Coagulation by Al(III) - Advances in Chemistry (ACS Publications)

9 Coagulation by Al(III) The Role of Adsorption of Hydrolyzed Aluminum

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in the Kinetics of Coagulation

HERMANN

H.

HAHN

and

WERNER

STUMM

Division of Engineering and A p p l i e d Physics, Harvard University, Cambridge, Mass.

The

kinetics

of coagulation

of silica dispersions rate of agglomeration quency which colloid

have been studied

destabilized

is a function

is determined

flects the stability been determined

as a function

of chemical

of the dispersed

zation of silica dispersions positively

charged

negatively

charged

ultimately

a reversal

in the

stability

solution

parame-

concentration

phase.

The

rehas and

destabili-

results from specific adsorption

hydroxo colloid

fre-

such as

factor which

This relative

ters such as pH and the ratio of coagulant surface concentration

The

gradients

efficiency

of the colloid.

systems

parameters

and velocity

and (2) of the collision

for Al(III).

of (1) the collision

by physical

size and concentration

medium;

by hydrolyzed

aluminum surface

complexes

onto

causing

a decrease

of sign of the surface

potential.

of the and

* T p h e a g g r e g a t i o n of particles i n a c o l l o i d a l d i s p e r s i o n proceeds i n t w o d i s t i n c t r e a c t i o n steps. P a r t i c l e t r a n s p o r t leads to collisions b e t w e e n s u s p e n d e d c o l l o i d s , a n d p a r t i c l e d e s t a b i l i z a t i o n causes p e r m a n e n t contact b e t w e e n particles u p o n c o l l i s i o n . C o n s e q u e n t l y , the rate of a g g l o m e r a t i o n is the p r o d u c t of the c o l l i s i o n f r e q u e n c y as d e t e r m i n e d b y c o n d i t i o n s of t h e t r a n s p o r t a n d the c o l l i s i o n efficiency factor, the f r a c t i o n of collisions l e a d i n g to p e r m a n e n t contact, w h i c h is d e t e r m i n e d b y c o n d i t i o n s of the d e s t a b i l i z a t i o n step (2).

P a r t i c l e t r a n s p o r t occurs either b y

Brownian

m o t i o n ( p e r i k i n e t i c ) or because of v e l o c i t y gradients i n the s u s p e n d i n g m e d i u m ( o r t h o k i n e t i c ) . T r a n s p o r t is c h a r a c t e r i z e d b y p h y s i c a l p a r a m e 91

Weber and Matijevi; Adsorption From Aqueous Solution Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

92

ADSORPTION F R O M

AQUEOUS

SOLUTION

ters. Particle destabilization is accomplished by different mechanisms of colloid chemical nature (Table I). The purposes of this investigation were to gain a better insight into the means of destabilization by hydrolyzed Al(III)

and to

describe

quantitatively the effect of the physical parameters and of the solution constituents on the rate of agglomeration.

The influence of the p H , the

amount of aluminum dosage, and the concentration of the colloidal phase upon particle agglomeration was evaluated in kinetic terms under con-


trolled transport conditions (temperature, velocity gradient, number and dimension of colloid particles). The results indicate that silica dispersions are destabilized by specific adsorption of hydroxo aluminum complexes (19)

onto the colloid surface.

The physical parameters determine the

particle transport and the collision frequency.

The solution variables,

influencing hydrolysis and specific adsorption of the destabilizing agent, affect the collision efficiency factor. The coagulation rate is given by the product of the collision frequency and the efficiency factor.

T h e effect

of chemical parameters on the transport step, owing to concentration changes which cause slight alterations in the viscosity of the suspending medium, are negligible. In a similar way, the influence of the temperature upon the rate of hydrolysis and polymerization of aluminum has no effect upon the collision efficiency as long as the rate of destabilization is much larger than the rate of transport.

Experimental Colloids. Silica dispersions have been selected for this study because specific physical and surface chemical properties of the silica colloids are well defined and reproducible. S i 0 particles are approximately spherical in shape and can be obtained in several sizes. The relative refractive index of amorphous silica particles with respect to various suspension media is described in the literature. T h e colloid chemical properties of silica in first approximation are similar to those of clays and of other solid material present in natural waters. The surface potential of silica colloids is negative within neutral p H ranges. The potential becomes increasingly negative when the p H is raised. T w o types of silica were used: Ludox L S ( E . I. DuPont de Nemours and C o . ) with an average diameter of 15 m/n for experiments under perikinetic transport conditions and M i n - U - S i l 30 (Pennsylvania Glass Sand Corp.) with an average diameter of 1.1 /* for the investigation of orthokinetic transport conditions. Particle diameters are determined from specific surface measurements. 2

Coagulant. Stock solutions were 10" Af in reagent grade A l ( 0 0 ) 3 and 1 0 M in H C 1 0 . Aluminum determinations for the standardization of stock solutions were made by alkalimetric titration. The amount of residual dissolved aluminum in adsorption experiments was determined absorptiometrically using "aluminon" (14). The agreement between both 2

-1

4


4

9.

H A H N

A N D S T U M M

Table I.

Coagulation

by A1(III)

93

Schematic Representation of Different Steps in Particle Agglomeration ( 2 2 ) Agglomeration

of Colloidal

Particles

Particle Agglomeration = Destabilization + Transport Rate of Agglomeration = C o l l . Efficiency Factor X Collision Frequency


o s

(1) Reduction of potential energy of interaction between particles. (a) Compression of double layer by counterions (Schultze H a r d y ) . (b) Decrease i n surface potential owing to specifically adsorbed counterions or owing to surface reactions.

(1) Brownian motion causes collision of primarily small colloids. (2) Velocity gradients trans port large colloids, b y impos ing different velocities upon neighboring particles.

H s

(2) Bridge formation. Specifically adsorbed polymeric species form bridges between colloids.

o

2

m e t h o d s of a l u m i n u m d e t e r m i n a t i o n w a s g o o d for A l ( I I I ) concentrations l a r g e r t h a n 10" Af. T h e c o a g u l a n t w a s f o r m e d b y r a i s i n g s l o w l y a n d u n i f o r m l y t h e p H of t h e s o l u t i o n . 4

Ionic Medium. S i l i c a dispersions w e r e f r e s h l y p r e p a r e d f o r e a c h e x p e r i m e n t i n solutions b u f f e r e d w i t h 1 0 " M H C 0 " / C 0 . T h e a m o u n t of species d i s s o l v e d f r o m t h e a m o r p h o u s s i l i c a surface d u r i n g t h e e x p e r i m e n t w a s n e g l i g i b l e because of t h e s m a l l rate of d i s s o l u t i o n reactions. T h e i o n i c m e d i u m i n w h i c h c o a g u l a t i o n a n d a d s o r p t i o n studies w e r e c a r r i e d o u t w a s k e p t constant: I — 1.0 t o 2.0 X 1 0 " M . T h e c o n d i t i o n s i n a l l a g g l o m e r a t i o n a n d a d s o r p t i o n experiments w e r e s u c h t h a t n o A l ( O H ) p r e c i p i t a t e d w i t h i n t h e p e r i o d of o b s e r v a t i o n . 3

