Physical aspect of flocculation process—II. Contact flocculation

Physical aspect of flocculation process—II. Contact flocculation

Haler Re.search Vol. 13. pp. 441 Io 448 Pergamon Press Lid 1979. Printed in Great Britain. PHYSICAL ASPECT OF FLOCCULATION PROCESS--II. CONTACT FLOCC...

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Haler Re.search Vol. 13. pp. 441 Io 448 Pergamon Press Lid 1979. Printed in Great Britain.

PHYSICAL ASPECT OF FLOCCULATION PROCESS--II. CONTACT FLOCCULATION NORIHITO TAMnO Department of Sanitary Engineering. Faculty of Engineering, Hokkaido University, Sapporo. 060, Japan and HrrosFrl HOZUMt Department of Civil Engineering. Muroran Institute of Technology, Muroran, 050, Japan

(Received 4 October 1978) Ahmraet--Kinetic equations which describe the process of contact flocculation in solids contact elarifiers were proposed. Decrease of micro-floes with the comact of high concentration and large diameter welt-grown-floes both in a turbulent flocculation chamber and in a floc blanket of upflow clarifier were discussed. First order equaiions with the micro-floc concentration were derived theoretically for both types of contact floc~ulation. By experiments, these kinetic equations were verified and their coefficients were evaluated. Finally, practical equations for the design of micro-floc removal process with the contact of wellgrown-floes both in a turbulent flocculator and in a floc blanket were proposed.

I. INTRODUCTION

of the grown-floes gives high GCT-values as was

In the preceding paper Tambo & Watanabe (1979)

reported in a previous paper (Tambo & Watanabe, 1979). Thence, it is possible to use upflow clarifier with higher overflow rate.

proposed a kinetic equation of fiocculation process evaluation and design charts of the process under a turbulent agitation condition. In this paper, the authors would like to discuss an application of the above treatise to contact flocculation operations, Contact flocculations can be characterized as a mode of flocculation in which larger well grown floc partides adsorb incoming minute fiocs onto the surface. For convenience sake, in this paper, the former is designated as 'Grown-floe' and the latter as "MicTofiOC". This process is typically seen in solids contact clarifiers and partially seen in conventional fiocculator with back mixing flow. In this paper discussions are concerned with the process in solids contact claritiers, In the solids contact clarifiers, well grown large floc particles, i.e. the grown-floc, of high concentration are circulated in a turbulent flow field or suspended in an upflow stream. Then, the collisions and aggiomeration between the grown-fiocs and the incoming micro-flocs occur. Through the collisions between these two kinds of floes which have greatly different floc size, adsorption like fiocculation occurs. Therefore, this flocculation can be dealt as a sort of adsorption of the microofiOCS onto the surface of the grownfloes, Through the existence of the grown-floe with high concentration,duration of flocculation operation can be shortened remarkably. In addition to this, the result of the fiocculation gives usually the final equilibrium floc size distribution under the agitation intensity, because the existence of a high concentration

In this paper, both contact flocculation under turbulent agitation fields and that in fluidized bed of the grown floe, i.e. floc blanket, in upflow clarifiers are discussed.

441 W.R. 13 5--("

2. EQUATIONOF CONTACT FLOCCULATION UNDER TURRULENT AGITATION As mentioned above, size distribution of the grown floes generally reaches the final equilibrium size distribution. Then, floc sizes are distributed, approximately ranging between the maximum floc diameter attainable under the agitation intensity, and a half of the maximum diameter as has been shown in the preceding paper (Tambo & Watanabe, 1979). In practice, the maximum floc diameter in a turbulent fiocculation chamber of solids contact clarifier is usually about 3 to 5 x I0 -2 cm~ On the other hand, incoming micro-flocs are considered to be in the range of about 5-20/~m. The contact flocculation occurs between those two floe groups with greatly different floc diameters. The number of collisions between the grown-floes and microoflocs per unit volume per unit time, F, can be described as equation (1) which is derived from Levich's equation (1962) modified by Tambo & Watanabe (1979). 12 n / ~ f D d) 3 F -- .~/~_~ ~/~-\-~ + ~ Nn, (1)

