The calculated and experimental t for various values of x, plotted in Figure 13, results in a straight line of slope 1. The present equation predicts the performance of a sparger reactor satisfactorily.
la7 1.6
-
1.51‘4
1.3
-
area of a bubble before reaction, sq. cm. area of a bubble after reaction, sq. cm. CA concentration of oxygen CA, initial concentration of oxygen CAa concentration of oxygen a t 6 C,, concentration of acetaldehyde D bubble diameter, cm. DAB binary diffusivitiy for system A-B, sq. cm./sec. AE = molal activation energy, cal./gram mole k = chemical reaction rate constant, gram mole/cc. min. kl I = chemical reaction rate constant, sec.-1 K = proportionality constant (NA),,= average rate of mass transfer of A , gram mole/sq. cm. sec. NAz = molar flux, gram mole/sq. cm. sec. No = number of bubbles in one mole of gas T = rate of reaction, gram mole/cc. min. = initial rate of reaction, set.-' = universal gas constant, cal./gram mole O C. SAo = solubility of nitrogen in acetic acid t = time of contact, sec. T = temperature, K. Vt = terminal velocity of rising bubble, cm./sec. X = conversion, moles of oxygen absorbed/mole of oxygen at the inlet Z = rectangular coordinate, cm. 6 = film thickness, cm. ‘4 0
=
Ai
= = = = = = =
2
CAS
7
= dimensionless concentration variable defined by -
1:
= dimensionless position variable defined by Z/g
CAO
literature Cited
Figure 13. Comparison between calculated and experimentally found t’s Nomenclature
A A’
= frequency factor =
(1) Bird, R. B., Stewart, W. E., Lightfoot, E. N., “Transport Phenomena,” pp. 535, 541, Wiley, New York, 1960. ( 2 ) Kumar, R., Kuloor, N. R., Brit. Chem. Eng. 9,400 (1964). ( 3 ) Sitaraman, R., Ibrahim, S. H., Kuloor, N. R., J . Chem. Eng. Data 8, 198 (1963).
RECEIVED for review May 3, 1966 ACCEPTED September 27, 1966
area of a bubble, sq. cm.
FORMATION OF SPHERES FROM FINELY DIVIDED SOLIDS IN LIQUID SUSPENSION C. E. CAPES AND J .
P. SUTHERLAND’
National Research Council, Ottawa 7, Canada
Finely divided solids suspended in a liquid are caused to agglomerate by agitating the suspension with a small amount of a second (bridging) liquid which preferentially wets the solid. Spherical agglomerates can be produced in a specially designed vessel shaken in a reciprocating fashion. The agglomeration of sands of various size distributions suspended in organic liquids and collected with aqueous solutions has been investigated as a model system. Spherical agglomerates were generally formed when the bridging liquid filled between 44 and 81 of the voids between the highly compacted sand particles. The ways in which the sphere size attained in the process may be controlled have also been investigated. The results are
yo
consistent with the postulate that the sphere size represents a balance between the destructive and cohesive forces acting on the agglomerates.
investigation concerns the process known as “spherical developed by Puddington et al. (6, 72) at the National Research Council of Canada. By this process, finely divided solids in liquid suspension are agglomerated and separated from the suspending liquid by the addition of a small amount of a second liquid which preferentially wets the solid and is immiscible with the first liquid. Subsequent agitation causes the solids to become coated with the second HIS
Tagglomeration’’
Present address, Chemcell (1963), Ltd., Edmonton, Alberta, Canada. 146
l&EC PROCESS DESIGN AND DEVELOPMENT
liquid and to agglomerate, being held together by the second (or bridging) liquid. Research into this agglomeration process has been directed along two main lines, selective agglomeration and spherical agglomeration. In selective agglomeration, one suspended solid can be separated from other suspended solids as well as from the suspending liquid by judicious zhoice of surface conditioning agents (as is done in the flotation of minerals) and of bridging liquids. The shape of the agglomerates produced in this case is not usually important. Examples of this separation technique have been given by Farnand, Smith,
and Puddington ( 6 ) ,and the fractionation of a tin-containing ore by selective agglomeration has been described (5, 7) in some detail. Sutherland (73) has demonstrated the separation of graphite from calcium carbonate in aqueous suspension in a drum agglomerator. I n spherical agglomeration, one is normally involved with only a single suspended solid component which is to be compacted into spherical shapes for a number of possible applications. Spheres of barium sulfate (72), graphite, and other materials (6, 73) have been made in this way. T h e present investigation concerned this latter area of sphere formation from liquid suspension. T h e agglomeration of silica sand suspended in various hydrocarbons and collected with water or aqueous solutions in a reciprocating shaker was used as a model system to study the process. Apparatus, Materials, and Procedure
