube

Mur CR He) apo,

ft Ao

27. = ng (A 72). fo

aW/dlag*

Whichever of the two means of analysis is used, the result is
a series of values of the yield function at various
‘concentrations. Cleary, in order to obtain data to enable
prediction under unit gravity, an extrapolation is required to
low values of Py. This tends to be somewhat unsatisfactory
since the $-dependence of Py at low er law-type
function of varying Index. However, provided that the
centrifuge is capable of stable, slow-speed operation, this
extrapolation may provide at least a useful estimate of th
yield point at low solids concentration. In general, however,
the Pulse Shearometry method is to be preferred at low $ for
these reasons,

329 Kinetics of Thickening

28. a

Initial setting rate at unit gravity
approach has yet to be tested but itis an attractive one
because of the relative ease and speed with which settling
curves at higher gravitational forces can be obtained. The
experimental data is easily available from the Stroboscopic
Centrituge [53]. This device uses an electrical or mechanical
triggering of a stroboscope which illuminates the interior of
the centrifuge for a very short time once per revolution. The
zone boundary in a sample tube Is easily
‘observed as a “frozen Image” through a perspex window In
the lid of the machine. Commercial machines are available
(Triton VRC Type TV161) but Its a relatively simple matter
10 modify an ordinary bench top centrifuge for the purpose,

‘Some words of caution are necessary, however, regarding
the use of accelerated tests to predict unit gravity
sedimentation. Many problems may ari
the various sedimentation mechanisms which
differently with "g". For example the setting of a single Inert
partice in a non-Newtonian fluid may not so easily be
correlated with the zero shear viscosity n(0), at high

se, the structure and shape of

29. a

Although the design of gravity thicke a broad and mature subjec
and perhaps better regarded as the province of the chemical engines
many features impinge on the principles already established in this
section. Figure 10 s chemati view of the sedimentation process
in typical continuous thickener. It can be seen that all or some of the
sedimentation mechanisms of Figure 1 may be simultaneously operating
at different levels. In order to understand the origin of the zone labeled as
the “critical zone", and its implications on design, one-dimensional
Continuity equations for the solids flux are derived. Coe and Clevenger
[50] were the first workers to tackle large-scale thickener operation in thi
way and they arrived at the equation:

ee

— A
We 1

Here G is the solids flux (Le., mass rate per unit area) at a given point in
the thickener where the ambient concentration is C. cu ist
concentration of the undertio

The influence of equation (28) on the operation of continuous thickening
devices Is Ilustrated in Figure 11, which shows the variation of solids flux
with concentration for a give Cu. Coe and Clevenger obtained

30. that in
ne.) imposes
ro depth requrement on the design ofthe thi

In practice, as a result of the theory due to Kynch and subsequent
modifications and applications toi, the area required to prevent cr
1e occurrence can in principle be deduced from a single batch setting
(Recall that in essenc ory permits the function U(c) to
be derived for a w ations greater than the Initial one.

These standard design procedures involve simple graphical constructions
based on Kynch's theory; the most famous being due to Oltmann, and to
Talmage and Fitch. Details and worked examples may be found In
references [1, pp147-160] and [ et seq)

In addition to the area demand of the non-compression,
regime in a gravity thickener, It Is often necessary to identity constraint
from other sedimentation mechanisms. Thus both clarification
the feed is at a concentration below that at which zone setting
Ind compression impose a detention time constraint on the

31. The sort jure outlined above are summarized in a simple
flow diagram and schema 1 constructions shown in Figure 13a-d. Much
greater detail for both the experimentation and calculation for th

In addition a de
process in the analogou
tion 3.4. A variant on th

Yoshioka is also given in that section. Although all these technique:

mploy some level of fundamental understanding of sedimentation, itis
evident that there is great scope for progress In the area. Thus although it
well known that Kynch's theory is not rigorous
Seting, no simple aerate i el in widespread use License te sor of
calculation o sion height, Hesnp, described above fast ak

ome ofthe results ofthe Buscall and White theory for
might well improve the situation here. Finally, it
should be remembered that other considerations based either on
economies of space or the need to wash the sedimenting solids may in
themselves Introduce new design constraints in terms of height and ar

32. 4.1. The Purification of Brine

The clarification of brine is an important process op
companies. A typical feed stream to the clarifier might comprise a
of 26.5% BaCI by weight (equivalent to -5 M), but containing suspended
solids such as CaCO; (in the paricle size range, 5-2
ved by flocculating with an anionic
pically hydrolyzed polyacı or acrylamide
, and then by sedimentation in a settler. In this context the

main variables to be optimized are the settling rates and thereby the clarity
of the overflow. The role of such flocculants may be understood by
referring to the schematic batch flux curves shown in Figure 14a and 14b.