3

2

3

3

Adsorption Experiments. T h e specific surface area of t h e d i s p e r s e d phase w a s o b t a i n e d f r o m B . E . T . a d s o r p t i o n isotherms, u s i n g n i t r o g e n as adsorbate. T h i s m e t h o d w a s d e s c r i b e d b y N e l s o n a n d E g g e r t s e n ( I I ) . T h e specific surface area f o u n d f o r L u d o x L S is 205 m e t e r / g r a m a n d for M i n - U - S i l 3 0 2 m e t e r V g r a m . T h e amounts of a l u m i n u m a d s o r b e d onto t h e s i l i c a surface w e r e d e t e r m i n e d f r o m t h e difference b e t w e e n t h e t o t a l dosages of A l ( I I I ) a d d e d a n d t h e r e s i d u a l i n t h e s o l u t i o n phase after a contact t i m e of 5 m i n u t e s . T h e p e r i o d s of contact w e r e c o m p a r a b l e to c o a g u l a t i o n r e a c t i o n times, a n d t h e results of t h e a d s o r p t i o n studies w e r e e x p e c t e d to reflect t h e extent of a d s o r p t i o n o c c u r r i n g i n the a g g l o m e r a t i o n process. A d s o r p t i o n e q u i l i b r i u m w a s n o t necessarily attained. 2

Perikinetic Coagulation. T h e c o n c e n t r a t i o n of s m a l l s i l i c a c o l l o i d s ( L u d o x L S d = 15 m/x) u s e d i n these studies w a s b e t w e e n 0.18 g r a m / l i t e r a n d 0.43 g r a m / l i t e r (36.5 - 86.0 m e t e r / l i t e r o r 5.0-11.5 X 1 0 p a r t i c l e s / m l . ) . T h e dispersion, contained i n a spectrophometric cell, was 2


1 3

94

ADSORPTION F R O M

AQUEOUS

SOLUTION

mixed instantaneously with the destabilizing agent and allowed to coagulate. The change in the absorbance of light (A© — 260 m/i) resulting from changes in the particle size distribution of the coagulating dispersion is recorded as a function of time (Figure 1). One can determine the initial rate of coagulation, — dN/dt, from such recordings when the size of the dispersed colloids, d, is within the range given by Rayleigh's law: d < 0.10 A (Equation 4).


0

0

40

Figure I .

80 tin* (sec)

0

40

80 tiM (MC)

0

40

80 time (MC)

Measurement of perikinetic coagulation rate under various solution conditions

The rate of coagulation is obtained from a recording of the change in light absorbonce (\o = 260mfi) with time. Light scattered by coagulating dispersions because of changes in particle agglomeration. Increase in light absorbance with increasing degree of agglomeration (A) Ludox = 0.4 gram/liter; Al = 8.4 X lO^M; pH = 5 . 2 5 ; (B) Ludox = 0.4 gram/liter; Al = 8.4 X I O " * M ; pH = 6.6; (C) Ludox = 0.4 gram/titer; Al = 1.75 X 10-*M;pH = 5.25

Orthokinetic Coagulation. Shear flow conditions, with average velocity gradients up to 100 sec." , were generated reproducibily i n a cylindrical reaction chamber with a turbine stirrer connected to a variable speed motor. The effective average velocity gradient or the actual collision frequency was obtained from a comparison of coagulation rates measured in this system and under well described perikinetic conditions. It was essential that the chemical conditions were the same in both experiments so that the collision efficiency factors were comparable. Dispersions were prepared from M i n - U - S i l 30 ( d = 1.1 /A) at concentration of 2 gram/liter (4 meter /liter or 10 particles/ml.). Samples were withdrawn in a microscopic counting cell and microphotographs were taken immediately after sampling. The decrease in total number of particles in suspension within the reaction time, —dN/dt, owing to agglomeration was determined by the counting of the total number of primary particles in each sample and comparing it with that fraction of primary particles incorporated into agglomerates (Figure 2). Other methods used for the evaluation of changes in the particle size distribution, such as light scattering techniques or Coulter Counter procedures, require the preparation of one or more dilutions prior to counting. Coagulant species may desorb partially as a result of dilution and such desorption would cause a change in the degree of agglomeration. 1

2

9


9.

H A H N

A N D

Coagulation

S T U M M

by

Al(III)

The Role of Adsorption in the Destabilization Dispersions by Hydrolyzed Al(III)

95 of

Colloidal

It is w e l l k n o w n that h y d r o l y z e d p o l y v a l e n t m e t a l ions are m o r e efficient t h a n u n h y d r o l y z e d ions i n the d e s t a b i l i z a t i o n of c o l l o i d a l d i s persions.

M o n o m e r i c h y d r o l y s i s species u n d e r g o c o n d e n s a t i o n reactions

u n d e r c e r t a i n c o n d i t i o n s , w h i c h l e a d to the f o r m a t i o n of m u l t i - or p o l y n u c l e a r h y d r o x o complexes.

T h e s e reactions take p l a c e e s p e c i a l l y i n

solutions t h a t are oversaturated w i t h respect to the s o l u b i l i t y l i m i t of Downloaded by UNIV OF NEW ENGLAND on February 11, 2017 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0079.ch009

the m e t a l h y d r o x i d e .

T h e o b s e r v e d m u l t i m e r i c h y d r o x o complexes

or

isopolycations are assumed to b e s o l u b l e k i n e t i c intermediates i n t h e t r a n s i t i o n that oversaturated solutions u n d e r g o i n the course of p r e c i p i t a t i o n of h y d r o u s m e t a l oxides. P r e v i o u s w o r k b y M a t i j e v i c , J a n a u e r , a n d K e r k e r (7);

Fuerstenau, Somasundaran, and Fuerstenau ( J ) ; and O ' M e l i a

a n d S t u m m (12)

has s h o w n that isopolycations adsorb at interfaces.

F u r t h e r m o r e , i t has b e e n o b s e r v e d that species, a d s o r b e d at t h e surface, d e s t a b i l i z e c o l l o i d a l suspensions at m u c h l o w e r concentrations t h a n ions that are n o t specifically a d s o r b e d .

Ottewill and Watanabe

S o m a s u n d a r a n , H e a l y , a n d F u e r s t e n a u (16)

(13)

and

h a v e s h o w n that the t h e o r y

of the diffuse d o u b l e l a y e r explains the d e s t a b i l i z a t i o n of dispersions b y s m a l l concentrations of surfactant ions that h a v e a charge opposite N/N

0

\.0 .9

.8 .7

.6

.5

30

0

Figure

2.