T h e apparatus used is shown in Figure 1. Azglomeration took place in a cylindrical container (with hemispherical ends) which had an inside diameter of 2l/4 inches and an over-all (inside) length of 5 inches. T h e vessel was machined from a solid rod of Teflon in such a way that one of the hemispherical ends could be removed for adding the charge. (Since the Teflon surfaces were more readily wetted by the hydrocarbon suspending liquid than by the aqueous bridging liquids, no problem was encountered in the systems studied with material sticking to the vessel.) The inside surfaces of the container were smooth and free from sharp corners and crevices so that no pockets would be available in which the solids to be agglomerated could accumulate. T h e vessel was mounted on the shaker arm as shown in Figure 1 with its long axis horizontal. T h e shaker arm was driven in a reciprocating action with a stroke of 4 inches by means of a drive wheel, a gear reducer, and a variable-speed electric motor. The speed was adjusted manually and measured by means of a stroboscope. TO GEAR REDUCER AND ELECTRIC MOTOR
d3
-
4 I n . STROKE
R E C I P R O C A T I N G ACTION
A
DRIVE WHEEL
The design of vessel described evolved from several preliminary designs as one which gave a high degree of sphericity in the agglomerated product. The apparatus imparted two types of motion to the agglomerates, the first being translational, which was of sufficient intensity to cause slight deformation of the agglomerates upon impact; and the second, rotational (caused by the curved internal surfaces), which ensured that the point of impact varied with each collision. Because of the control over the rate of shaking, the energy input to the agglomerating charge could be varied widely. The properties of the sands which were agglomerated are summarized in Table I. The first three closely sized sands were prepared by repeated screening with standard sieves or with micromesh sieves. The sands were crushed materials and were irregular in shape. Prior to use, the sands were acid-washed and were dried at a high temperature (500' C.) to ash any small amounts of organic impurities present. The various suspending liquid-bridging liquid pairs used in the study were equilibrated mixtures-that is, the liquids were in contact for several hours before being used to ensure that they were mutually saturated. The systems used were all essentially immiscible. Thus the bridging and suspending liquids could be considered completely insoluble in each other, T o charge the vessel, the required amount of suspending liquid was first added to the container. A weighed amount of sand was added next, followed by the desired amount of bridging liquid. I n all the runs, except those with benzene as suspending liquid, the density of the suspending liquid was such that the aqueous bridging liquid floated on top of the suspending liquid while the sand settled to the bottom. Hence the solids and bridging liquid did not come in contact until the vessel was shaken. The vessel was then attached to the shaking arm by means of a vice-like device and shaken at the preset speed for the required period of time. Growth of Spherical Agglomerates
Initial experiments were performed to establish the effect of adding small amounts of water to agitated suspensions of sand in carbon tetrachloride. Previous work (6, 72) had shown that, depending upon the amount of water added, one could expect to find a voluminous suspension of flocs, a number of compact agglomerates, or perhaps a combination of these two products. The course of such experiments may conveniently be represented by a plot of sedimentation volume against the amount of water added. (In this work, sedimentation volume was determined as the settled volume of the suspension after it had been allowed to settle undisturbed for 24 hours in a 100-cc. graduated cylinder.) Such a plot for the 44- to 53-micron uniformly sized sand is shown in Figure 2. When no water is added, the sedimentation volume is small. There is little tendency for the particles to flocculate so that they form a relatively compact layer.
Table 1.
Properties of Sands Used in Study
Particle Size Range Tyler mesh numbers Microns
+ +
-270 325 -115 150 95 wt. yo -100 250
+
TEFLON VESSEL Figure 1. Reciprocating shaker
++ +
-31 15 -53 44 -124 104 95 wt. yo -149 62 95 wt. 7 0 -70
+ + 10
ClosePacked Apparent Density, pa, G./Cc.
Vaid Volume, Cc. Void/ G. Sand
1.38 1.40 1.50 1.69
0.35 0.34 0.30 0.22
1.72
0.21
True density of sand l/p,
- l/p,
= l/p,
= p. = 2.67 g./cc. Void volume = - 0.37 cc. void/g. sand.
