cently (Hankinsoii e t al., 1970; Tassios, 1969) ill evaluatiiig activity coefficients a t finite solute concentrations.
SVBSCHIPTS
Conclusions
SUP1~:RSCRIPTS 0 = infinite dilution
The accuracy and simplicity of the proposed technique in relationship to still measurements or conventional gas-liquid chromatography approach, where a special columii for each solvent must be prepared, should provide a useful tool in solvent screening for extractive distillation. The requirement that the solutes have higher vapor pressure than the solvent is consistent with the conditions of estractive distillation. Although the solvent amount employed in extractive distillation does not correspond to the infinite dilution conditions for the solutp, it is often large enough to approach them. Hence, the obtained F,, values should provide a reliable w e e n ing. Nomenclature dk
= distance bet’weeii iiijectioii point and peak maximum
for component k , in. distance between peak maximums for air and component k , in. F 2,3 separation factor for misture of compounds i and j H I o = infinite dilution partition coefficient d f , = moles of stationary liquid phase per unit volume P = total pressure, a t m PkO = vapor pressure of pure k , atm x = mole fract’ion,liquid phase Y = mole fraction, vapor phase volume, carrier gas which V k = uncorrected retention passes through column between sample injection and peak maximum for compound k , cc Vk0 = corrected retention volume for espansion of gas phase in column, cc 171 = volume occupied by liquid phase in column, cc
Dk
=
GRI,I:KLLTTLRS = relative volatility y = activity coefficient
a
=
air
Ac knowledgment
The author is iiidebted to Vince Rickey for his assistance in obtaining tiic esperiineiital data. literature Cited I)eal, C. H., ])err, E. I{.>Ind. Eng. Chcm. P r o c ~ s sDcs. Devclop., 3 , 394 (1964). I)iiring, c. %., Chemistry, 1, 347 (1961). I)reisbach, l t , I?,,“Physical Properties of Chemical Compornids,” Advances in Chemistn, Series. N o . 15. Arnerican Chemical -~ SocietS, Washingtor;, I$.C.,~19%\,pp 11, 12, 441. Ureisbach, 11. I{., “Physical Properties of Chemical Compounds 11,” Advances in Chemistry Series, No. 22, American Chemical Society, Washington, D.C., 1959, pp 12, 24. Gerster. J. A , . Gort,on. J. A , . Eklund. 11. B.. J . Chem. Eno. D a h . 5 . 42k ilR60i. James, A.‘T., h r t i n , A. J. P., Biochc’ni. J., 50, 679 (1952). Hafslund, E. I?., Chem. Eng. Progr., 6 5 , 9, 58 (1969). Hankinson, R. UT., Langfitt, B. I)., Tassios, I). P., AIChEI
~~
I l l I Q Aleeting, I)envef; Colo. (1970);! Kwarites, A,, Rijnders, G. PV. A,, Gas Chromatography,” I>. H. I>esty, Ed., Academic Presu, London, England, 1958, p 125.
Pierotti, G. J., Ileal, C. H., ])err, E. L., 1)ocnment No. 5782, American 1)oriimentation Institute, Washington, D.C. (1958). Pierotti, G . J., Ileal, C. H., Ilerr, E. L., Ind. Eng. Chem.., 51, 9*5 (19.79). Porter, P. I)., Ileal, C. H., Stross, F. H., J . iitner. Cham. Soc., 78, 2999 (1956). Rock, H., Chcm. Ing. Tech., 28, 485 (19,56). Sheets, 11.R , , Marchello, J. hI., P~trol.Refiner, 42, 99 (1963). Tassios, I). P., Abstracts, Ilivision of Industrial aiid Engineering Chemistry, 54, 160th Meeting, ACS, Chicago, Ill., September 1970a. Tassios, I). P., 62nd AIChE Xeeting, Washington, D.C., (1969). Tassios, I). P., Hydrocarbon. Process., 4 9 (7), 114 (1970b). Warren, G. W,, Warren, 11. R., Yarborough, V. A., Znd. Eng. Chcm., 51, 1475 (1939). RECEIVF:D for review Koveinber 4, 1970 ACCEPTEDJuly 23, 1971
Settling of Flocculated Suspensions of Titanium Dioxide and Alum Mud in Water Samuel W. Bodman,’ Yatish T. Shah,’ and Michael C. Skriba Department of Chemical Engineering, C’niversity of Pittsburgh, Pittsburgh, Pa. 15213
T h e rate of settling of particles from a liquid-solid slurry is a critical factor in the design and optimization of many chemical processes. This type of study was first reported by Nichols (1908) who focused his attention on thickener operations. The settling of flocculated suspensions was first studied in detail by Coe and Clevenger (1916), and, subsequently, Ward and Kammermeyer (1940) summarized the work on sedimentation prior t’o 1940. 1 Present address, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02139. 2 To whom correspondence should be addressed.