60

Evaluation flocculation

90

min

of orthokinetic rate

The relative decrease in the total concentration of particles because of orthokinetic coagulation was determined from microscopic observation. The rate constant k« is obtained from the slope of the semilogarithmic plot (Equation 9) (Min-U-Sil 30 = 2 gram/liter; Al = 4.6 X 10r*M; pH = 5.5; (du/dz) = 110 seer ) 1


to

ADSORPTION

F R O M AQUEOUS

-log(c) (M)

0

2

4

6

8

10

12

14 pH

100%

75%-

7.0 PH

ICT0R

.0150

>-

.0125

FICIE

.0175

.0100

LU

LLISIC


RANGE OF EXPERIMENTS

i

-

1

/

/

-

/

/

.0075 .0050

/

o

a

1 J 1

1

i

/

.0025

' 4.0

1 5.0

LUDOX 0.24g/-f

-

A* 5.6-10~ M 5

1

1 6.0

1 7.0 pH

Figure 3. Hydrolysis of Al(III) and the effect of hydrolytic Al(III) species upon the coagulation rate (A) Logarithmic diagram of Al(III) solubility as function of Al concentration and pH, derived from thermodyn. equilibrium constants. (B) Extent of Al-hydrolysis as function of pH. (C) Variation of the coagulation rate, expressed as collision efficieny factor, with pH at constant Al dosage (a values determined from Equation 3)


SOLUTION

9.

H A H N

A N D

Coagulation

S T U M M

by A1(1II)

97

that of the colloids. However, one must include an energy component for specific adsorption in the total energy balance of the double layer interactions. Hydrolysis of Al(III) and Destabilization Effects of Hydrolyzed A l ( I I I ) . Figure 3 shows the observed correlation between the degree of hydrolysis of Al(III) and the effects of those aluminum species on the coagulation rate, expressed by a collision efficiency factor.

Coagulation

rates were measured under well defined perikinetic transport conditions Downloaded by UNIV OF NEW ENGLAND on February 11, 2017 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0079.ch009

and collision efficiency factors determined from a comparison with the known collision frequency under these conditions. Diagrams of the p H dependence

of aluminum solubility and of the extent

of aluminum

hydrolysis under thermodynamic equilibrium conditions are presented together with a graph of the p H dependence of the measured collision efficiency factor, the fraction of all collisions that lead to permanent agglomeration.

A comparison of these figures leads to the assumption

that Al(III) becomes an efficient destabilizing agent when it is present in hydrolyzed and multimeric form.

The diagrams show that p H and

aluminum concentration were such that the solutions were oversaturated 3x10*

I

I

I

I

I

I

I

I

I

I

I

I

I

I

EQUILIBRIUM C0NC. OF At(M) Figure 4.

Adsorption of hydrolyzed Al(III) on colloidal silica

Curves are computed from Langmuir isotherms that have been fitted to the observed adsorption data


98

ADSORPTION F R O M AQUEOUS

with respect to the solubility product of solid " A l f O H J g . "

SOLUTION

However, no

precipitation of aluminum hydroxide was observed within the time span of the experiments.

The species that cause effective destabilization of

colloidal dispersions are therefore assumed to be soluble isopolycations. It must be pointed out in this connection that direct application of known hydrolysis equilibrium constants is not meanignful under conditions of oversaturation. Furthermore, the polynuclear species appearing in the diagrams of Figure 3 are only representative of the type of isopolycations that are possibly encountered under these circumstances. Neither thermoDownloaded by UNIV OF NEW ENGLAND on February 11, 2017 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0079.ch009

dynamic equilibrium data nor information from adsorption and coagulation experiments permits at the present a more quantitative description of these multinuclear hydroxo complexes. The Adsorption of Hydrolyzed A l ( I I I ) . O'Metia and Stumm

(12)

have shown that specific adsorption of hydrolyzed Fe(III) species accounts for the observed coagulation and restabilization of silica dispersions. A model was formulated on the basis of the Langmuir adsorption isotherm and was shown to explain the observations adequately.

The

authors derive a relationship between the surface area concentration of the dispersed phase S (in meter /liter and the applied coagulant ion 2

concentration C e (in M ) necessary to reach a certain fraction of surface t

coverage.

The extent of destabilization or of restabilization can be con-

cluded from the amount of surface coverage on the colloidal particle: Cte=

g

(

1

,

g

)

C + 1

K

S

r

m

( i - *)]

(1)

sorption capacity (moles of metal ion/meter ) Langmuir s adsorption-desorption equilibrium constant ( M ) fraction of surface covered—ratio of the amount of metal ion adsorbed at colloid surface and the total sorption capacity (dimensionless) 2

_ 1

The adsorption of hydrolyzed Al(III) on silica is described by the isotherms in Figure 4. The data can be fitted by the Langmuir equation as was the case for the adsorption of hydrolyzed Fe(III) on silica

(12).

This agreement between experimental data and the Langmuir isotherm, derived for an adsorption-desorption equilibrium, cannot be used to conclude that adsorption in this instance is fully reversible or that equilibrium had been reached in the experiments.

Figure 5 compares the

adsorption of hydrolyzed Al(III) onto silica and the effects of addition of multimeric Al(III) hydroxo complexes to colloidal dispersions on the coagulation rate of these suspensions, as expressed by a change in the collision efficiency factor. The following qualitative explanations for the observed destabilization and restabilization of colloidal silica with hydrolyzed Al(III) can be derived from Figure 5: (1) The colloidal suspension


9.

H A H N AND STUMM

99

Coagulation by A1(III)

becomes unstable, as shown by collision efficiency factors larger than zero and begins to coagulate at the critical coagulation concentration ( c . c . c ) , where a certain minimum surface coverage on the colloid occurs. The

experimental evidence supports the assumption, that specific adsorp-

tion of isopolycations on the colloid surface leads to a decrease of the surface potential to a critical threshold value and causes destabilization; (2)

further increase in the coagulant concentration C

t

brings about a

restabilization of the dispersion, shown by decreasing collision efficiency


factors (extrapolation to zero efficiency factor gives the critical stabiliza-

Figure 5. The variation of relative colloid stability, expressed as collision efficiency factor, with A1(III) dosage as compared with colloid surface coverage from adsorption of A1(IU) (A) Surface coverage as a function of total amount of A1(III) added, Ct, at constant pH—computed on the basis of a Langmuir adsorption isotherm (K = 6.2 X lO-'M"', T = 2.75 X IO' moles I meter*, Ludox LS = 0.3 gram I liter (B) Relative colloid stability as a function of the total concentration of coagulant added, Ct, at constant pH—obtained from the measurement of perikinetic coagulation rates according to Equation 3. (Ludox LS = 0.3 gram /liter) m

6


100

ADSORPTION F R O M

tion concentration ( c . s . c ) .

AQUEOUS SOLUTION

L a r g e amounts of specifically a d s o r b e d cat

i o n i c h y d r o x o a l u m i n u m complexes c o v e r the o r i g i n a l l y n e g a t i v e l y c h a r g e d surface to a l a r g e extent a n d cause r e v e r s a l of surface c h a r g e a n d p o t e n t i a l . T h e c o l l o i d a l particles r e p e l e a c h other electrostatically u n d e r these c o n d i t i o n s a n d suspensions are stable a g a i n .

