Orthokinetic flocculation of latex microspheres

Che,md Engmeenng SctenceVol 34 pp 983-991 Pergamon Press Ltd 1979 Pnnted IO Great Br~tam

ORTHOKINETIC

FLOCCULATION K

Umverslty

College London,

OF LATEX

MICROSPHERES

J IVESt

Cower

Street, London

WClE

6BT, England

and A4 Aquastat

AL DIBOUNIS Ltd. London England

(Recerued 6 October 1978, accepted 10 January 1979)

Abstract-Orthokmetlc flocculation of pvc latex mlcrospheres (approx I Km) was studled m a mml-couette apparatus wnh lammar velocity gradients up to 10 s-’ Measurements with a Coulter Counter showed the growth of up to 1600-fold aggregates Flocculation m a fixed porous bed mdlcated some aggregate formulation but the results were masked by a pronounced filter effect Flmdised bed flocculation m both smgle pass and recycle stages showed very slgnificani pa&e aggregation

INTRODUCTION

for such a suspension which closely simulated those encountered in water treatment practice, the progress of particle aggiomeratlon could only be followed by the reiatlveiy crude measure of turbldlmetry Also the closed ends of the cylinders caused clrcuiatlon patterns which destroyed the uniform shear gradients through about 75% of the annular volume Although these were mterestmg mvestlgatlons more closely related to practice, and gave useful comparisons with the standard stlrred JEU test laboratory floccuiator, they were not well-defined enough for the present study Consequently, a vertical co-axial cyhndrlcal floccuiator of small volume (mml-Couette) was designed and the floccuiatlon of destabdlsed polystyrene latex (approx 1 pm) was followed by Couiter Counter particle size analysis As the latex was very expensive the subsequent fixed bed and fluldlsed bed apparatuses were also built on a small scale to reduce the reqmred volumes of suspension However,

Flocculation IS defined, for the purposes of this paper, as the aggregation of coiioldai or mlcroscoplc particles suspended m water, mto clusters of particles called floes There 1s no attempt to use different defimtlons for destablhsatlon by indifferent electrolytes or specific countenons, and aggregation by relative particle movements However the perlkmetlc phase, caused by Browman (thermal) motion, and the orthokmetlc phase of flocculation, caused by apphed veioclty gradients, are dlfferentlated both theoretically and expertmentally Orthokmetlc floccuiatlon IS a common mdustrlai unit operation, and 1s partlculariy apphed m water treatment Apart from conventlonai processes employing paddle stirrers, or baffled (iabyrmth) floccuiators, there IS an established interest m flmdlsed bed floccuiatlon (floe blanket cianficatlon), and a more recent growing interest m fixed bed floccuiatlon (contact floccuiatlon or fiitratlon) In order to study these treatment processes a basic measure of floccuiatlon was required m the form of an orthokmetlc floccuiator with a well-defined velocity gradient, treatmg a monodlsperse suspension Using this basic system, the more complex fixed bed and flmdlsed bed floccuiators could be assessed m terms of performance Previous studies m the Public Health Engineering Laboratories at Umverslty College London had used horlzontai co-axial cylinders, outer cylinder rotatmg for maximum hydrodynamic stablhty, contammg clay suspenslons with aiummmm suiphate floccuiant m the cyimdrlcai annular gap [ 1,2] Both batch and continuous ffow floccuiatlon was studied, and the honzontai axis was chosen because lt mmlmlsed sedlmentatlon effects for the relatively large (- 1 mm) floes which were formed

FLOCCULATION KINETICS Perlkmetlc and orthokmetlc flocculation were first anaiysed by von Smoiuchowskl[4] m 1917, but a recent review by Ives[5] summansed the results with the foilowing conclusions

Penkrnettc flocculatron For an mltlaliy monodisperse suspension of particles of type 1, radius r,, subject to aggregation by Browman diffusion, with the Stokes-Emstem dlffuslon coefficient D,, the rate of doccuiatlon IS second-order with respect to particle number concentration N The concentration N, of type-l particles remammg after time t, as a fraction of the mlhai concentration No IS

tProfessor of Pubhc Health Engmeertng STechmcal Executrve Formerly Postdoctoral Research tant, Uruverslty