46
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 1, 1972
In recent’ years the sett,liiig study in thickener operatioils was carried out by Coulsoil and Richardson (1955) and by Shannon aiid his co-workers (1963, 1964, 1965). Wadsworth and Cutler (1956) studied the effects of flocculating agents on the set,tling rates of kaolin suspensions, while Smellie aiid LaMer (1956) and Laller et al. (1957) correlated these settling rates by the Darcy filtration equat’ion. Bramer and Hoak (1966) and Bramer et al. (1966) studied the sedimentation of flocculated kaolin suspeiisions, and Piroska (1963) investigated the effect of electric current on the settling bed. Fitch (1966) has given a critical revie17 of some of the established met’hodsof thickener design.
An experimental investigation was carried out to study the settling of two industrially important slurries, titanium dioxide and alum mud in water. The independent system parameters investigated in the present study a r e the solids concentration in the slurry; pH, salt, and flocculating agent concentrations of the slurry; settling container size; mixing prior ta the settling; and the slurry temperature. The system conditions which would induce the flocculation or the agglomeration of the suspended solid particles in a solid-liquid slurry were also examined in the present work. The correlations for the settling rate of flocculated suspensions developed by Michaels and Bolger have been found to apply well to the systems investigated.
All these works, however, lacked a quantit.ative explanation
of the relation betneen the floc microstructure and the settling rate. Michaels and Bolger (1962a,b), on the other hand, developed equations which correlate the settling rate of flocculated particles with the floc microstructure and various physical properties of the surrounding fluid. These theoretical results were tested by Michaels and Bolger (1962a,b) for the settling of kaolin suspensions in brine solution having various values of pH. The purpose of the present paper is twofold: first, to report the experimental study of the setting processes of two industrially important chemicals. The chemicals examined in the present study are the anatase form of titanium dioxide (TiOz), used extensively in the paper industry for whitening paper or as a pigment in some grade of paints, and alum mud, a useful intermediate in the manufacture of various alum products. The latter chemical is the suspension of silicate skeletons which remains when bauxite ore is dissolved in sulfuric acid. Second, this paper reports on the testing of the applicability of the Michaels and Bolger settling correlations for the titanium dioxide and alum mud systems. This test is critical since Michaels and Bolger prepared their slurries by careful laboratory procedures; the slurries used in the present work were ohtained directly from industrial processes. Also, the slurries examined in the present study differ markedly, both chemically and physically, from the one studied by Michaels and Bolger (1962a,b). Experimental
The titanium dioxide used in the present study was in the anatase form having a particle size of 0.2 I" and purity of 98% (E.I. du Pout de Nemours & Co., Inc.). The flocculating agent used in the titanium dioxide system was provided by Calgon Corp., Pittsburgh, Pa., with the trade name WT-2870. Although the exact chemical composition of this product was not availahle, it has the structure of a quarternary amine. Alum mud was provided by Inorganic Chemical Division, American Cyanamid Co., Linden, N.J. The settling rate determinations for both titanium dioxide and alum mud systems were conducted in lo&, 250-, 500-, and 1000-ml graduated cylinders placed in a constant. temperature bath. I n the case of the titanium dioxide system, the experiments were carried out a t various temperatures, solid concentrations, pH levels, salt contents, and flocculating agent concentrations of the slurry. For the alum mud system, experiments were carried out a t *various temperatures, mud concentrations, and alumina contents in the slurry. Before the start of each experiment, the slurry was mixed properly by inverting the cylinder l(t30 times. Precautions were taken to ensure that no air bubbles were incorporated into the suspension before settling began. The height of the liquid-slurry interface was then measured a t time intervals of 30 see-1 min. The temperature of the slurry was checked a t the beginning and the end of each experiment.