442

NORIHITO TAMBO and H r r o s m HOZUM!

where, Co: effective mean rate of turbulent energy dissipati°n [ e r g c m - 3 s - ~ ] " /~: abs°lute viscosity [ g c m -1 s - l ] . D and d: mean diameter of the grownfloes and the micro-floes, respectively [cm], N and n: numbers of the grown-floes and micro-floes per unit volume, respectively Ecru-3]. An equation which describes the process of contact flocculation can be derived from equation (1) as equation (2) by taking the following conditions into account. (a~ The grown-floes are in the final equilibrium (ultimate) floc size distribution. Then, the collisions between the grown-floes are not effective for the flocculation. (b) Collisions between micro-flocs are performed with a collision diameter of d. The collision diameter d is much smaller than the collision diameter between the grown-floes and micro-floes, i.e. 1/2(D + d). Therefore, in practice, the collisions between the micro-floes are considered to be negligible in respect of the collisions between the grownfloes and micro-flocs for the progress of contact flocculation. (c) Because of the great difference of diameters between the grown-floes and micro-flocs, the collision diameter between these floes can be written as 1/2(D + d) ~- 1/2.D. (d) Conditions of D ,> d and ND3>> nd 3 generally hold. Hence, relative rate of the floc volume increase with flocculation time is small. Therefore, the floc volume is usually kept constant by means of a suitable way of adjustment, i.e. draw off. Thence the condition of VI ~ ND 3 -:--const. can be assumed. (e) Among F collisions between the grown-floes and micro-floes, /SF collisions are effective for the flocculation. -

~

9 ~ ND3n - - \ -15 - p

On . 2\ 3n15 P ~17 "--

Vrn, (2)

where, VI: volumetric concentration of the grownfloes [ - ] , Vs = ~/6' ND 3, if flocs are assumed to be spheres, t: flocculation duration Is], P: mean collision-agglomeration factor between the grown-flocs and micro-ttocs [ - ] . From equation (2), the contact fioccalation can be characterized as first order reaction with regard to n. The rate constant is proportional to \ / ' ~ . Vf. This means, the progress of the contact flocculation is also defined by GCT-value as proposed in the previous paper (Tambo & Watanabe, 1979), where, G, C and T denote \ ~o/#, and volumetric concentration of floes, and detention time of flocculation, respectively. This first order flocculation function with n can be written as equations (3) and (4).

dt K = " -n 9 _ K~, =

--P,

n = no at t = to as equation (5). n (\~(~PVyt) -- = exp = exp(-Kclt). (5/ n° The ratio of flocculated micro-floes is written as equation (6), r = 1 - --=n 1 - e x p l - K~t), t6) no where, no: number of the micro-floes per unit volume at the initial state t -- 0 Ecru-3], r: ratio of flocculated micro-floes at time t I--'1. The number of micro-floes per unit volume is proportional to the turbidity of the micro-floc suspension T*. Thence, the relationship of n/no = T*/T~ holds. Therefore, equation (5) can be rewritten as equations (7) and (8). log~o(T*/T~) = - K ' ~ t (7) 9- - l o g l o e P , ~ eo//~- Vy, (8) ~, 15 where, T*: turbidity of the micro-floe suspension [T.U.], To*: turbidity of the micro-floe suspension at t = 0 [T.U.]. K'c~ = Kcl logtoe =.

3. EXPERIMENTAL VERIFICATION oF THE EQUATION OF CONTACT FLOCCULATION UNDER TURBULENT AGITATION AND ESTIMATION OF THE MEAN COLLISION-AGGLOMERATION FACTOR To verify the above equations, bench scale batch contact flocculation experiments were performed. Two kinds o f p a d d l e flocculators as shown in Figs. 1 and 2 were used. Fioc volume of the grown-flocs was calculated by photographed floc diameter distribution in a volume of suspension after equation (9). =--~-I--~-D~ VI ~A . f 6 ' (9) ~5o

[

o ~

.:

(3) eo/ta'Vf,

[1

!