College,

Nt N,=

Assls-

London

983

1 1+8?rD,r,Not

(1)

K J

984

The halvmg time fIi2 1s reached t Substltutmg

IVES and M

when N, = NO/~

1 “’ = 8?rD,r, No

for the diffusion

coefficient

D,

where k 1s Boltzmann’s constant 1 38 x 10mz3JK-‘, T 1s absolute temperature degrees K(Y + 273), p IS dynamic viscosity kgm-’ sP1 (4) and eqn (1) becomes 1 1 + t/t,,2

(5)

Orthokrnetrc jlocculat~on In a uniform velocity gradient duldz, the rate of collision of particles of radu r, and r, assumes coalescence to form particles of radius rk The assumption means that the volume V, of an r-particle IS I tunes volume of a pnmary l-particle, rt IS also the volume of a particle of radms r,

Ill3

=

16 3

a%

llrz - 1/ro* l/G2 - llroZ

where w(r) 1s the angular velocity at radius r, and subscripts I and 0 refer to inner and outer cylinders This produces an angular velocity dlstrlbution across the gap as shown on Fig 2, for which a lmear assumptton 1s a close approximation The expenmental points show a good agreement with theory at a height of 24 mm above the fixed base In fact, a detailed mvestlgation, to be published, has shown that above about 10 mm, the end effect can be neglected Also the growth of Taylor vortices from the bottom of the gap has been studied, showing that they begin to develop below 0 5 of the crltlcal Taylor number given by the theory for Infinitely long cylmders

(7)

r,3

The rate of reduction of total number given by the second-order equation dN, --c-r, dt

Ity, a rotating inner cylinder was used for mechamcal slmphclty Usmg the crlterra established by Taylor m 1923[7] to retain lammar flow m a reasonable operating range of du/dz (+ 10 s-l), the drmensions and rotational speed of the muu-Couette were established The apparatus IS shown on Fig 1, it has a 27 mm diameter rotating inner cylmder, with a 3 mm annular gap to the outer fixed cyhnder 150 mm high, having a capacity of about 40 ml The motor and variable speed gearbox are cylinder, mounted above the rotatmg providing 21 rev mu-’ for du/dz = 10 s-’ Velocity gradients across the gap of 0 to 10 s-’ could be obtained while retaining tammar flow These are mean values of du/dz assuming a hnear variation of velocity across the gap The true variation of velocity, for infinitely long cylinders, IS given by eqn (9) w(r) -= 0,

Nt _=No

Consequently

AL DIBOUNI

concentration

N* IS

g N,2k * 1

where p represents the limit of particles radius r,, beyond which they are broken by shear gradient disruption The size dlstnbution curves resulting from applying Smoluchowski orthokmetic flocculation equations to mittally monodlsperse suspensions have been computed by Ives and Bhole[6] for various conditions of floe disruptlon at an aggregate hmlt size p However, it has been dficult experimentally to verify these size distributions m detal due to a Iack of knowledge of the factors affecting p and the mode of ffoc disruption, and due to the assumption of an mteractmg radius (r, + fi) when the particles do not coalesce (I e with sohd particles such as latex or clay) DESIGN OF THE MINI-COUEITE

FLOCCULATOR

To reduce the end effects which were found m previously used horizontal co-axial cylmdrrcal flocculators, a vertical axis cyhndncal Couette flocculator was deslgned with a free water surface Although a rotating outer, and fixed Inner, cylinder has more hydrodynamic stabd-

Fig 1 Mun-Couette flocculator

Orthokmetlc

flocculation

of latex mlcrospheres

985

The velocity gradlent (G, bemg a space-averaged mean of du/dr) m such a clean fixed bed filter can be calculated from the power dlsslpated m head loss[8] as given m eqn (10)

where P/V 1s the power per umt the hydraulic gradient, u IS the filtration, E IS the porosity of the density and dynamic viscosity of Using the Kozeny equation for eqn (IO) becomes

hquld volume, H/L IS approach velocity of fixed bed, p, p are the water the hydrauhc gradlent.