I n the experiments with titanium dioxide system, the pH of the slurry WRS measured by a pH meter a t the beginning of each experiment. When thorough experiment mixing was desired in this system, the slurry was stirred with a Waring high-speed blender for approximately 1 min. The flocculating agent was then added dropwise into the mixed slurry to ensure uniform distribution. I n the settling experiments with alum mud systems, the sulfuric acid concentration of the slurry was sufficiently high to assure the complete solubility of all the alumina in the mother liquor of the alum mud slurries. Results and Discussion
The basic flow unit in the settling offlocculated suspensions is not the primary particle, but the small e11uster of particles (plus enclosed solvent) commonly called a floc. At low shear rates, the floes tend to group into clusters dlesignated as agSnxx ".> gregates. The aggregates may come togethe," tr. yv l y l l l l -.,tended network (Figure 1). The results of a settling experiment are conventionally presented as a graph of the height of the interfacial plane between the slurry and the supernatant liquid as a function of time. The three general types of settling curves shown in Fieure 2 have been observed by previous iuvestiga tors, Michaels and Bolger (1962a). . tne ,. For a settling curve of Type A, the floes are m aiiute concentration regime and they settle as separate entities, r l
Y
..,.
Dilute Concentration Regime
The dilute concentration regime is characterized by the settling curve of Type A in Figure 2. Michaels and Bolger (1962a) have proposed the following empirical correlation for the settling rate in this regime.
-
8
i 20
0
I
1
20
M
I 60
$
- 400
I 2 200
1 80
100
T'UE iMli
Figure 2. Examples of types of settling curves obtained in present work
essentially in Stokes flow. For a settling curve of Type B, the flocs are in the intermediate concentration regime and they settle as a coherent network. I n this regime, the initial settling rate is low owing to the time lag required for alignment of flocs. The settling rate in this case also depends on the diameter and the height of the settling tube. A settling curve of Type C is obtained for settling of slurries having a high solids concentration and a correspondingly high bulk slurry viscosity. This type of settling usually has little significance in a n industrial settling process. I n the present study, the effects of various system parameters on the maximum settling rate in settling curves of Types A and 13 are analyzed. The important parameters in the settling of flocculated suspensions are investigated with the help of following experimentally measurable and/or controllable quantities: Concentration of solids in the slurry Chemical treatment to the slurry Settling container size Mixing variation prior to the settling process Slurry temperature In the titanium dioxide system, different chemical treatments to the slurry were accomplished by the variation of pH, halt content, and the flocculating agent concentration of the slurry. In the case of alum mud system, a chemical treatment to the slurry was given by changing the dissolved alumina content iii the mud liquor.
where the exponent, n, for the small value of ( ~ F / Dis) given by Richardson and Zaki (1954) as to be equal to 4.65. The applicability of Equation 1 for the systems investigated here was examined by calculating the floc diameter from the equation for the typical values of experimentally measured settling rates and the fluid properties (such as viscosity and density). For this purpose, QO1/4 85 was plotted vs. &. The values of dF and CAScalculated from the slopes and the intercepts of such plots for typical system conditions are shown in Table I. For the alum mud system, the calculated dr values agreed well with the values 90 i. 15 I.( measured under a microscope. For the titanium dioxide system, the photomicrograph of a typical floc network is shown in Figure 1. This photo-
:::I\
0 12
0
Table 1.