:1:: ,.,q

i

\A¢itanon ~e

!o

/.~.i..t.i!~ , i ' .: 1,.:, ! i~ . :, ,

(4)

where, K~t: rate constant of the contact flocculation under a turbulent agitation condition, This equation is integrated under the condition of

~-~

"--g-'~-'*-"";I \ /

TramspGren~/

front

Front view

Fig. l. Flocculator Type I.

Side view

Physical aspect of fiocculation process--II .A0mtio, blocle ~

i

tor. (b) Kaolinite clay, flocculation aids and pH control agents were added to the water with rapid mixing• Then, coagulant (Alum) was added with rapid mixing for five minutes. (c) After this, 40 rain of slow flocculation agitation was applied to bring floes into the final equilibrium floc size distribution• Then, the final floc size distribution was photographed to calculate the fioc volume concentration VI. (d) To the grown-floe suspension, the micro-floes which had been made in another fiocculator (jar tester) was added quickly• (e) With various flocculation time, the contact flocculation was performed. Then, after several minutes of quiescent settling, the grown-floes settled out and only unflocculated micro-floes remained in the supernatant. (f) The supernatant was siphoned and its turbidity was measured.

~=

__

T [ o

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,

I"1 -10

=*

i[

T ~

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-co~ S ~

:,, •-'~ii

="

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443

The

"-

results

of those

experiments

are

shown

in

where, V$: volume concentration of the grown-floes [ - ], A : photographed area [cm=], f: focus depth of the photography [cm], Di: measured floc diameter

Figs. 3 to 6. Figure 3 shows the relationship between the microflOC concentration and the contact flocculation time in respect of various flocculation intensity and volume of the grown-riots experimented in the fiocculator. Figure 4 shows the same results in the flocculator II. Both of the experimental results show the linear decrease of the micro-floe concentration with the floeculation time on the semi-logarithmic plot and verify

[cm].

the r e l a t i o n s h i p o f the a b o v e m e n t i o n e d

The experiments were carried after the following procedures with various combinations of volume concentration of the grown-flocs and the rate of agitation blade rotation. (a) Tap water was filled in a floccula-

Figure 5 shows the relationship between floc volumes of the grown-flocs and the rate constant of the first order contact flocculation equation in the flocculator II with fixed rate of agitation blade

,~ Front view Slde view Fig. 2. Fiocculator Type ll.

3O 20

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II

2

3

4

5

~

2

3

4

5

g

2

3

4

5

6

Agitation duration t,

rain

Fig• 3. Relationship between the micro-floe concentration and flocculation time. With Type l flocculator•

l

/

vf ,0.2-0.4%

50 =

3o

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2

4

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10 2

4

6

8

Agitation durotion t.

I0

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I 2

I

I

I -I

4

6

rain

Fig. 4. Relationship between the micro-floe concentration and flocculation time. With flocculator.

Type l I

444

NORIHITO TAMBO a n d HITOSHI HOZUMI

~0

I

I

I

I

4"0

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~

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l=

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I0 I I I t 3 4050

5

Rote of imDeller bloOes rOtoTion Floc volume concentrotion

V~,

%

Nr,

rev rain H

Fig. 5. Relationship between the rate constant and floc volume,

Fig. 7. Relationship between total mean turbulent etmrgy dissipation ~. and rate of agitation blade rotation Nr.

rotation at 20 rev m i n - i . The result shows the rate constant Kct is proportional to the volume of the grown-floes. Figure 6 shows the relationship between the rate of agitation N r revmin -1 and the value of K',t/'VI on the logarithmic paper. These plots show the value of K'ct/V I is proportional to the 3/2 powers of the rate of impeller blade rotation Nr. The mean rate of energy dissipation in a turbulent flocculator is known as proportional to the third powers of Nr and this relationship is also hold in this case as Fig. 7. Thereafter, the relationship that K',~/V I is proportional to the 1/2 power of the total mean rate of energy dissipation E, as has been anticipated from equation (SL is proved.