F i g u r e 5 shows t h a t the

extent of surface coverage is v e r y s m a l l at the p o i n t of b e g i n n i n g s o l d e s t a b i l i z a t i o n (6 ss 0.03 at p H =

5.25)

a n d that the c o l l i s i o n efficiency

factor, c h a r a c t e r i z i n g the i n s t a b i l i t y of the c o l l o i d s , decreases a g a i n for surface coverage values l a r g e r t h a n 0 =

0.10 ( p H =

5.25). T h e s e obser


vations l e a d to the c o n c l u s i o n that b r i d g i n g b e t w e e n c o l l o i d a l particles b y means of p o l y m e r i c h y d r o l y s i s p r o d u c t s does not p l a y a significant r o l e i n the d e s t a b i l i z a t i o n w i t h h y d r o l y z e d A l ( I I I ) at these p H values. F i g u r e 3 indicates t h a t the c h a r a c t e r of the h y d r o l y s i s species

is

strongly d e p e n d e n t u p o n the p H of the s o l u t i o n . T h i s m a y e x p l a i n t h e l a r g e effects of the p H of the s o l u t i o n u p o n the s o r p t i o n t e n d e n c y of the h y d r o l y z e d a l u m i n u m species.

F i g u r e 6 s u m m a r i z e s the a d s o r p t i o n d a t a

a n d shows that t h e t o t a l s o r p t i o n c a p a c i t y r

m

increases m a r k e d l y w h e n

t h e p H is r a i s e d i n the r a n g e f r o m 4.5 to 5.25.

C o a g u l a t i o n experiments

h a v e s h o w n t h a t the a m o u n t of h y d r o l y z e d A l ( I I I ) necessary to o b t a i n c o l l i s i o n efficiency factors l a r g e r t h a n zero ( c . c . c ) , a n d the dosage at w h i c h m a x i m u m c o l l i s i o n efficiency factors o c c u r w i t h i n the p H r a n g e f r o m 4.5 to 5.25 Al(III)/meter

2

S i 0 and C 2

t 0 P

(c.c.c. =

t — IO" ± 6

(C pt)

4 X

are constant

t0

10"

7

±

10"

I O " moles A l ( I I I ) / m e t e r 7

2

7

moles Si0 ). 2

T h e increase w i t h p H i n the s o r p t i o n c a p a c i t y a n d the constancy of the necessary c o a g u l a n t dosages over a c e r t a i n p H r a n g e e x p l a i n the decrease i n the f r a c t i o n a l surface coverage necessary to r e d u c e the surface p o t e n t i a l of the colloids to a c r i t i c a l t h r e s h o l d v a l u e or to effect a t o t a l r e v e r s a l of the potential. T h e a p p r o x i m a t e c o n s t a n c y of c.c.c. a n d C

t o p

t w i t h i n the i n v e s t i g a t e d

p H range is i n a c c o r d w i t h the hypothesis that the d e s t a b i l i z a t i o n of c o l l o i d a l suspensions

is c a u s e d

by

specific

a d s o r p t i o n of

hydrolyzed

A l ( I I I ) o n the c o l l o i d surface. T h e o b s e r v a t i o n suggests that the dosage of A l ( I I I ) necessary to effect a c e r t a i n r e d u c t i o n of the surface p o t e n t i a l of the c o l l o i d is r e l a t i v e l y i n d e p e n d e n t of the n a t u r e of the h y d r o l y s i s species. T h i s c a n b e e x p l a i n e d i n p a r t b y the fact t h a t the l i g a n d n u m b e r of a l u m i n u m h y d r o x o species

( O H ' b o u n d p e r A l ( I I I ) - i o n ) , w h i c h is

i n d i c a t i v e of a n average net c h a r g e o n the i o n , r e m a i n s n e a r l y unaffected b y changes i n the s o l u t i o n p H w i t h i n c e r t a i n l i m i t s ( 1 8 ) . concluded

from

a l l reported

observations

It m u s t b e

that the d e s t a b i l i z a t i o n b y

h y d r o l y z e d A l ( I I I ) is p r e s u m a b l y the result of a p a r t i a l or

complete

n e u t r a l i z a t i o n of the n e g a t i v e surface charge b y p o s i t i v e l y c h a r g e d m u l t i n u c l e a r a l u m i n u m h y d r o x o complexes specifically a d s o r b e d o n the s i l i c a


9.

HAHN AND STUMM

Coagulation

by

101

Al(III)

surface. Results of a recent investigation on the electrophoretic mobility of silica colloids at different C

t

and p H , by Kane, L a M e r , and Linford

( 5 ) support this model of adsorption coagulation. Forces of Adsorption. The mechanism of attachment of isopolycations on solid surfaces and the nature of the forces that hold the adsorbate are not well understood. However, Stumm and O'Melia

(20)

have given a few qualitative arguments that explain in part the observed specific adsorption of hydrolyzed Al(III) on silica.

First, the effective


charge density of the central ion is reduced with increasing degree of hydroxidation and multimerization. Hydrolyzed species are larger and to a smaller extent hydrated than non-hydrolyzing ions.

The hydroxo

aluminum complexes are less "hydrophilic" if compared with the strongly hydrated, non-hydrolyzed aluminum ion.

Correspondingly, these iso-

polycations will accumulate at the solid solution interface. Results from studies on the role of hydration in the adsorption of certain earth alkali ions onto quartz by Malati and Estefan ( 6 ) supplement these qualitative arguments. Second, these multimeric species contain more than one O H " group per ion that can become attached at the colloid surface. Iso- and heteropolyanions (polysilicates, silicotungstates) have been found to show a similar tendency for specific adsorption as isopolycations.

Kinetics of Coagulation:

Particle Transport

as Rate Determining

Step

It is known that the rate of coagulation can be increased by increasing

the concentration of the suspended solid mass or by stirring the

suspension more intensively. O n the other hand, solution variables have seemingly a pronounced effect on the rate of particle agglomeration, as indicated in Figures 3 and 5. These observations can be explained, when the different reaction steps in the coagulation process and the relative effect of these reactions on the observed coagulation rate, — dN/dt,

are

considered. One can distinguish the following steps in the agglomeration of silica dispersions with hydrolyzed aluminum: ( 1 ) hydrolysis and multimerization of Al(III) to isopolycations; ( 2 ) diffusion of these aluminum hydroxo complexes to the colloid surface and adsorption; and ( 3 )

transport of

suspended particles and collision resulting in certain instances in attachment of colloids.

The transport of colloids to each other has

been

observed to proceed more slowly than all other steps under the given circumstances ( 3 ) .

It follows that the rate of agglomeration, — dN/dt,

is

obtained from the collision frequency, as determined solely by the trans-


102

ADSORPTION F R O M

AQUEOUS SOLUTION

p o r t m e c h a n i s m , c o r r e c t e d b y a c o l l i s i o n efficiency factor, that describes the f r a c t i o n of collisions r e s u l t i n g i n p e r m a n e n t a g g l o m e r a t i o n . T h e v a l u e of the c o l l i s i o n efficiency factor d e p e n d s u p o n the extent of d e s t a b i l i z a t i o n


of the d i s p e r s i o n .