G = 13 4 “(I--/) Relattva gap radtus.

‘-5 /r,-7

Rg 2 Observed and theoretical dwtrlbutlons of angular velocity across gap of mnu-Couette flocculator at a height of 8 x gap = 24 mm

Consequently, any flocculation observed at velocity gradlents nommally over 10 s-’ would be m non-uniform condltlons of the shear field The lammar condltlon m the upper part of the mm&ouette was demonstrated VISUally usmg the prmclple of reverslblhty of flow, which IS only true m a lammar regime Spots of neutrally buoyant mgrosme dye were placed about 50 mm below the water surface m the annular gap, usmg a long reach hypodermlc needle After several rotations the dye spot was “smeared” round the cylinder, and almost mvlslble By reversmg the rotation the same number of revolutions, the dye spot was re-established at its orlgmal location, only enlarged by dlffuslon. rndlcatmg the reverslblhty of the flow Although this techmque has been demonstrated m highly VISCOUShqmds such as glycerine, It IS beheved to be the first demonstration of this effect with water This experiment has been recorded on cme film A quantltatlve measure of the velocity dlstnbutlon across the gap has subsequently been made using 125-150 pm fraction polystyrene spheres as visual markers, suspended m NaCl solution for neutral buoyancy Usmg a low frequency stroboscopic plane hght beam, the particle tracks at various radu have been recorded and measured by photographlc time exposures, vlewmg up through the transparent base of the annular gap The results of such a series of measurements IS shown on Fig 2, which confirm the lammar velocity dlstnbutlon DESIGN OF FIXED AND FLUIDLSBD

BED FLOCCULA~I(S

Fued bed Because of the high cost of latex suspensions, a fixed bed (filter) was required usmg small volumes of suspenslon Consequently, a muu-filter was constructed 21 mm diameter and 20mm deep contammg 0 55 mm glass spheres This gave a vessel/filter gram diameter ratlo of approximately 40, which gives an error m the pressure drop due to wall effect of about 2% In most larger scale experimental filters this ratlo IS mamtamed at 50 or more

(11)

d IS the gram dmmeter By settmg G at 10 s-l, so as to be comparable with the mml-Couette flocculator, and with the porosity of the glass beads at 0 40, the resultmg approach velocity was 0 1 mm s-l This reqmred a flow rate of 2 1 ml mm-‘, and gave a residence time of 80 s m the filter pores The approach velocity of filtration was low, bemg about l/l0 of that used m water treatment practice However, If the velocity were to be Increased by 10 times, the gram diameter also must be Increased by 10 times, to 5 5 mm, to keep G = 10 s-l (E cannot be vmed slgmficantly m a fixed bed) The vessel diameter would then have to be Increased by 10 times, therefore Its area by 100 times The combmatlon of tenfold increase m velocity, and one hundredfold Increase m area, would mean 1000 fold increase m flow rate to 2 11 mm-‘, which was lmpractlcal mamly because of the cost of the latex This hmltatlon had a marked effect on the experiment because with small glass beads, and a low filtration velocity, the filter was very efficient as a filter, even though Its efficiency as a flocculator was at a controlled, moderate level where

Fhdrsed bed As the same cntenon of small volume flow rate was reqmred, as for the fixed bed, a muu-fluldlsed bed flocculator was used of maximum capacity 4Om1, of which less than half was occupted by the expanded fhudlsed bed The diameter of the vessel was 21 mm with a variable packed bed depth, to give different resrdence The flmdlsed bed media conslsted of ap times proximately 100 pm polyvmylchlonde mlcrospheres, density 1400 kg me3 In a flmdlsed bed the mean velocity gradlent (G) IS provided by the power dlsslpated m flmd drag past the

fluldtsed spheres[9],

and IS given by eqn (12)

where ps IS the density of the fluidned IS the approach velocity of fluldisation

particles

(PVC), 0

K

986 Using the Rlchardson

and Zakl relatlonshlp

J

IVES and M

AL DIBOUNI

of eqn (13)

v = v*c”