The value of e, was measured by the torque meter method after equation (10). To.~ % = Vr , (10)

:f .... ,o

,o

~t-

9/-

~

collision-agglomeration factor t' is necessary to evaluate. The mean collision-agglomeration factor/3 between the grown-floes in the final equilibrium size distribution and the micro-floes can be calculated from the collision-agglomeration function ~ which was proposed in the previous paper as equation (II) by

zI

#

i

Tambo and Watanabe (1979L~ (

:i .... ~

~o ~

,

~o

,oo

Rote of impeller blades

rotation

Nr,

i

4 ;

i

~r to° "~ ~:

rev rain-~

where, ~, : total mean rate of turbulent energy dissipation in a flocculator [ergem 3 s - t ] , T: torque of the agitation blade axis [g.cm], co: angular velocity of the agitation blade r o t a t i o n - - 2 x N r [sec-t-L Nr: rate of agitation blade rotation [r.p.s.], Vr: water volume of the flocculator [cm3]. The mean effective rate of turbulent energy dissipation ~o is considered to be proportional to t h e t o t a l dissipation rate ~o as e, - ~o. From the above mentioned experimental results, the basic equation of the contact flocculation is considered to be acceptable. For a quantitative appli-

/

,o-Z

,o

i

,

~ io ~'o

i

,oo

Ra*e of impeller blades

rotationNr,

rev rain-~

Fig. 6. Relationship between K',.t/V I and rate of agitation blade rotation Nr.

P=:~o

X,

1

R ) 6,

s+i

(ll)

where, ~o: initial collision-agglomeration factor depending upon the coverage of the coagulant onto the primary particles I--], R: number of the primary particles contained in a grown-floe under consider-

Physical aspect of flocculation process--lI

445

Table 1. Estimation of P. Sffi50

Sffi 75

l-s+--- ~ x. 1-~-~-/

e

x.

6-10 11-15 16-20 21-25 26-30

0.02 0.10 0.28 0.32 0.20

0.84 0.75 0.65 0.55 0.45

0.008 0.090 0.022 0.010 0.003

31-35

0.08

0.35

--

P ffi ao ~ Xa 1 -

e

x.

1-10 11-20 21-30 31-40 41-50

0.01 0.06 0.33 0.41 0.18

~- 0.021

P ffi ~o ~ Xa 1 -

l-s--g- / x. l - ~ - T i 0.93 0.80 0.67 0.54 0.41

0.007 0.016 0.032

0.011 0.001

-:- 0.022

* where, ao .~ 1/3. ation [ - ] , S: number of the primary particles contalued in a maximum size floc under a given agitation intensity, Xa: weight ratio of R-fold particles in the grown-floes which are reached to final equilibrium size distribution, By using the final equilibrium fine size distribution calculated by computer simulation of ttoc growth process of Tamho and Watanabe (1979), the mean collision-agglomeration factor P can be estimated after equation (11). Examples are shown in Table 1. These results show that the value of P is about 1/45. The mean collision-aulomeration factor P can also be estimated by the experimental data such as shown in Figs. 6 and 7 and equation (4). For the estimation, the value of the total mean dissipation rate of turbulent energy e. which was experimentally obtained as shown in Fig. 7 should be rewritten by the effective mean rate Eo. Although it is known that the value eo is proportional to e,, the proportionality constant is dependent to the turbulent flow patterns. Therefore, in this case, as the first step in the discussion, the relationship is assumed to be • o # (0.1 ~ 0.2)~o after several experimental data which show 65-85% of the total energy is consumed in the near vicinity of agitation blades and more than several percent is consumed at the surface boundary of the vessel wall where flocculation is not effectively performed, Examples of this estimation method for the evaluation of the mean collision-agglomeration factor are