Figure 6. Sorption capacity and surface coverage by hydrolyzed AI(1U) on colloidal silica as function of pH The values given have been computed on the basis of Langmuir isotherms that were fitted to the experimentally observed data. (Ludox LS = 0.3 gram/liter) Perikinetic Coagulation. I f c o l l o i d a l p a r t i c l e s are of s u c h d i m e n sions that t h e y are subject to t h e r m a l m o t i o n , the transport of these p a r t i c l e s is a c c o m p l i s h e d b y this B r o w n i a n m o t i o n . C o l l i s i o n s Occur w h e n one p a r t i c l e enters the sphere of influence of another p a r t i c l e . T h e c o a g u l a t i o n rate m e a s u r i n g the decrease i n the c o n c e n t r a t i o n of particles w i t h t i m e , N ( i n n u m b e r s / m l . ) , of a n e a r l y m o n o d i s p e r s e suspension corre sponds u n d e r these c o n d i t i o n s to the rate l a w for a second o r d e r r e a c t i o n (15): - d N / d t = Jfc N p

2

(2)

T h e rate constant k is g i v e n i n terms of p h y s i c a l parameters ( B o l t z m a n n C o n s t a n t K , the absolute t e m p e r a t u r e T, a n d the absolute v i s c o s i t y rj) that c h a r a c t e r i z e these t r a n s p o r t c o n d i t i o n s . I n the case of not c o m p l e t e l y d e s t a b i l i z e d c o l l o i d s , w h e n a c c o r d i n g to v. S m o l u c h o w s k i s o - c a l l e d s l o w c o a g u l a t i o n is o b s e r v e d , the rate constant contains i n a d d i t i o n the c o l l i s i o n efficiency factor, a , the f r a c t i o n of collisions l e a d i n g to p e r m a n e n t a t t a c h ment under perikinetic conditions: v

B

p


9.

HAHN

AND STUMM

Coagulation

103

by A1(III) 4K T B

(3)

According to this kinetic model the collision efficiency factor «

p

can

be evaluated from experimentally determined coagulation rate constants (Equation 2) when the transport parameters, K T , v are known (Equation B

3).

It has been shown recently that more complex rate laws, similarly

corresponding to second order reactions, can be derived for the coagulation rate of polydisperse suspensions.

W h e n used to describe only the


effects in the total number of particles of a heterodisperse suspension, Equations 2 and 3 are valid approximations

(4).

Changes in the cumulative particle size distribution, describing the decrease in the total number of dispersed colloids caused by agglomeration have been determined in this instance by a light scattering method. Troelstra and Kruyt (23) have derived an equation for the light absorbance, A , describing scattering effects of coagulating colloids, on the basis of Rayleigh s law: (4)

Abs = B t f V 2 ( l + 2fc N t) 0

0

p

0

B — optical constant of scattering system, depending upon the refractive indices of the solid scatterers and the suspending medium, the wavelength of the light used and the length of the light path; N , V are the concentration and volume of the colloidal particles at reaction time t = 0; 0

0

fc = p

rate constant of second order reaction, defined in Equation 3;

The equation derived by Troelstra and Kruyt is only valid for coagulating dispersions of colloids smaller than a certain maximum diameter given by the Rayleigh condition, d ^

0.10 A . Equation 4 applies in G

cases where particles are transported solely by Brownian motion.

Fur-

thermore, the kinetic model (Equations 2 and 3) has been derived under the assumption that the collision efficiency factor does not change with time. In the case of some partially destabilized dispersions one observes a decrease in the collision efficiency factor with time which presumably results from the increase of a certain energy barrier as the size of the agglomerates becomes larger. A l l the assumptions discussed hold during the first part of the reaction. Figure 1, a recording of the change in light absorbance with time of a coagulating dispersion, shows a straight line relationship according to Equation 4 for short reaction periods. Only after extended reaction times does a deviation from predicted values occur. Consequently, only the initial coagulation rate and the incipient collision efficiency factor can be evaluated from these measurements by determining the quotient of slope over ordinate intercept of the initially straight line.

The total


104

ADSORPTION F R O M

AQUEOUS SOLUTION

r e c o r d e d r e a c t i o n times i n these experiments are i n the order of 3 to 5 minutes. O r t h o k i n e t i c C o a g u l a t i o n . I f the c o l l o i d a l particles are v e r y l a r g e i n c o m p a r i s o n w i t h m o l e c u l e s , the transport of the colloids to each other w i l l d e p e n d p r e d o m i n a n t l y u p o n v e l o c i t y gradients w i t h i n the m e d i u m of the suspension, r e s u l t i n g f r o m a g i t a t i o n or c o n v e c t i v e currents. T h e effects of B r o w n i a n m o t i o n o n these dispersions are c o m p a r a t i v e l y s m a l l . Smoluchowski (15)

Von

has g i v e n a n e q u a t i o n for the n u m b e r of collisions


b e t w e e n c o l l o i d s of a m o n o d i s p e r s e suspension subject to v e l o c i t y g r a d i ents, r e s u l t i n g f r o m shear flow of viscous m e d i a . T h e rate of c o a g u l a t i o n , expressed as a decrease of the t o t a l n u m b e r of particles i n suspension p e r u n i t t i m e is f o u n d f r o m the c o l l i s i o n f r e q u e n c y , as d e t e r m i n e d b y the transport c o n d i t i o n s a n d the c o l l i s i o n efficiency factor, w h i c h d e p e n d s u p o n the extent of d e s t a b i l i z a t i o n of the suspension. l a w for n e a r l y m o n o d i s p e r s e

suspensions

T h e r e s u l t i n g rate

corresponds

to a first o r d e r

reaction: -dN/dt T h e rate constant k

Q

(5)

= kN 0

for o r t h o k i n e t i c c o a g u l a t i o n is d e t e r m i n e d b y

p h y s i c a l parameters ( v e l o c i t y g r a d i e n t du/dz, floe v o l u m e r a t i o of the d i s p e r s e d phase, = volume),

s u m over the p r o d u c t of p a r t i c l e n u m b e r

a n d the c o l l i s i o n efficiency

factor «

0

observed

under

and

ortho

k i n e t i c transport c o n d i t i o n s : *o = « o

4

(

d

"

/

d

Z

7T

)

*

(3)

T h e o v e r a l l rate of a g g l o m e r a t i o n of a n y suspension, that is p r e p a r e d e x p e r i m e n t a l l y a n d consists of s m a l l a n d large c o l l o i d s , is o b t a i n e d

by

a d d i n g the expressions d e r i v e d for p e r i k i n e t i c a n d o r t h o k i n e t i c c o a g u l a tion (Equations 2 and 5 ) : -dN/dt

=

a

v

^ N * Or)

+

N

a o

(7)

7T

F r o m a c o m p a r i s o n of the t w o c o l l i s i o n f r e q u e n c y terms, d e s c r i b e d i n d e t a i l i n the E q u a t i o n s 3 a n d 6, one obtains the r e l a t i v e c o n t r i b u t i o n s of the p e r i k i n e t i c a n d o r t h o k i n e t i c t r a n s p o r t to the t o t a l p a r t i c l e a g g l o m eration. T h e r a t i o is a f u n c t i o n of the r a d i u s of the c o l l o i d , r , a n d the absolute v a l u e of the v e l o c i t y g r a d i e n t ^orthokinetic

_

du/dz:

4 r q (du/dz) 3

^

^perikinetic

It c a n b e s h o w n w i t h E q u a t i o n 8 t h a t b o t h transport m e c h a n i s m s

con

t r i b u t e e q u a l l y to the c o a g u l a t i o n of a L u d o x L S d i s p e r s i o n , c o n t a i n i n g


9.