1

(13)

1

where v, IS the termmal settlmg velocity of a spherlcal gram, n IS 5 for lammar, and 2 5 for turbulent condltlons, G

l&Y1

=

( or

- E)(& - PII? I’* 1 W

G = K(K’(

S-Serum cop sample pord

(14)

1 - E))“’

(15)

where K

=

(Vt(Ps- Pk P

Dlfferentlatmg dG _=de

G with respect

K “_-l(l -e)]_“‘[(l_ 2 lE

I’*

(16)

>

to porosity

E

E)(n - I)&-*-

En-‘] (17)

The maxlmum value of the velocity gradient G occurs when dG/dr = 0, which can only be met when the term m the second bracket of eqn (17) equals 0 Fig 3 Circuit diagram of fluldlsed bed flocculation apparatus

For lammar condltlons n = 5, l = 0 8, turbulent condltlons n = 2 5, l = 0 6 So the maximum velocity gradlent m a flmdlsed bed occurs when the porosity hes between 0 6 and 08, depending on the flow regime Usmg a porosity of 0 6, to obtain the maximum fiocculatlon effect, the fluldlsed bed gave a mean velocity gradient of 22 s-’ for the 100 +rn polyvmylchlorlde microspheres From eqns (15) and (16), substltutmg Stokes Law for u,,

This shows that G IS directly proportional to d, and, therefore, to obtain G values m the range up to lOs-‘, pvc particles ~45 pm would be requrred for the flmdrsed bed As these were not available at the time of the experiments the value G = 22 s-’ was used Residence times could be varied by using different bed lengths, and the apparatus was incorporated III a clrcult so that suspension could be recycled to give several passes of the fluldlsed bed, thus extending the effective residence times The clrcult diagram IS shown m Fig 3 EXPERIMENTAL

DATA

Suspenston Commercmlly available polystyrene latex microspheres (Dow Chemical) with a peak size of 1 2 pm diameter (see Fig 5, curve 1) were suspended m dlstdled water containing 0 1 M Ca(NOX)* which destabthsed the particles

Partrcle sI.ze analym A Coulter Counter Model T, with variable threshold adapter, was used with a 30 pm ordice The variable threshold adapter enabled any size intervals (as opposed to an instrument preset series) to be used in the 15 counting channels This Coulter Counter will calculate, Indicate and record (on paper chart) either number, weight or volume frequencies This IS an advantageous facility IS flocculation studies, for as the floes grow m size their numbers grow less and the count may not be sensitive enough, but then volumes are important m the flocculation process (See the orthokmettc equations m Ref [51) At one stage the Model T was away for repair, and a Model ZB with Channelyzer was substituted However, although this entailed more mampulatlon of Instrument and data, the results could still be used Couette f?occulation

The followmg velocity gradients were applied to the latex suspension 0, 3 5,5 0,7 5, 10 and > 10 s-’ At zero velocity gradient the flocculation IS penkmetlc, so any changes m particle number and size dlstrlbutlon beyond the value of du/dz = 0 s-l were attributed to orthokmetlc flocculation This concept of addltlvlty of penkmetlc and orthokmetlc ffoccufatlon has been challenged m a rigorous hydrodynamic analysis by Van de Ven and Mason[lO], but the assumption may be sufficient for the present data when other uncertamtles are considered These uncertamtles arise from the sampling procedure from the Couette annular gap, by dipped pipette transfer to a beaker, containing NaCl solution (for the Coulter counting) and brief manual stirring to provide homogeneity This transfer and mtxmg may cause additional