shown as Table 2. The results show P is in the range of (2.8-1.9) × 10 -2, i.e. 1/36-1/53. The mean of the estimated value almost coincides with the value of 1/45 which is estimated by the equation (11) under the assumption of the final equilibrium floc size distribution of the grown-floes in a contact flocculator. Then, the relationship between e, and ee in the experimental flocculator could be assumed that e0 is about 15% of e,. From the above discussion, a practical equation of the contact flocculation in a turbulent flocculator is given as equations (12) and (13). dn - 1 --ffi N/:~ V/n = - K c l n (12) dt 5~:/1"5 Kcl ffi 1/5x/~" ,v/e0/'---'P. (13) 4. EQUATIONOF CONTACT FLOCCULATION IN A FLOC BLANKET In a floc blanket of an upflow clarifier, the microfloes entering into the floc blanket from the bottom contact and agglomerate with the suspended grownflocs. This is another type of contact flocculation from the one in a turbulent flncculator. Decrease of incoming micro-flocs by the contact flocculation with the passage through a blanket can be formulated as equation (14) under the following assumptions. (a) Grown-flocs with mean diameter of

Table 2. Estimation of the mean collision-agglomeration factor P from experimental data of energy ¢omumption rates and decrease of the micro-floes in the contact flocculation. S [rev min -~ ] 25

30 35 40 where, P -.

e.

~o ffi (0.1--0.2)¢.

K'c]/V:

[ c r g c m - 3 s -1 ]

[ e r g c m - 3 s -1 ]

Is -1 ]

[-'1

4.2 x 10 ° 7.7 x 10°

(4.2-8.4) x 10 - I (7.7-15) x 10-1

1.8 x 10 -5

(2.8-1.9) x 10 -2

1.3 x 101 1.9 x 101

(1.3-2.6) x 10° (1.9-3.8) x 10°

2.4 x 10-1 3.1 x 10-I 3.9 x 10-I

(2.7-2.0)× 1 0 - 2 (2.7-1.9)× 1 0 - 2 (2.8-2.0)x 10-2

(K~,IV/)I(91x/-i-5"x/e~)

== ( K ' d / V $ )/(logsoe'9/~/15'

pffiO.Olgcm

- I s -1.

x/Co~p)

446

NORIHrro TAMBO and HFFOSHIHOZUMI

D are suspended statically in an upflow of velocity V,. (b) Micro-floes with diameter of d move upward with upflow of velocity V, without slipping. (c) Collisions of the two kind floc particles with the diameter D and d in an upflow occur by a relative approaching velocity V, and a collision diameter of /~(D + d). Where,/~ denotes collision efficiency of these particles, (d) Collisions between the micro-floes are negligible for the flocculation and between the grown-floes are ineffective for. (e) Collision-agglomeration factor x is considered. ---_

_

dn dt

71

2

-~qVs(D + d)2Nn = - ~ q V , D Nn, 4

Progress of the contact flocculation in a floc blanket is characterized as the first order reaction with the micro-floc concentration n. The rate constant of the flocculation K¢, is determined by these three parameters such as the suspended grown-floc diameter D, its volumetric concentration Vs, and the flocculation coefficient q. 5. EXPERIMENTAL VERIFICATION OF THE EQUATION OF CONTACT FLOCCULATION IN FLOC BLANKET

d ~ D, (14)

To verify the above equations and to estimate a value of the flocculation coefficient q, a series of experiments were carried out by a pilot scale upflow claritier with variable depth floc blanket as shown in Fig. 8. The capacity of the plant is 2.5 m 3 day - t when the overflow rate of the floc blanket type clarifier is set at 6 cm m i n - ~. Kaolinite clay suspension was coagulated by alum at neutral pH. Created micro-flocs were introduced into the upflow clarifier from bottom of the blanket with or without flocculation. The diameters of incoming micro-floes d are about 2 x 10-3.cm to 8 x 10 -3 cm and in the order of 10-'*cm with and without preceding flocculation, respectively. This inflow suspension to the bottom of floc blanket was passed through a perforated baffle bottom to minimize floc blanket disturbance induced.