H A H N

A N D

S T U M M

Coagulation

by A1(ni)

105

s i l i c a c o l l o i d s of a n average d i a m e t e r of 15 m/x, o n l y w h e n t h e v e l o c i t y gradients are e x t r e m e l y large, i n the o r d e r of 3 X 10 sec." . T h i s leads to the c o n c l u s i o n that a g g l o m e r a t i o n of sufficiently d e s t a b i l i z e d L u d o x L S dispersions occurs i n its e a r l y stages t h r o u g h B r o w n i a n m o t i o n alone. T h e p h y s i c a l v a r i a b l e s i n E q u a t i o n 3 therefore are u n a m b i g u o u s l y defined a n d p e r m i t a d e t e r m i n a t i o n of the c o l l i s i o n efficiency factor f r o m the m e a s u r e d rates. S i m i l a r l y , at average v e l o c i t y gradients of about 100 sec." w h i c h w e r e generated i n the shear flow a p p a r a t u s , a l l particles l a r g e r t h a n 215 m/x are p r e d o m i n a n t l y t r a n s p o r t e d b y v e l o c i t y gradients. A g a i n i t c a n be c o n c l u d e d that the c o a g u l a t i o n of M i n - U - S i l 30 dispersions w i t h c o l l o i d s of d i a m e t e r 1.1 /x, f o l l o w s the o r t h o k i n e t i c rate l a w a n d the c o l l i s i o n efficiency v a l u e c a n be d e t e r m i n e d a c c o r d i n g to E q u a t i o n 6. 1

5


1

T h e a c t u a l decrease of the t o t a l n u m b e r of particles of a d i s p e r s i o n c o a g u l a t i n g u n d e r o r t h o k i n e t i c c o n d i t i o n s is d e s c r i b e d b y a l o g a r i t h m i c f u n c t i o n o b t a i n e d f r o m the i n t e g r a t i o n of E q u a t i o n 5: l n ( N / * J = - a

0

± ^ ^ *

(9)

7T

F i g u r e 2 is a s e m i l o g a r i t h m i c g r a p h of the m i c r o s c o p i c a l l y deter m i n e d decrease w i t h t i m e of the t o t a l n u m b e r of particles, r e l a t i v e to the i n i t i a l n u m b e r of c o l l o i d s , c a u s e d b y o r t h o k i n e t i c c o a g u l a t i o n . It depicts the expected l o g a r i t h m i c decrease for short r e a c t i o n times a n d a d e v i a t i o n f r o m values p r e d i c t e d b y the k i n e t i c m o d e l after e x t e n d e d r e a c t i o n periods. P r e s u m a b l y , this results f r o m the i n c r e a s i n g p o l y d i s p e r s i t y of the suspension a n d the decreasing c o l l i s i o n efficiency factor w i t h t i m e . I n i t i a l c o a g u l a t i o n rates a n d c o l l i s i o n efficiency factors are o b t a i n e d f r o m the slope of the i n c i p i e n t l y straight line. R e a c t i o n times w e r e i n these instances i n the o r d e r of 1 to 2 hours. T h e c o l l i s i o n efficiency factors, d e s c r i b i n g the extent of the c o l l o i d d e s t a b i l i z a t i o n , w i t h i n c e r t a i n l i m i t s are e q u a l u n d e r p e r i k i n e t i c a n d o r t h o k i n e t i c c o n d i t i o n s (3). The Effect of Solution Variables on the Coagulation

Rate

C h e m i c a l parameters d e t e r m i n e the surface characteristics of the s u s p e n d e d c o l l o i d s , the c o n c e n t r a t i o n of the c o a g u l a n t a n d its effects u p o n the surface properties of the d e s t a b i l i z e d p a r t i c l e s , a n d the influence of other constituents of t h e i o n i c m e d i u m u p o n the c o a g u l a n t a n d t h e colloids. T h e extent of the c h e m i c a l a n d p h y s i c a l interactions b e t w e e n the c o l l o i d a l phase a n d the s o l u t i o n phase determines the r e l a t i v e s t a b i l i t y of the s u s p e n d e d colloids. O n e speaks of stable suspensions w h e n a l l collisions b e t w e e n t h e colloids i n d u c e d b y B r o w n i a n m o t i o n or b y v e l o c i t y gradients are c o m p l e t e l y elastic: the c o l l o i d a l particles c o n t i n u e t h e i r


106

ADSORPTION F R O M

AQUEOUS SOLUTION

separate m o v e m e n t s after t h e c o l l i s i o n . A d i s p e r s i o n is t h e o r e t i c a l l y c o m p l e t e l y d e s t a b i l i z e d , w h e n a l l collisions b e t w e e n the s u s p e n d e d p a r t i c l e s l e a d to p e r m a n e n t attachment.

T h u s , the c o l l i s i o n efficiency factor is a

q u a n t i t a t i v e measure of the r e l a t i v e s t a b i l i t y of a sol. T o g e t h e r w i t h the t o t a l n u m b e r of collisions o c c u r r i n g b e t w e e n the p a r t i c l e s , t h e c o l l i s i o n f r e q u e n c y , w h i c h is d e t e r m i n e d b y the t e m p e r a t u r e , the v e l o c i t y g r a d i e n t a n d the n u m b e r c o n c e n t r a t i o n a n d d i m e n s i o n of the c o l l o i d a l p a r t i c l e s , the c o l l i s i o n efficiency

factor describes

the o b s e r v e d

coagulation

rate


(Equation 7). Colloid Stability as a Function of p H , Q , and S. T h e effects of pertinent solution variables ( p H , A l ( I I I )

dosage C , A l ( I I I ) t

dosage

r e l a t i v e to surface area c o n c e n t r a t i o n of the d i s p e r s e d phase S u p o n t h e c o l l i s i o n efficiency, h a v e b e e n d e t e r m i n e d e x p e r i m e n t a l l y for s i l i c a d i s p e r sions a n d h y d r o l y z e d A l ( I I I ) . H o w e v e r , one cannot d r a w a n y c o n c l u s i o n f r o m the e x p e r i m e n t a l results w i t h respect

to the d i r e c t r e l a t i o n s h i p

b e t w e e n c o n d i t i o n s i n t h e s o l u t i o n phase a n d those o n the c o l l o i d surface. I t has b e e n i n d i c a t e d b y S o m m e r a u e r , S u s s m a n , a n d S t u m m (17)

that

l a r g e c o n c e n t r a t i o n gradients m a y exist at the s o l i d s o l u t i o n i n t e r f a c e w h i c h c o u l d l e a d to reactions that are not p r e d i c t a b l e f r o m k n o w n s o l u t i o n parameters. F i g u r e 7 gives the r e l a t i v e s t a b i l i t y of S i 0

2

c o l l o i d s i n terms of t h e

o b s e r v e d c o l l i s i o n efficiency as a f u n c t i o n of A l ( I I I ) dosage C

t

for d i f

ferent p H values. S u c h d a t a c a n b e u s e d to define q u a n t i t a t i v e l y s i m i l a r l o g C t - p H d o m a i n s of c o a g u l a t i o n a n d r e s t a b i l i z a t i o n , expressed as t h e c r i t i c a l concentrations of b e g i n n i n g d e s t a b i l i z a t i o n a n d c o m p l e t e r e s t a b i l i z a t i o n (c.c.c. a n d c.s.c.) as g i v e n b y M a t i j e v i c et al. (8, 9, 1 0 ) .