Ortholcmetlc

flocculation

uncontrolled orthokmetlc flocculation After the suspenslon has been dduted m the beaker, it IS assumed that the kmetlcs are so reduced that further flocculation IS mslgmficant Total number reductron Figure 4 shows the reduction m total particle numbers, as flocculation proceeded for 150 mm, with samples taken for Coulter countmg trutlally every 2 mm for IOmm, then every 5 mm up to 30mu1, and finally at 10 mm Intervals until 150 mm, with some varratlons from this pattern The results have been normahsed on the total number ordmate, by dtvldmg the total number of particles, by the uutial total number at time = 0 Due probably to the samplmglmlxmg procedure, the mitml total numbers varied from experiment to experiment within a range around the mean of +8 0% to -12 5% As was expected, the higher velocity gradients wrth the exception of du/dz = 10 s-l, which may be due to the produced progressively more rapid normahsatlon, flocculation The orthokutetlc flocculatlons each tended to a hmlt number of particles, probably estabhshed by the shear strength of the aggregates These equihbrmm values were not determmed, as it would have reqmred more than 150mm of flocculation At such long times some particles seem to be lost from the system (see Fig 7), mamly by sedlmentatlon, which has been subsequently confirmed by usmg neutrally buoyant particles to elurunate sedlmentatlon effects Some particles may have been also lost by adherence to the flocculator walls, so m either case any conclustons would be doubtful from long flocculation times Frequency drstnbutlons Usmg the Coulter Model Za with Channelyzer, the differentsal frequency dlstnbutlon of Fig 5 was obtamed This IS one of several such dlstnbutlons, and Illustrates

of latex nucrospheres

987

well the almost monodlsperse nature of the orlgmal latex (hne 1, actually going off-scale) centred on 1 2 Frn diameter Samples taken at successive times of flocculation (lines 2 and 3) show very clearly the reduction m smgle particle numbers, and the progressive rise In the numbers of doublets (around 1 5 pm) and an increase m triplets at around 1 7 to 1 8 pm Cumulative weight frequency dlstrlbutlons normahsed to lOO%, are shown on Fig 6, for velocity gradients of 0, 5 0 and 10 0 s-l, with various flocculation times up to 156 mm The move to the right of the dlstrlbutlons shows a progressive coarsening of the size range due to flocculation Total volume of particles Although the total number of particles will reduce due to flocculation, the total weight (or mass) should be constant as no particle matter IS created or destroyed However, It has been a matter of conjecture as to whether the total volume remams constant, as It IS known that non-coalescmg floes entram water mto the floe structure mcreasmg their geometric volume The total volume of particles during flocculation at the various velocity gradients 0 to 10 SK’ IS shown on Fig 7 After an mltlal period of approximately constant voIume, the total volume actually decreases with time, the effect bemg mcreasmgly apparent with Increased velocity gradlent The slgmficance of this wrll be discussed, although already reference has been made to the loss of particles due to sedimentation Fured bed Jlocculatron As shown m the design of the fixed bed flocculator an approach velocity of filtration of 0 1 mm s-l gave a mean velocity gradlent m the filter pores of 10 s-l, and a residence time of 80 s

10

0

20

40

60

80

Tme.

l+g

4 Observed

residual total number of particles, Rocculatlon time for various velocity

loo

120

mm

as a function of orlgmal total number, gradients m the mml-Couette flocculator

as a function

of

988

K

Ag

5 Observed

J IVESand M

AL D~OUNI

trace of number frequency of latex partrcles as a sue dlstnbutlon, at three successive flocculatron, showmg appearance of doublets and trlplets

times of

devised to separate these effects, particularly, attempts to make the glass beads non-retaining by electrical double-layer repulsion. also InhIbited flocculation by the same effect The change m cumulative size dlstrlbutlon after 80 s residence time m the pores, can be seen on Fig 8, but the coarsenmg of the dlstrlbutlon IS shght, and the reltablhty of the data IS doubtful due to the low numbers m the filtrate After several unsuccessful tnals to separate the filtration and flocculation effects, the fixed bed expenments were reluctantly abandoned Flurdlsed bed fiocculatlon

G-100

Slzc

s-’

-

p-n

Fig 6 Observed cumulative weight-aze dlstnbutlons, becommg coarser wtth mcreasmg flocculation times, more accentuated at higher velocity gradients These expenments of passmg the latex suspensions through the fixed bed were frustrated by a large retention of parttcles by the glass beads, so that reductions m numbers of particles m the filtrate could be attnbuted to filtration, flocculation, or both No techniques could be