where, n: number of the micro-floes per unit volume in the upflow [cm-3], t: contact time [sl, D,N: diameter and number in unit volume of the suspended grown floes consisting floc blanket, respectively [cm'] and [cra-a'], q: flocculation coefficient = atfl [ - ] . This equation is the same type of the Camp's equation for flocculent settling (Camp, 1945). Equation (14) can he rewritten as equations (15) and (16) to show the decrease of number concentration of the micro-floes with the distance traveled from the blanket bottom, d.

dz = -

qDZNn = -y}q ~ n = - K c z n Kc2

(15)

VI ~ qD2'S

=~qv":

(16)

where, z: distance from the blanket bottom [cm], dz = V,dt, Vs: volume concentration of floes in the

The depth of the floc blanket was changed by adjusting the height of a floc blanket weir. Experiments were carried out with combinations

floc blanket [ - ] . This equation is integrated under the condition of n -- no at z = 0 as equation (17). . n . . T* . no T~

e x p ( - Kc2z)

of various floc blanket depth and upitow velocities (overflow rates). Figure 9 shows relationships between turbidity of the clarifier overflows and depth of blankets with respect to each combination. The initial turbidity was 20 T.U. In cases of combination A, B, C and D, their higher upflow velocity gave carry overs of the suspended grown-floes with such shallower floc blanket depth as the experiments. Thus, only the cases of upflow

(17)

or

logto(n/no) = loglo(T*/T3) = -K',2z K~2 = Iogtoe'K,2.

Heacl tonl~

(17') (18)

F'lash-m,xer ~) ~

Flocculotor "

.

Overflow orifice : . Variable '.

i

height

floc blanket weir

Perforatect baffle eaffle

Kaolimte solution

reservoir

ThicKner"~ overflow

i);,~:.:~;.

Thickner Fig. 8. Schematic diagram of the pilot plant with floc blanket type clarifier.

Physical aspect of flocculation process--lI

24

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V~cmwdn'e)I

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\"

2o

b~

t~

~

o

¢

3

[ Symbol | A l B J C I D I E IF I G I H

F

Nr:rote of flocculotio~ blode rofotion

~

2

~

x

' I0

5

I' ,,m, / 01'0t o1 1'01 o1"01'0" B~

0

8

2o 2o 8o 2o oo ,o

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~

12

447

20

Jl

50

'' 40

_

,,¢

_

' 50

Depth of flo¢ bloftket L,

2__

_

60

' 70

' 80

cm

Fig. 9. Relationship between floc blanket depth and overflow turbidity. velocity 3 cm rain- ! are used for quantitative discussions, Figure 10 is the replot of the Fig. 9 on the semilogarithmic paper. The case of the micro-flocs without flocculation, i.e. the Case H, gives a good straight line relationship and proves the validity ofthe above mentioned equation of the contact floeculation in a blanket. The cases of the micro-flocs with preceding flocculation, i.e. d - 2 0 - 4 0 / m a , decrease rates of their concentration were very high. Thence, within the 10cm of the blanket depth, reaction of the contact flocculation has almost ceased. However, much thinner floc blanket depth was impossible to keep because o f t h e inflow disturbances. Thus, the decreasing rates are estimated equal to or higher than the rate exhib r e d by the dotted lines. These inclinations give the values of K'~2 such as 0.019, 0.125 or more and 0.132 '

'

'

'

'

'

'

'

'

'

'

so 4o 3o ~ zo ?

~ ~

U \x \\

i o

3

or more in respect of the cases H, F and G, respectively. To estimate the flocculation coefficient q from equation (15) and Kc, values obtained by the above experiments, it is necessary to know the floc volume concentration Vs and the suspended grown-floc diameter D. The grown-floc diameter D and volumetric concentration of the floc blanket at 3 cm min- ' upflow rate were estimated as D .~0.15cm and Vf # 0.30, and, thence, the value of Vy/D is estimated about 1/2. From this value of Vf/D - 1/2 and Ke2 obtained by the above experiments, values of the floeculation coefficients q are about 0.015 for the Case H, i.e. diameter of the micro-flocs is in the order of 10 -4 cm without preceding flocculation, and about 0.1 for the Cases F and G, i.e. diameter of the micro-flocs is in the range of 10-3cm with short period of preceding flocculation. Only a short period of preceding flocculation with relatively intense agitation which enables an increase in the micro-floc diameter from the order of 10 -4 to l O - 3 c m can improve the rate of contact flocculation in a floc blanket more than six times. For the collisions between a discrete suspended grown-floc and micro-floes, the collision efficiency // is theoretically given as equations (19) and (20) (Fuchs, 1964). For potential flow,

~F

2

/$ =

1+

1 + (d/D) 6" 3

.