48
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 1 , 1972
002
003 O D 4 0 0 5 006 0 0 7 008 Is!ml T802/ml WATER)
009
Figure 3. Maximum settling rate as a function of the volume fraction TiOt-basic region
Solid Concentration in Slurry
The amount of solids in the durry has a marked effect on the nature of the settling curve. *is indicated by Michaels and Ijolger, the increase in solid content' of the slurry will shift the nature of the settling curve from Type X to B and finally to C a t high solid concentrations. The settling rate, in general, should decrease with a n increasing solid content of the slurry. This is shown in Figure 3 for a typical case of sett,ling of titanium dioxide. As indicated in this figure, the break point,s between the two t'ypes of sett,ling curves are not PO clearly defined as they appear to have been in the kaolin system studied by Michaels and Bolger (1962a).
001
Floc Characteristics in Dilute Concentration Region
Slurry
d F , CC
CAa,
ml aggregate/ ml solid
TiOz settling a t 25°C pH=25 i>H = 12 4 Flocculated F Flocculated F
= =
10 5 12 0
Alum mud settling a t 70°C 0% A1203 1 07% A1203 2 60% i i 1 2 0 3
121 195 423 108 69 30 65 60 70 70
10 17 42 32
9 4 5 1
8 80 8 40 8 79
''1
0 13 00 1121 1
4
0-
0 IO
55 50
L
'a
- 5 44 o t
0 04 0 03
::I ;
i
-0
5
, , , 2
I 4
I
wH.15 TEMP = 23'C
,
8 TIME (MINI
6
1 1
0
1
1
,
I 1
4
j,
Figure 4. Settling plots for TiO, in intermediate concentration regime
'"1*120
L
LEGEND
e o c h c
REGIME 6 0 0 0 0 5 -E= 0 015 INTEOMEDATE Go5 0 0 2 0 INTERMEOIATE
at
0 025 INTERb4EDlATE
Figure 5. Maximum settling rate vs. initial slurry height for settling of TiO,
micrograph iiidicat,es that the floc structure of the sample taken from the slurry is nonuniform and t'he floc size varies from 50 to 600 p. Intermediate Concentration Regime
The intermediate concentration regime is characterized by sett,liiig curves of Type I3 in Figure 2 . l\lichaels and Bolger (1962a) developed the follon.ing correlation for t,he settling rate in this regime:
where Q1 is the settliiig rate in a n infinite container while D, and 2, are "yield" diameter a i d height for the settling colitainer. For the values of container diameter and height of the slurry below D , m d Z,, respectively, there will be no settling of the aggregate.*.Equation 2 thus correlates the sett,ling rate jvith the container diameter and the initial slurry height in the intermediate coiicentratioii regime. Figuie 4 shorn the settling plot.< for varioms initial ~1urry heights in the same container. -4s shown, the settling rate
0 02 0 01 0
0 01
002
0 03
0 04
0, ml Ti02/ml WATER
Figure 6. Maximum settling rate change, effect of container diameter a t various +a
decreases markedly as the initial slurry height is decreased. This is because there is less time available for channel formation and the slurry settles slowly in the short' height runs. If container diameter is large compared to yield diameter, Equation 2 indicates that a plot of &o vs. l/Zo should give a straight, line. Also, in the dilute concentration regime where t'he settling rate is independent of slurry height, such a plot should be a horizoiit,al line. Both of these relat.ionships are verified in Figure 5 for t,he settling of t'it'anium dioxide. Figure 6 shows the effect of container diameter on t,he settling rate. As shown in the figure, the diameter has essentially no effect on the settling rate in the dilute concentration regime, but has a marked effect in the intermediate concentration regime. In the intermediat'e concentratlion regime, the settling rate decreases with a n increase in container diameter. This is in qualitative agreement with Equation 2 . With the help of xet'tling rate data a t various container diameters (and for all otherwise identical settling conditions) , a value of yield diameter can be calculated from Equation 2 . The yield diameter calculat,ed in t'his manner was 0.5 cm for one particular slurry. A test was then made in a tube with an i d . of 3:/16 in. (0.47 cm), aiid it was observed that t,he aggregate net,work would no longer settle as a coherent struct.ure, but settled extremely slowly in sections with clear liquid between the sections (see Figure 7 ) . Thus, the assert'ion of Michaels aiid Eolgei (1962a) that no sett'ling would take place in the container of diameter smaller than D, has been found to be valid for the titanium dioxide system. Chemical Treatment to Slurry
