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Powder Technology, 11 (1975) 75-84
@ Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
Sedimentation of CompressibleMaterials: Analysis of Batch Sedimentation Curve
C.C. HARRIS, P. SOMASUNDARAN and R.R. JENSEN
Henry Krumb School of Mines, Columbia University, New York, N. Y. 10021 (U.S.A.)
(Received April 22, 1974; in revised form Auaust 6,1974)
SUMMARY
Batch sedimentation curves or dilute phos-
phatic slimes o which small amounts of coarser
particles were added to hasten settling are ana-
lysed. The curvesare markedly reverseS-shaped,
without a constant settling rate period, and
with pronounced asymptotic behaviour ndica-
ting compressiblematerial; no flocculants
were added but the slimes were observed o
flocculate into small clusters of particles which
grouped nto aggregates.
The system s complicated and, as a pre-
cursor to an analytical approach, an idealized
model is proposed as a framework for future
discussion.
Several egions of the curve are identified.
Each region indicates a specific sedimentation
mechanismwhich predominates over a con-
centration range. Phenomenologicalmodels
for the regions are proposed and expressed n
their simplest mathematical form. The result-
ing equations consist of logistic, logarithmic,
and exponential decay erms, and they fit data
within experimental error.
size fraction of hard regular particles- for
example, clean unflocculated glass pheres
in the approximate range 250 - 25 11m t a
volume concentration about 10
-
25%. n this
case,batch settling is characterizedby a linear
suspensionheight versus ime relationship
termed "constant settling rate period". It is
easily amenable o analysisalong the lines of
the modified Kozeny [26] model for flow
through porous media. Data correlation can be
handled by the dimensionlessgroups: resistance
coefficient and modified Reynolds or Blake
number [5,16,17]. Settling endsabruptly
with little further decreasen height [18]; the
material is said to be incompressible.
In contrast, the sedimentation curve of di-
lute suspensions f subsieve lay materials
displays a reverseS-shapewhich is so curved
that no region could be describedas exhibiting
a constant settling rate period [23]. Moreover,
settling continues at an ever decreasing ate
over an extremely long time period, suggesting
that the material is compressible.
In an earlier paper [23], stagesn the sedi-
mentation processof compressible limescon-
taining substantial quantities of fibrous ma-
terials [27] were briefly described;part of the
curve was reported to ~e fitted approximately
by a Weibull type equation [28].
The purpose of this note is to propa8ea
phenomenologicalmodel describing he entire
sedimentation processas a framework for more
rigorous future treatment. It is basedon the
observation of the sedimentation systemsand
the analysisof the simplest plausible equations.
INTRODUCTION
* In some terminologies "sedimentation" refers to the
upward growth of settled material; in the present
usage, sedimentation" is synonymous with "..bsi-
dence".
As a suspensionof fine particles n water
settles under gravity, an interface forms be-
tween the suspensionand the supernatant
water. A graph of the interface height versus
time is known as J1e edimentation curve.
Summariesof the present state of research nto
sedimentation and thickening can be found in
severalpublications (1
-
25).
The simplest sedimentation curve is pro-
duced by a suspension onsisting of a narrow
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~
76
thereby transporting small quantities of very
fine particles which are visible on close nspec-
tion.
The nature and duration of the sedimenta-
tion behaviour describedabove depend signi-
ficantly on the number of coarseparticles
present n the system. When he coarseparticle
additives exceedabout one gram n 100 ml
of 2.6% phosphatic slimes, he pace and extent
of channel formation increase n intensity.
This results n increasedwater movement
throughout the slurry and massive oc& cata-
racting circulation with transport of dilute
slurry upwards and concentrated slurry down-
wards. During the later stages,now of water
through clearly defined canalscan be observed
near the wall of the container, and from acti-
vity occurring at the slurry - water interface it
is inferred that the canals ntersperse he entire
sedimenting mass.
35 Milt
2 Hr.
4 Hr.
Fig. 1. Settling prOCeDeaor batch conditions (dia-
grammatic only). Conditions. 2.6% phosphatic slimM,
0.5 g coarse graphite tracer. Observations. (i) Sua-
pension gels almost immediately followinl mixing,
thus terminating rotational movement. (ii) -10 min;
rising air bubbles (-0.1 mm diam.) and descending
particles create vertical tears. During subsequent
-
30 min water concentrates into lensesaround the
tears. (iii) -2 h; channeling and microvolcanoes en-
hance dewaterinl process. (iv) With 2 g of coarse ad.
ditives, massive egional circulation occurs.
BATCH SEDIMENTATION CURVE
Close nspection of the reverseS-shaped
sedimentation curvesof compressiblematerial
indicates complex behaviour during tlle initial
severalhours of settling. This can be shown
clearly by logarithmic plotting of the time axis
which expands he small time region and con-
tzacts he long time region. A composite sketch
is given n Fig. 2; the various features are pre-
sent to different extents in different systems.
igure 1 illustrates the observedsequenceof
the formation of floccular aggregates nd
channelsduring batch settling in a cylinder.
In only a second or two after mixing, the ro-
tational movement of the suspension eases
due to gelling, a processwhich appears o de-
velop over a period of severalminutes. The
movement of the coarseparticles through the
suspensionduring the first few minutes does
not leave rails, but subsequentmovement of
particles and micro-bubbles results n tears
developingalong their wakes. This leads o
fissures n which water collects and transports
forming lens-shapedwater-filled cavities. Ad-
ditional tears develop eading to channels
connecting various enses, hereby providing
seepage aths, eventually opening at the slurry -
water interface. Theseoutlets have he appear-
ance of miniature volcanoesboth in shapeand
in the behaviour of fine particles entrained in
the exiting liquid. Liquid also seeps o the
surface long he container-
lurry interface,
~.
~-;(I,)I
.
.
.
I C A A -;
0 .
-L---i
. ~--
: I
FLOCCUA
:= ~l-' 0I: , TE
I 0 ASYMP O 1-
_1 : . ~ II
. I 0
0 .
I .
t
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i
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Fig. 2. Batch sedimentation curve. Diagrammatic re-
presentation of height of suspension
-
supernatant
interface, H(t) w. log t plot showing principal points
and regions. The intensity and duration of the stales
depend upon the characteristics of the solid and the
experimental conditions. Fixed water may be re-
moved only through application of additional forces,
e.,. centrifugation.
i
~ ~I
. 2'
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