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147
n
I AIR
TOTAL WATER +CCl,)
t
3-
WATER
2-
I
DE
I
0
,
I
3
4
VOLUME WATER A D D E D , cm3
V O L U M E WATER A D D E D . c r n 3
Figure 3. Analysis of materials in pores of spheres
Figure 2. Effect of water content on agglomeration of 44- to 53-micron sand
--/
2
10 grams of 44- to 53-micron sand 75 CC. of carbon tetrachloride
limits of water content for satisfactory sphere formation
10 grams of sand 75 cc. of carbon tetrachloride 300 r.p.m.
3 0 0 r.p.m. 2-hour shaking
2-hour shaking
With the first additions of water, however, the settled volume increases rapidly. The water is selectively adsorbed on the hydrophilic sand particles and displaces part of the organic suspending liquid. The particles collide under agitation and stick together because of the formation of water bridges between the particles. The particles settle as clusters and form a loose settled structure of large volume. With further additions of water, the sedimentation volume decreases rapidly from its maximum value to an approximately constant, considerably lower value. As the sedimentation volume decreases from its maximum value, a few relatively compact agglomerates are noted among the flocculated sand. When the sedimentation volume becomes constant, the sand is essentially all in the form of highly compacted spherical agglomerates. If the ultimate particles are considered as spheres of uniform diameter, the number of junctions associated with an individual particle will vary from a minimum of about two in the chain-like floc structure to a maximum of 12 within the body of a hexagonally packed structure (6). As the water content of the charge is increased, one moves from a region in which only a few bridges per sphere are possible, so that flocs result, into a region in which multiple bridges are possible. Agitation brings the sand particles into contact and spherical agglomerates result. Agglomerates are formed over a fairly wide range of bridging liquid contents (Figure 2). They are reasonably spherical and have a narrow size distribution. The mean sphere size is essentially independent of water content over most of the range of bridging liquid contents. The sand particles are compacted to a porosity very close to that which can be obtained by compacting the dry sand to its minimum porosity in a cylinder [after the method of Roller (77)]. T h e agglomerates contain carbon tetrachloride and air, in addition to bridging liquid (water in this case). The amount of air is equivalent to approximately 5% of the pore volume, while the amount of carbon tetrachloride decreases as the bridging liquid content of the charge increases, as is shown in Figure 3. There is, of course, a limit to the amount of water which one may add to the suspension and still obtain spherical agglomerates. Eventually a small number of irregular agglomerates which can easily be deformed and stick readily to each other are formed. This behavior signals the start of a region of bridging liquid contents in which, eventually, two immiscible liquid phases 148
l&EC PROCESS DESIGN A N D DEVELOPMENT
result, with the sand particles being transferred from the original suspending liquid to the aqueous phase. Selective agglomeration in this range of bridging liquid concentrations has been described (5, 7) and the phenomenon may perhaps best be designated as “liquid-liquid particle transfer,” analogous to liquid-liquid extraction of soluble constituents. Bridging Liquid Concentration Required for Sphere LIQUIDDENSITY, SAND Formation. EFFECTSOF SUSPENDING In some experiments PARTICLE SIZE,AND SIZEDISTRIBUTION. spheres were formed from charges composed of the closely sized sands and sands of wider size distribution listed in Table I, suspended in various liquids and collected with water. The results of these experiments should be useful in predicting the amount of bridging liquid required to form spherical agglomerates in systems similar to those discussed. In each case, 75 cc. of suspending liquid and 10 grams of sand were shaken together with the stated amount of water at 300 r.p.m. for 2 hours in the Teflon vessel. The sedimentation volume and sphere size (by sieve analysis) were determined for the product in each case. The experimental results are shown in Figures 4 to 6. In Figure 4, the curves of sedimentation volume us. water content for the 44- to 53-micron sand suspended in carbon
mc W
401
2,
P
3oc
0
2-0b.o
I VOLUME WATER
2
ADDED,cm3 Figure 4. Effect of suspending liquid density agglomeration of 44- to 53-micron sand
3
on
0 Suspended in CCla(p = 1.60 g./cc.) 10 grams sand 75 cc. of suspending liquid A Suspended in C&,CI ( p = 1.1 1 g./cc.) 0 Suspended in C8Hs ( p = 0.88 g./cc.) 300 r.p.m. 2-hour shaking Limits of water content for satisfactory sphere formation
1---1