A

s i m i l a r p r o c e d u r e for the d e t e r m i n a t i o n of the c.c.c. a n d c.s.c. c o n c e n t r a t i o n l i m i t s has b e e n p r o p o s e d b y T e o t T h e v a r i a t i o n of a w i t h C

t

(22).

at constant p H c a n b e e x p l a i n e d b y the

c h a n g e i n d e s t a b i l i z i n g effects of different concentrations of c o a g u l a n t at t h e c o l l o i d surface,

a i n i t i a l l y increases w h e n C

adsorbed t

larger because of i n c r e a s i n g amounts of specifically a d s o r b e d

becomes isopoly

cations C , that cause a progressive decrease of the surface p o t e n t i a l of the a

c o l l o i d . F u r t h e r increase i n C a n d c o n s e q u e n t l y C t

a

w i l l e v e n t u a l l y cause

charge n e u t r a l i z a t i o n , i n d i c a t e d b y m a x i m u m a. T h e surface p o t e n t i a l becomes n o w m o r e a n d m o r e n e g a t i v e because of c o n t i n u e d a d s o r p t i o n of isopolycations. c o a g u l a n t concentrations.

specific

T h i s explains the decrease i n a for l a r g e

T h e non-linear relationship between

C

t

and

C , e s p e c i a l l y w h e n the s o r p t i o n c a p a c i t y is a l r e a d y n e a r l y exhausted, a

m a y p r i m a r i l y account for the a s y m m e t r i c a l shape of the f u n c t i o n d e s c r i b i n g the v a r i a t i o n of a w i t h C . It is possible t h a t other factors, s u c h t

as changes

i n the electrostatic r e p u l s i o n of the S i 0

2

colloids or their


9.

H A H N

A N D

S T U M M

Coagulation

107

by A1(III)


LUDOX 0.3 g/J

c.c.c. (by extrapolation)

c. s.c. (by extrapolation)

Figure 7. Effects of pH and A1(III) dosage upon relative colloid stability, expressed as collision efficiency factor, for constant surface concentration Diagrams such as these can be used to establish pH, Al(III),S domains, describing the limits between stable, unstable, and restabilized suspensions o r i g i n a l l y s t r o n g l y h y d r o p h i l i c c h a r a c t e r w h e n t h e c o l l o i d surface i s covered

t o a large extent w i t h i s o p o l y c a t i o n s , also c o n t r i b u t e t o t h e

o b s e r v e d difference i n dosages necessary t o o b t a i n a c e r t a i n degree o f d e s t a b i l i z a t i o n a n d r e s t a b i l i z a t i o n . T e o t ( 2 2 ) u s i n g A l ( I I I ) as c o a g u l a n t and O ' M e l i a and S t u m m ( 1 2 ) studying coagulation w i t h also find t h a t the o p t i m u m c o a g u l a n t dosage C m u m c o l l i s i o n efficiency

is m u c h closer

t 0 P

Fe(III)

t resulting i n maxi

t o c.c.c. t h a n t o c.s.c. T h e

increase o f a w i t h p H at the p o i n t o f o p t i m u m c o a g u l a n t dosage, w h e r e r e v e r s a l i n the s i g n o f the surface p o t e n t i a l occurs, is not too w e l l u n d e r stood.

A q u a l i t a t i v e e x p l a n a t i o n is p e r h a p s that the decrease i n surface

coverage at C

t o p

t , as the p H increases, p e r m i t s p a r t i c l e s to a p p r o a c h e a c h

other m o r e closely u p o n c o l l i s i o n . T h i s increases the effect o f the L o n d o n v a n - d e r - W a a l s forces o f a t t r a c t i o n o n the c o l l o i d s . n a t u r e o f the h y d r o x o a l u m i n u m complexes

T h e change i n the

w i t h p H m a y b e another

f a c t o r a c c o u n t i n g for the decrease i n c o l l o i d s t a b i l i t y at C

t 0 P

t.

F i g u r e 8 illustrates the r e l a t i o n s h i p b e t w e e n the surface c o n c e n t r a t i o n of the d i s p e r s e d phase S a n d the c o a g u l a n t dosage C necessary t o affect a c e r t a i n d e g r e e o f c o l l o i d i n s t a b i l i t y a t constant p H . I f the d e s c r i b e d m o d e l o f d e s t a b i l i z a t i o n is correct, one s h o u l d observe a d i r e c t r e l a t i o n t


108

ADSORPTION F R O M

AQUEOUS SOLUTION

s h i p b e t w e e n S a n d C—i.e., the larger the surface c o n c e n t r a t i o n of the d i s p e r s e d phase the m o r e coagulant has to b e a d d e d to a t t a i n c e r t a i n a-values.

T h e so-called s t o i c h i o m e t r i c r e l a t i o n s h i p b e t w e e n

S and C , t

w h i c h c a n b e f o r m u l a t e d o n the basis of a L a n g m u i r a d s o r p t i o n i s o t h e r m


( 1 2 ) , has b e e n f o u n d i n these experiments.

Figure 8.

Stoichiometric relationship between surface concentration colloidal phase and necessary Al(lll) dosages

of

An increase in colloid concentration requires increased Al(IIi) dosages to obtain comparable values of relative colloid stability Concluding

Remarks

T h e rate of c o a g u l a t i o n depends u p o n the c o l l i s i o n f r e q u e n c y , w h i c h is c o n t r o l l e d b y p h y s i c a l parameters

d e s c r i b i n g p e r i k i n e t i c or

ortho

k i n e t i c p a r t i c l e transport ( t e m p e r a t u r e , v e l o c i t y gradient, n u m b e r

con

c e n t r a t i o n a n d d i m e n s i o n of c o l l o i d a l p a r t i c l e s ) , a n d the c o l l i s i o n effi c i e n c y factor a m e a s u r i n g the extent of the p a r t i c l e d e s t a b i l i z a t i o n w h i c h is p r i m a r i l y c o n t r o l l e d b y c h e m i c a l parameters. T h e c o l l o i d a l s i l i c a dispersions

are d e s t a b i l i z e d w i t h

hydrolyzed

A l ( I I I ) p r i m a r i l y because of a d s o r p t i o n of p o l y h y d r o x o a l u m i n u m cations o n the c o l l o i d surface w h i c h reduces p o t e n t i a l of S i 0

2

the i n c i p i e n t l y negative

colloids ( a d s o r p t i o n c o a g u l a t i o n ) .

surface

T h e pertinent solu

t i o n v a r i a b l e s d e s c r i b i n g the d e s t a b i l i z a t i o n r e a c t i o n are p H , t o t a l a l u m i n u m c o n c e n t r a t i o n C , a n d the r a t i o of a l u m i n u m dosage to the c o l l o i d t

surface c o n c e n t r a t i o n S.