The capacit'y of solids suspended in liquid to agglomerate and form a floc depends, in general, on the ionic conductive capacity of the liquid and the nature of the surface charges on the primary particles (Riddick, 1967). When the solid particles are suspended in liquid, they have a tendency to adsorb preferent,ially specific ions on their surface and to polarize the surrounding fluid. These induced charges then provide sufficient repulsire force to prevent agglomeration of any similarly charged particle?. The measure of this type of repellent' force is called zeta poteiit'ial rhich Riddick has defined as a measure of the net electrical potential (in millivolts) carried by particles in size range of 10 A to 10 p . The larger the zeta potential the les-jer the likrlihood of the formatioii of a floc or a n agglomerate. If, lionever, the electrolyte concentration of the liquid is high, then the liquid can act as a n ionic conductive Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 1 , 1972
49
.
... .-:’.-.~.~..~ .^.,”
.
.. -
. .
. .
’ . . .
. .
, ,
.
,
. .. . . . .. . .
.. . .
.. . . .. .. ... . .. . .. . .
. .. .. . . sal, C m C I N I A I T , O N IUOLlWLRElll
Figure 9. Effect of salt concentration on settling rate of TiO, in dilute concentration regime
Table
pH ‘ 2 5 Temp = 25°C lls = 0 2 Figure
7. Separation of the settling column in narrow tubes
II.
Zeta Potential of TiO, at Various pH l e v e l s for TiO, Water System (Du Pont, 1970) Zeta pOtenlial,
PH
mV
4 5 6 7
0 to -2 -7.5 -6.75 (f6.50) (-5.75) -26.5 -31.0 -35.0
8 9 10
Figure 8. pH effect on settling rate of TiO,
medium which could reduce the zeta potentials and deposit sufficient charges of the opposite characteristics to form a floc or an agglomerate. Thus, the flocculated suspensions would result only when the zeta potential for the particles in the slurry is low. The chemical treatment to the slurry can usually a,chieve the necessary reduction in zeta potential (Barrow, 1961). I n the titanium dioxide system, the settling rate a t various levels of pH showed unusual behavior. As shown in Figure 8, no clear liquid-slurry interface was obtained for the pH value between approximately 4 and 12. This type of behavior is believed due to the large values of zeta potential (see Table 50 Ind. Eng. Chem.
Process Der. Develop., Vol. 11, No. 1 , 1972
11) and the small values of ionic concentration between the pH range of 4 and 12 which prevent the agglomeration and the settling of the particles. Below a pH of 4, the zeta potential is small and hydrogen ion concentration in the solution is so high that the agglomeration would occur. At large values of pH (above 12.5), high concentration of hydroxyl ion could cause the agglomeration. Within the pH range of clear settling, the increase in pH is believed to increase the floc size (Jacquelin and Bourglas, 1964). Until the value of pH approximately equals 13.1, the nature of the settling curve was found to be Type A (see Figure 2). The characteristics of the floc evaluated from the Michaels and Bolger correlations for this type of curve a t two different values of pH are shown in Table I. These data show that the floc diameter and the amount of solvent conceutration in the aggregate increase with the increase in pH. At a pH of ca. 13.1, the floc and the aggregate size become so large that a coherent network is formed and a floc no longer settles as a separate entity; a t this point the nature of the settling curve changes from Type A to B. It should be noted that the viscosity of the slurry remains essentia.lly unchanged with the variation in pH. Thus, the nature of the settling curve is a function of pH of the slurry for the eitanium dioxide system. Within the range of no settling (pH range of 4-12) e g l o m eration should be achieved by increasing the electrolyte Concentration of the solution. This was demonstrated in the present study by the addition of salts in the slurry and measuring the settling rates. Two types of salts, sodium sulfate (NanSOn)and sodium chl .de (NaCl), were used for this purpose. A small quantity of the salts, approximately 0.3M was found to initiate the agglomeration, and settling took place wit.hin the pH range of 4-12.