The fluldlsed bed flocculator contammg 100 pm pvc mtcrospheres at a porosity of 0 6, gave a mean veioclty gradtent of 22 s-l The residence ttme was vmed by using two different bed lengths correspondmg to 1 mm and 5 mm with a smgle pass of the latex suspension Figure 9 shows the change m cumulative particle size dlstnbutlon, with a very slight effect for 1 mm, but much more pronounced at 5 mm On the 5 mm curve, uutlally 10% were coarser than 3 pm (IO-fold particles), whereas after 5 mm fluldlsed bed flocculation 10% were coarser than 5 pm (45-fold particles) t By recycling the suspension, residence times up to 25 mm could be achieved, I e five passes of 5 mm each At each pass the size dlstnbutlon was measured, and ts shown cumulatively on Fig 10 where the progressive coarsenmg can be seen Also on Fig 10 IS a dtierentlal volumetnc frequency showing the presence of 230-fold aggregates (8 5 pm diameter) after 25 mm There IS some progressive

tin these fluldlsed bed expenments the pnmary latex particles were measured as 14 Nrn, due to changes of Couker Counters, whereas they were prevtously aven as 1 2 pm Thrs mdlcates some unrehabthty m the absolute size, but there LS no reason to doubt relative sizes

loss

of particles

from

suspension

attributed

bed particles Possible flocculation effects attnbutable to the pump and pipe flow were not mvestlgated, but they would cause some unrehablhty m the data by addtng additional velocity gradient and residence tune effects to the orthokinetic flocculation to

some

adherence

to

the

pvc

fluldlsed

Orthokmetw 36-

I

i

I

I

flocculation I

w‘0 x

24

,

989 I

I

I

__--____---_

----______’ _-

I

of latex nucrospheres I

I

___

---\

-

x: 2 $“B g

3 e e E

P6-

\

-,75s-’ \

K-

____

.

\

-_

100 s-’ \

am 4I IO

0

I 20

1 30

I 40

I 50

I 60

I 70

I 90

I 60

I 100

I 130

I

I

110

120

140

Time. mm

Fig 7 Observed

total volume

of latex parttcles as a functlon

of flocculation

time, at various

velocity

gradients

G= 21 9 6’ t = I mm I - Inlet 2 - outlet

Rg

8 Observed cumulatwe after filtration wth

weight-we a resrdence

dlstnbutlon before and time of 80 set

DISCUSSION

Paftuzle sue analysis The Coulter Counter has produced number-size, weight-size and volume-size frequency d&nbutlons which show the progressive aggregation of particles from the uutlal monodlsperse suspension An mterestmg feature of the results has been the ldentlficatlon of the doublet and tnpIet formatlon of Rg 5 With the smgle particle diameter at 1 2 pm, and usmg eqn (7), r, =

1’f3r,

or

d, = t”3d,

Consequently

dZ=2”3x12~m=15~m

and

d~=31’“+12~m=17~m

closely with the observed This corresponds very diameters of Zfold and 3-fold particles However, eqn (7) assumes coalescence of the particles when flocculated, which could not be true for the sohd latex mlcrospheres It must be concluded, therefore, that the Coulter Counter only measures the solid volume of the aggregates, and any included water 1s not measured This

t=5 mln

0

I

2

3

4

5

6

7

8

9

IO

II

12

Fig 9 Observed cumulative weight-size dlstnbutrons before and after fluldlsed bed flocculataon. with residence hmes of 1 and 5 mm single pass

seems reasonable consldermg the mob&y and small size of the Na’ and Cl- ions carrymg the current m the Coulter onfice, for they would pass through the included water as readily as through the external water round the aggregates Further evidence 1s provided by Fig 7 where the total volume of the particles remams constant dunng ffocculatlon (before sedlmentatlon removes some of the

IVES and

K J

990

M

AL DIBOUNI

comcldence countmg (passage of two particles slmultaneously), which IS made mslgmficant by usmg appropriate dllutlon of the suspension The questlon of the slgmficance of Coulter Counter data for floe size was raised by Camp in 1%9[11] who also surmised that only the sohd volume was bemg measured G=21 7 s-’

