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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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TIME' (I_I '. ...1..

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'