As can be seen in the curve, the dependence of batch solids flux on
Concentration is described by a characteristic curve containing at least
three of the mechanistic regimes for sedimentation: free settling, hindered
setting and compression. The interpretation of the batch flux curve
together with an assoc ine is illustrated in Figure 14a. In
essence the curve "a" represents the experimentally measured property of
the v. This flux ‘equal to the product of the concentration, ,

33. Hence the operating line does not depend upo ‚pension properties
but merely on geometric and operating conditions. However, only if the
line falls below the point X in the Figure will the suspension properties
permit stable thickening
The maximum stable flux, a most efficent operation, results
when the operating line is tangential to the suspension batch flux curve at
X. This maximum, stable flux is called the critical flux, GC. The above
arguments as summarized in Figure 14a are know

uction by some authors. (The reader

Tuming to Figure 14b, It can be understood that a tangent to the
ing the y-axis at flux G wil yield an under
|, The addition of a suitable flocculant translates the bate
‘own In the figure and hence yields an Improved underflow
concentration and enhanced supernatant clai
feed rate, Or, can be achieved at fixed underflo
equation (30)). These batch flux curves, Flux, G
etting velocity, (u), may be generated either by a series of jar test
Section 3.3.4(a) and the paper of Coe and Clevenger and subsequent
rences to it) or in a single batch
Kyni

34. a

Location A

Location B

4.2 Distiller Blow-Off, DBO [52]

Distiller Blow-Otf, or DBO, is the name given to an effluent stream
originating from an ammonia recovery stil in a European ammonia-soda
producer. This stream is hot (85 °C) and contains a wide range of
suspended matter ranging from micron sized particles including CaCO:
MgCO3 and CaSO4. to larger scale grt (total suspended solids "1%). To
clean up this effluent a Dorr-Oliver clarifier is used in a somewhat unique
fashion. The approach utlizes the fact that DBO is less dense than
concentrated brine and hence when introduced on top of the later in a
settler, the two phases remain essentially distinct. By this means the DBO
solids pass through the it ‘and are drawn off in the concentrated
(10% solids) brine underflow. Once again anionic polyelectrolyte
flocculants (with diferent optima from the brine purification process) are
employed to enhance solids setting rates.

In this DBO clarification both the relative position of, and the density
difference across, the interface of the DBO and brine phases require

36. Porchas, *Sol1d/Ligutd
y 198

chs, Trane à Chen

A Buchten

Di Gregorio and E © Koninek,
font in the CPI" che

RM Okey,

1978.

Srarovaky, "sesimentas Kirk-Othner, Encyclopedia
ard 2 pres

X Glide, + Szanto, K Varga and © 7 Glide, "seas
hasta Payo Chea, 20. 145,

Kor, ge te
gin 789, november 1977.

ocevlant
AEC", AICHE Journal, 23, 919, 1979,

Kasten 7: 87, 1868.

Bo vote erases, "2
Nedelling :

1984, 420.

37. ications", Aer fest of Chex Eng, 1989

st Chem Bagre, 32, 35, “

De tng Chen emos

Eros,

Moxa,

Golteta interr Set, aA, 70, 1982

38. Kichoels

Trans Inet ches Bag, 44, TIES, 1986

Trans Inst Chen Engrs, 43, 169, 1968

hen Eng Bei, 24, 447, 1970.

2 Polytteperse

Xe,
106, Tose

22, 980, 1989.
Flocevient Proc Amer Soc
198, do BES, 805, 1980.

x 2 melb, "one Theory
Compressibie, Sarticulata 5 Colloid Intert Set
Pre

Boscanı

40. of Flocculated
Partie.

41. icle fl
denotes particle

Kynch Model for Sedimentation Showing
Propagation of Constant Concentration “Characteristics”

51. low Sheet for Thiskener Sising

Sehe

TE

Léger tc

an av

à dei my be

iS Line
(a Chapter à

52. Height of Interfa

Schematic Dingram of Procedure for Estimating
comprenne ant Menos Dop of Campe

han Zune in Thieköner

Identify corresponding time Qu in batch test aber

Estimate the detention time for compression in 0

in the batch tes

Hence, the required dept

ho thickener
panal felacion ofthe form Me

54. Estimation of Critical Flux, G
Coe and Cie, Equation

(This approach is commonly employed where the suspension f
exhibit a clear compression point.)

1) A series of batch sel ats is set up. For each the
settling velocity. U, in the constant falling rate se
measured as a function of the st concentration.

‘The settling rate 2 ageinst. UC) as shown
above

The tangent to the experimental curve passing through the
reciprocal of the chosen underflow concentration, 1/0
constructed (in the rogion 1/€ > 1/00).

The slope of this tangent is given by. uft/e = 1/Cu}',
hence may be identified directly with the critical flu
fined im the Coe and Clevenger Equation (Equsts

55. perianal à suspension property
ai fis imp ea Hat
the linear equation for a sets

56. Batch Flux
=ue flux =
and bene

ca Ci, a higher critical Flux

ling Velocity u (at or

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