(19)

G

For viscous flow, o

o

Floc banket depth

zo L,

B~

1+

-~

1+

l

+2(1+(diD))

cm

Fig. 10. Semi-logarithmic plot of relationship between floc blanket depth and overflow turbidity.

=."

(20) 2\D/ "

448

NORIHITO TAMBO a n d HITOSHI HOZUMI

If D and d are assumed such as 0.15cm and 0.004 or 0.0004 cm, respectively. The value of/] for the case of potential flow is about 0.08 or 0.008 and for the case of viscous flow is about 0.001 or 0.00001. By assuming ~ ~-1/3, we can obtain the flocculation coefficient q = ~'tL The values calculated by the case of potential flow are smaller than the experimental value and that of viscous flow are far smaller. However, in practice, none of these discrete grown-floes are existing in the floc blanket. Thence, the estimation of the flocculation coefficient should be performed by an experiment, because no theory can effectively handle the complex floc blanket collisions, From above discussions, it is recommended that floc blanket clarifiers may equip a preceding flocculatot of relatively high agitation intensity which aims to make about 50/~m micro-flocs and of short detention period. In the case, contact flocculation in a floc blanket can be described by the following equation,

incoming micro-flocs, with respect to flocculation time. dn L P //__ -'- __ EO dt " ,, 15 x/ Vf..

dn -d-z -:- -0.15 VIn. D

Through experiments, the relationship was verified and the flocculation coetT'vzient q was estimated. This shows that when a short duration of preceding flocculation with relatively higher agitation which cause around 40-50/zm diameter micro-floes is applied,

(21)

In these cases, in practice, the required depth of a floc blanket is decided after considerations to keep stable floc blanket but not by the requirement to removing the incoming micro-flocs.

By experiments, this first order equation with the mici'o-floc concentration n was verified. And the coUision-agglomeration coefficient P was evaluated. The following practical equation can thus be proposed for the design of a turbulent contact flocculator. d n _. _ 0.05 . I/in. dt For the contact flocculation in a floc blanket, incoming micro-floc to a ttoc blanket from the bottom is decreased their concentration n aRer the following first order equation with the distance traveled. dn d--z= - ~q -~ n.

the following equation can be used in practice. dn --dz"

6. SUMMARY AND CONCLUSIONS Kinetic equations which describe the process of contact flocculation in solids contact clarifiers were discussed. The authors characterized the contact flocculation such as that larger well grown suspended flOes adsorb incoming minute floes onto the surface. As the typical cases of contact flocculation the authors handle the contact flocculation in a turbulent flocculator and a floc blanket of the solids contact clarifier. For the contact flocculation in a turbulent flocculator, the following kinetic equation was proposed to evaluate the decrease of turbidity, i.e. number of the

Vs D

-0.15--n.

Thus, it is considered that in an ordinary floc blanket, the depth required to adsorb incoming micro-flocs are smaller than that to damp out inlet disturbances. REFERENCES Camp T. R. (1945) Sedimentation and the design of settling tanks. Trans. Am. $oc. cir. En#rs ~ , 895-958. Fuchs N. A. (1964) The Mechanics of Aerosols. pp. 15%180.Pergaman Press, Oxford. Levich V. G. (1962) Physicochemical Hydrodynamics. pp. 213-219,Prentice,Hall, Englewood Cliffs, New Jersey. Tambo 14. & Watanabe Y. (1979) Physical aspect of flocculation process--l. Fundamental treatise. Water Res. 13, 429-439.