Flocculation

The perlkmetlc flocculation curve (G = 0 s-‘) on Fig 4 indicates a halvmg-ttme tl12 = 65 mm, or 3900 s From eqn (4)

t

3cL Ii2 - 4kTNo (4)

No=&-

I II

Size

12

j.Lm

Rg 10 Observed cumulattve waght-srze dlstrlbutmns after varmus residence times m a fluldlsed bed flocculator, multiple

pass

larger

Lower chagram

volume frequency-size dlstrlbutlons IO and 25 mm d fluldlsed bed flocculation

aggregates)

measured,

If

included

water

were

also

at 0.

to

be

there would be an apparent Increase m total volume during flocculatton as more water IS included m the larger aggregates Consequently, the Coulter Counter only measures the total solid volume m an aggregate, and, by its normal data analysis, reports the diameter of a sphere of equal volume to that total solid volume With this knowledge, and usmg eqn (7), It can be seen on Fig 6 (G = 10 0 s-l) that after 120mm there are 10% by weight of particles greater than 8 pm diameter, correspondmg to 300-fold aggregates These cumulative weight frequency observations have indicated the presence after mini-Couette flocculation of particles of at least 14 pm diameter, correspondmg to 1600-fold aggregates The envelope diameters of the aggregates must be greater than the Coulter Counter reported diameters, and If the envelope diameters were measured by other means, e g by Royce Counter, or by mlcroscoplc exammatlon, the volume of included water (I e the porosity) of the aggregates could be calculated At the present time, the porosity of floes 1s very difficult to measure without dlstortmg or destroymg the floe structure It has been argued that the passage of floes through the Coulter Counter orifice (30 pm diameter m thrs study) could disrupt the floes during measurement However, as the Coulter Counter only measures the sohd volume It IS Immaterial whether the floe IS whole or m two or more parts, as long as the parts are m the orifice measurmg zone simultaneously This IS slmdar to the problem of

L/Z

At 2O”C, p = lo-’ kg/m s, T = 293 K, therefore No = 5 0 X 1CP particles/m3 = 5 0 X 10’ particles/ml The total number of particles reported at time = 0, IS 17 3 x lo4 particles, which was m a measured volume of 0 05 ml Therefore, the concentration m the beaker of the Coulter Counter was 3 46 x lo6 partlcleslml, but this had been diluted 76 times with sahne solution, so the original particle number concentration m the mm&ouette flocculator was 2 63 x 10” partlcleslml This compares reasonably with the number (5 0 x 10’) predlcted by the perrkmetlc halving-trme eqn (4), consldermg the sensltlvltles of number concentrations to samplmg, ddutlon and Coulter Counting Unfortunately, it ts not possible to check the orthokinetic equations with the Coulter Counter data, because they are based on the colhslon radu of the particles As the Coulter Coulter radu are the equivalent sohd volume radn, and the colhslon radn are slgmficantly greater due to Included water (I e the geometry of packmg of the aggregated spheres), no direct comparison would be valid The trends of orthokmetlc flocculation are consistent, with higher velocity gradients and longer flocculation times producing more flocculation, but quantitative comparisons must await further data on the porosity of flocculated aggregates The fixed bed flocculation experiments were frustratmg due to the strong filtratton effect and only a shght flocculation effect could be detected However, flocculatlon appears to be lmphclt m the results, as It IS wellestabhshed[l2] that 1 pm IS the least filtrable size of particles Yet filtration was extremely effective, probably due to particle aggregation by the velocity gradients m the filter pores Research at Delft University, Netherlands, IS using the change m filter efficiency due to size dlstrlbutlon changes, as a measure of flocculation wtthm filter pores usmg latex suspensions [ 131 Theoretical studres using Smoluchowskl kmetlcs and filter theory equatlons have already established that the changes should be slgmficant and detectable Fhudlsed bed flocculation was successful although no direct comparison with the mml-Couette velocity gradients was possible due to the restricted size of the pvc fluidised bed particles Flocculation was carried out