The effect of a salt concentration on settling rate a t two different values of solid concentrations was evaluated. These results are summarized in Figure 9. As seen in this figure, initial, small additions of salt increase the floc size and produce an increase in settling rate. Eventually the salt increases the fluid viscosity t o such an extent that settling is impeded. The effect of the flocculating agent on the settling of titanium dioxide is shown in Figure 10. The data reported in this figure were obtained for a pH range of 4-12 in which no settling as found in the absence of t'he flocculating agent. As indicated in the figure, a certain amount of flocculatingagent concentration is needed to reduce t'he zeta pot'ential to a value low enough to permit settling. Once the settling has been initiated, the rate of settling increases rapidly with increasing flocculating-agent' concentration; this effect is more pronounced for the smaller values of t'he solid concentration. At high coiiceiitratioiis of the flocculating agent, the set,tljiig rate reaches a maximum value and then starts decreasing; ultimately the material deflocculates and no clear settling occurs. The decrease in settling rate and the deflocculation a t high concentrations are probably due to the self-induced double layer created by high concentrations of flocculating agent a t partirle surfaces. These self-generated layers can, under extreme conditions, cause interparticle repulsion and the resulting deflocculation (Calgon, 1970). I n the alum mud teni, the coucentration of AlVOsin the surrounding fluid has a strong effect, on the iiatuie of the settling plot. This effect can be attributed either to the increasing viscosity of t'he alum solution as the A1203 concentration is increased or to the increase in the experimentally measured floc size (see Table 111).The higher viscosity of the surrouiiding fluid causes a n increased viscous shear force on the flocs and a corresponding time lag for the alignment of floc a t the initiation of set'tling. The larger floc size could cause the
hindered settling. The settling plot which results a t high Al203 concentrations has the shape of curve Type B in Figure 2. Mixing Prior to Settling
Michaels and Bolger (1962a) reported that the type and intensity of mixing prior to settling had a significant effect on the settling of their kaolin suspensions except when the slurry had a low pH. To explain this, they postulated that for high slurry pH values, high shear mixing produces the larger aggregates. I n the present study, this effect was examined for the titanium diovide system; the results are summarized in Table IV. A s indicated by these data, mixing prior t o settling has little effect on the settling rate for either low or high pH values. Thus, unlike the kaolin system, the strong mixing did not produce large aggregates a t high values of pH in the titanium dioxide system. It appears that the cohesive forces within aggregates are strong in the titanium dioxide system, and a high shear field does not appreciably change the aggregate size. Slurry Temperature
I n general, the temperature could have an effect on aggregate microstructure as well as on the fluid properties such as viscosity and density. For several experimental conditions in both alum mud and titanium dioxide systems, the settling rates were measured a t various temperatures. If the temperature affects only the fluid viscosity and not the fluid density or the floc microstructure, Equations 1 and 2 indicate that plots of settling rate vs. fluid viscosity should correlate settling data taken over a range of temperatures. Figure 11 indicates this to be the case for both titanium dioxide and alum mud systems. Hence, the effect of slurry temperature on the settling rate can be, in general, evaluated from the measurement of the change in fluid viscosity with temperature and by use of the Michaels and Bolger correlations. 7 ' I-' ' " Settled Bed Density By assuming flocs t o be spherical and packed uniformly in a random, close fashion in the lower portion of the settled bed, Michaels and Bolger (1962a) derived the following relationship between the height of the settled bed and that of the initial slurry:
where b is the constant additional height added by the presence of the upper, nonuniform, low-density zone of the settled ~
10
0
20
30
40
50
60
o,
i Y O L U L l i DDm T U l W 7 02
Figure 10. Effect of flocculating agent concentration on settling rate of TiO,
Table 111. Typical Average Floc or Aggregate Diameters for Alum Mud Setlling at 70°C Ala03 in slurry,
% 1.07 6.1 8.3
Average floc or aggregate diameter measured by microscope,
90 i 15 150 15 250 =k 15
Table IV.