9.

H A H N

A N D

S T U M M

Coagulation

by

109

Al(III)

T h e rate of c o a g u l a t i o n b y A l ( I I I ) c a n b e i m p r o v e d o p e r a t i o n a l l y : (1)

b y increasing the collision frequency

through raising the velocity

gradient a n d ( 2 ) b y adjusting the solution variables ( p H , C , S ) such t

that t h e c o l l i s i o n efficiency factor becomes o p t i m a l . F i g u r e 9 s c h e m a t i c a l l y


illustrates h o w p h y s i c a l a n d c h e m i c a l factors affect t h e c o a g u l a t i o n rate.

Figure 9.

Relative effects of collision efficiency factor and velocity gradient on coagulation rate

The coagulation rate depends upon physical parameters (temperature, velocity gradient, number and dimension of colloid), determining the collision frequency and upon chemical parameters (pH, Al(III) dosage, surface concentration of dispersed phase S), affecting the collision efficiency factor a (A) Al = 5.2 X 10-*M, (du/dz) = 100 seer ; (B) pH = 5.5, (du/dz) = 100 seer ; (C) pH = 5.5, Al = 5.2 X I 0 " ' M ; MIN-U-SIL 30 = 1 gram/liter 1

1

It m u s t b e k e p t i n m i n d that t h e efficiency of the c o a g u l a t i o n process i n p r a c t i c e is n o t solely d e t e r m i n e d b y t h e a g g l o m e r a t i o n r a t e ; t h e a t t a i n m e n t of c e r t a i n d e s i r a b l e floe p r o p e r t i e s m u s t b e i n c l u d e d i n d e l i b e r a t i o n s d i r e c t e d t o w a r d t h e o p t i m i z a t i o n of the process.

Nomenclature A a a

0

a

v

B C C Ce a

t

t

Ctopt

o.c.c. c.s.c. d

= L i g h t absorbance i n 4 c m . c e l l = C o l l i s i o n efficiency factor — C o l l i s i o n efficiency factor, m e a s u r e d u n d e r o r t h o k i n e t i c conditions = C o l l i s i o n efficiency factor, m e a s u r e d u n d e r p e r i k i n e t i c conditions — O p t i c a l constant o f scattering system ( R a y l e i g h c o n s t a n t ) = Concentration of adsorbed coagulant [ M ] = T o t a l c o n c e n t r a t i o n of c o a g u l a n t a d d e d [ M ] — T o t a l c o n c e n t r a t i o n of c o a g u l a n t necessary t o a t t a i n surface coverage 6 [ M ] = T o t a l c o n c e n t r a t i o n o f c o a g u l a n t necessary t o a t t a i n o p t i mum a [ M ] — C r i t i c a l coagulation concentration [ M ] — C r i t i c a l stabilization concentration [ M ] = D i a m e t e r of c o l l o i d a l p a r t i c l e [/x] o r [m/x]


110

ADSORPTION F R O M

r ax

=

I K K k fc A

— = — = = =

m

AQUEOUS

SOLUTION

Amount of coagulant adsorbed at surface saturation [M/meter ] Ionic strength of suspending medium [ M ] Langmuirs adsorption equihbrium constant [ M " ] Boltzmann constant Reaction rate constant of orthokin. coagulation [sec. ] Reaction rate constant of perikin. coagulation [sec. cm. ] Wavelength of light used in scattering experiments [m/x] (in vacuum) Total concentration of particles suspended [numbers per ml.] Total concentration of particles suspended; volume of particles suspended; at time t = 0 Coagulation rate [sec." cm. ] Absolute viscosity of suspending medium Surface area concentration of colloidal phase [meter / liter] Absolute temperature Fractional surface coverage Floe volume ratio of dispersed phase 2

B

0

p

0


N

=

NV

=

dN/dt n S

= — =

T 0

— — =

0

Q

1

-1

-1

1

8

3

2

Acknowledgment This work was supported in part by Research Grant W P 000 98 of the U.S. Public Health Service and the Federal Water Pollution Control Administration.

Literature (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18)

Cited

Fuerstenau, M. C., Somasundran, P . , Fuerstenau, D . W . , Trans. Inst. Mining Met. 74, 381 (1965). H a h n , H. H., Jahrbuch vom Wasser 33, 172 (1966). H a h n , H. H., Stumm, W . , J. Colloid Interface Sci. 2 8 / 1 , 134 (1968). H i d y , G . M., J. Colloid Sci. 20, 123 (1965). Kane, J. C., L a M e r , V . K . , L i n f o r d , H. B . , J. Colloid Interface Sci. (in print). M a l a t i , M. A., Estefan, S. F., J. Colloid Interface Sci. 22, 306 (1966). Matijević, E., Janauer, G . E., Kerker, M., J. Colloid Sci. 19, 333 (1964). Matijević, E., et al., J. Phys. Chem. 57, 951 (1953). Ibid., 64, 1175(1960). Ibid., 65, 826 (1961). Nelson, F . M., Eggertsen, F. T . , Anal. Chem. 30, 1387 (1958). O ' M e l i a , C . R., Stumm, W . J., J. Colloid Interface Sci. 23, 437 (1967). Ottewill, R. H., Watanabe, A., Kolloid Z. 170, 38 (1959). Packham, R. F., Proc. Soc. Water Treat. Exam. 7, 102 (1958). v. Smoluchowski, M., Z . Phys. Chem. (Leipzig) 92, 129 (1917). Somasundaran, P., Healy, T . W . , Fuerstenau, D . W . , J. Colloid Interface Sci. 22, 599 (1966). Sommerauer, A., Sussman, D. L., Stumm, W . , Kolloid Z . und Z. Polymere (in p r i n t ) . Stumm, W . , Morgan, J . J., JAWWA 54, 97 (1962).


9.

H A H N

(19)

A N D

S T U M M

Coagulation

by Al(III)

111

Stumm, W . , "Principles and Applications of Water Chemistry," p. 520, S. D . Faust, J . V . Hunter, E d s . , John W i l e y & Sons Inc., N e w York, 1967.

(20) (21)

Stumm, W . , Stumm, W . , Karlsruhe, (22) Teot, A . S.,

O ' M e l i a , C . R., JAWWA 60, 514 (1968). H a h n , H. H., Symp. Proc. Coagulation Flocculation, Univ. of Germany (September 1967). Conf. Polymer Sci., New York Acad. Sci., New York ( M a y

1967).

(23)

November 2 4 ,

Beihefte 54,

225

(1943).

1967.


RECEIVED

Troelstra, S. A., K r u y t , H. R., Kolhidchem.


Coagulation by Al(III) - Advances in Chemistry (ACS Publications)

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