Orthokmetic flccculatron of latex rmcrospheres

at near optimal expanded porosity (0 6), but contmumg research will test whether this IS truly opttmal, and whether flocculation performance IS sensitive to porosity varratlons Also other fltudlsed bed particles WIU be used to obtam velocity gradients less than 22 SK’ Other forms of flocculator are bemg studied. such as a hellcat capfflary, and bubble flocculators The prmclpal techmcai objective of these studies IS to produce good laboratory techniques which could be Introduced mto water treatment control, and to gam insight mto the flocculation process wlthm flmdlsed Rot blanket clardiers, to complement the hydrauhc performance and stabdlty studies which have been already completed CONCLUSIONS (1) Polystyrene latex approximately 1 pm diameter, forms a nearly monodisperse suspension in water, very suitable for fundamental flocculation (2) The Coulter Counter Model T with vmable threshold adapter, usmg a 30 pm or&e, IS a good mstrument for followmg changes m size dlstnbuhons durmg flocculation, and up to 16OCLfold aggregates have been detected However, only the sold volume of aggregates, and not included water, IS measured (3) A mnu-Couette flocculator conslshng of vertical axis co-axial cyhnders contams lammar flow at Its destgn rotational speeds The bottom end effect IS resticted to a height from the base of about 3 x annular gap, which comprises about 7% by volume of the flocculator (4) At velocity gradients up to 10 s-‘, both penkmetic and ortholunetlc flocculation have been demonstrated, with reductions of up to 90% m total particle counts after 150 mm The perikmetlc flocculation results compare reasonably with theoretical predictions of number concentrations (5) Indlcatlons of flocculation m the pores of a mlm-

CES Vol 34 No ‘l-l=

991

filter were gwen by a coarsenmg of the size dlstrtbutions of the filtrate compared with the mlet However, a high filter retention masked detaded and reliable assessment of any flocculation effect (6) A fluidlsed bed of 100 pm pvc spheres was used at optunum (for flocculation) porosity of 0 6, g~vmg a velocity gra&ent of 22 s-l With residence tunes of 1 and 5 mm for single pass, and up to 25 nun for multiple pass recycling, orthokmetic flocculation was observed with up to 23@fold aggregates bemg formed Acknowledgements-This study was financed by Science Research Councd Grant FJ/RG/2181Fmre 2. and 1nformatlOn On the mm&ouette end effect and Taylor voruces, were kmdly suppbed by Dr T P Elson (Pubhc Health Engmeenng, Unlverslty College London) RRFERRNCRS

[I] Van Duuren

F A, J San Engng lh (Pmc Am Sot CIO Engrs) 1968 94 (SA4) 671 121Ives K J and Bhole A G , Wuter Reseurch 1975 9 1085 131Ives K J and Bhole A G , Wder Rewurh 1977 11209 [4] Smoluchowskl M von. Zdschr Pi~ys Chem 191792 129 [5J Ives K J , In 7Xe Saentrfic BUSIS of Floccuhtwn (Edrtcd by Ives K J ) NATO AS1 Seres SlJthOff & Noordhoff, Alphen a/d RIJII. Netherlands. 1978 [6] Ives K J and Bhole A G . 3 Enuwvn Engng &I (Pmc Am Sot CIU Engrs) 1973 99 (EEI) 17 [7l Taylor G I, Phd Tmns Roy Sot 1923 223A 289 [8] Ives K J , Cnt Reu m Envrmn. Cot& 19712 293 [9] Ives K J , Z+uc Znst CIV Engrs 196839 243 [lo] Van de Ven T G M and Mason S G , CoUouiundPoiym Sci 1977255794 [l I] Camp T R , I San Engng hr, (Proc Am Sot Cw Engrs) 1%9 9s (SA6) 1210 [I21 Ives K J , In 27~ Scren@c Basu of Filtralwn (Ekhtd by Ives K J ). NATO AS1 Senes Noordhoff. Leaden 1975 [13] Vreeken C , Personal commumcatron Laboratory of Chem~cal Technology. Umversdy of Technology, Delft, Netherlands 1977