~-
Effect of M i x i n g Prior to Settling on the Settling Rate
Mixing type
Region
Settling rote, cm/sec
Inverted Blended Inverted Inverted Blended Inverted Inverted Inverted Blended Inverted Inverted
Acid dilute-+, = 0.006 Acid dilute-+, = 0.006 Acid dilute-+, = 0.006 Acid intermediate-$, = 0.02 Acid intermediate-+, = 0.02 Acid intermediate+, = 0.02 Basic dilute = 0.007 Basic dilute $ 8 = 0.007 Basic dilute + s = 0.007 Basic dilute +* = 0.007 Basic dilute = 0.007
0.094 0.093 0.089 0.029 0.032 0.035 0.087 0.082 0.093 0.090 0.088
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 1, 1972
51
Acknowledgment
The authors are grateful to A. G. Potter and C. M. Vanderwaart of the American Cyanamid Co. for their assistance in planning and executing the experimental program for alum mud system. The help of Westiiighouse Research Center for the experimental study with titanium dioxide system is gratefully acknowledged.
No menc lat ure
5
0 03
O 0 I /
0
I
IO
05
I 5
20
25
30
3 5
Figure 1 1 . Correlation between settling rate and fluid viscosity
GRIC~~K pw = viscosity of solution, CP p = density, g/cm3 # A = aggregate volume concentration pF = floc volume concentration = solid volume concentration
20 18 16
--
14
.-
12
Pi-
10 -
5
= =
le 1*
0 02
-
ordinate intercept of straight line of Equation 4, c m ratio of volume concentration of component i to component j , equal t o @i/@j, dimensionless D = diameter of settling tube, cm d~ = average (equivalent) aggregate diameter, D, = yield diameter, cm F = volume ppni of flocculating agent/g of Ti02 g = local gravitational acceleration, 980 cm/sec2 .\I = molar concentration, moles/l. Q0 = initial or maximurn settling rate, cm/sec &, = maximum settling rate in an infiiiitely large set’tling tube, cm/sec - initial height of slurry column, em Z , = final height of settled bed, em Z , = yield height of slurry column, em
b Ci,
004
SUBSCRIPTS s = solid F = flocs A = aggregates f = final conditions
~~
literature Cited 0
2
4
6
8
10
ZOO$
12
14
16
18
ICm/
Figure 12. Correlation of final and initial sediment heights in Ti02-water system
bed. Equation 3 indicates that a plot of Zfvs. Z0@& (for constant C F ~should ) give a straight line. The validity of this equation was examined for one set of system conditions in the settling of titanium dioxide. The results of thiq study, as shown i n Figure 12, indicate that Equation 3 applies well to the settling of titanium dioxide. Conclusions
The problem of agglomeration of the primary particles suspended in liquid can be partially handled with the knowledge of the zeta potential and the ionic coiicentratioii of the slurry. The optimization of t’he settling process would, in general, require a knowledge of the effects of various standard chemical treatments to the slurry on the aggregate structure and the fluid properties. If the aggregate structure is known, the correlations developed by Michaels and Bolger can be used for the design of a settling process for the system which is chemically and physically different from the one studied in t,heir work. 52 Ind.
Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 1 , 1972
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