tetrachloride, monochlorobenzene, and benzene are shown. The densities of these liquids are, respectively, 60% greater than, slightly greater than, and slightly less than that of water, so that in the first two systems, the bridging liquid and solid were kept separated until agitation started, while in the last system, the bridging liquid could wet the solid prior to agitation. Spherical agglomerates are formed in the three systems over the same range of bridging liquid concentrations. This is not surprising, however, since even if the solid and bridging liquid are separated until shaking starts, the bridging liquid is not dispersed evenly throughout the suspension but becomes associated with only a fraction of the solid in the early stages of agglomeration. After extended agitation, however, the water apparently becomes evenly distributed among the solid particles with the formation of uniform spheres. Hence any effects which might have been expected when the bridging liquid can wet pockets of the solid (at random) prior to agitation-e.g., localized sphere formation in the areas of high water content-would tend to be removed because prolonged agitation allows the bridging liquid eventually to become evenly distributed over the solid. Similarly one would expect that zdding water as fine droplets during the first few seconds of agitation, so as to distribute it evenly in the suspension, would not affect the bridging liquid requirements for sphere formation. However, in cases in which the bridging liquid is held more rigidly in the particulate solid than in the case of these sand-water-organic systems-e.g., when the bridging liquid is held by chemisorption on the solid-the manner in which the bridging liquid is introduced would probably be important in determining the agglomeration behavior. Figures 5 and 6 give the results of the tests with the uniformly sized sands and with sands of wider size distribution, respectively. In each of these experiments, carbon tetrachloride and water were used as the suspending liquid and bridging liquid, respectively. I t is evident that the bridging liquid concentration required for sphere formation is influenced by the particle size distribution. These results may be better understood by considering the summary of data given in Table 11. The bridging liquid concentration, in cubic centimeters of water per gram of dry sand, at which spheres are first formed and that a t which a small number of tacky, easily deformable, and irregular agglomerates are formed for
0
I 2 VOLUME WATER ADDED, crn3
3
Figure 5. Effect of particle size on agglomeration of uniformly sized sands
A
1 5 - to 3 1 -micron sand
0 4 4 - to 53-micron sand 1 0 4 - to 124-micron sand
(---I
Limits of water content for satisfactory sphere formation 10 grams of sand 75 cc. of carbon tetrachloride 300 r.p.m. 2-hour shaking
40
30
I
I I
0
Figure 6. Effect of particle size on agglomeration of sands of wide size distribution
0 10- to 70-micron sand A 62- to 149-micron sand
/ - --I
Limits of water content for satisfactory sphere formation 10 grams of sand 75 cc. of carbon tetrachloride 300 r.p.m. 2-hour shaking
each system are tabulated and expressed as a fraction of the measured close-packed void volume for the respective sands when dry (as given in Table I). With the exception of the 104to 124-micron sand, satisfactory spherical agglomerates were formed when the bridging liquid occupied between 44(*2)% and 81(+4)% of the void space in the agglomerates. The balance of the void space is occupied by the suspending liquid and entrapped air (see Figure 3). A study (3) of normal granulation (in a revolving drum in air rather than under a blanket of liquid) has shown that granules are formed and continue to grow a t a significant rate only when bridging liquid contents are used which are greater than about 90% of the amount required to fill the voids between the sand particles when they are highly compacted. Such liquid contents apparently ensure that the granules have a degree of plasticity and readily available liquid a t their surfaces. These conditions are considered necessary for granule growth which occurs, initially, by the sticking together of small granules (3, 9 ) . The present work is in accord with these observations if one notes that (Figure 3) a t the upper limit of water content for satisfactory sphere formation, approximately 10% of the voids are filled with entrapped suspending liquid. In other words, irregular plastic agglomerates which tend to stick to one another are formed in the present process, as well as in normal granulation, when more than 90% of the void space is filled with liquid. In both processes ab0u.t 5% of the void space is occupied by entrapped air ( 2 , 9 ) . The reasons why the 104- to 124-micron sand formed spherical agglomerates a t relatively lower fillings of the void space than the other four sands studied are not entirely clear. This behavior may be associated with the fact that displacement of a nonwetting fluid from a porous agglomerate by a wetting fluid depends primarily upon capillary pressure as a driving force (7). The capillary pressure produced by the water in the 104- to 124-micron sand would be less than in any of the other sands, since this decreases with increase in particle size and porosity. Hence the 104- to 124-micron sand may retain larger amounts of the nonwetting suspending liquid than the other sands, so that the voids would be relatively more filled with liquid a t the same water content. Consequently spherical agglomerates would be formed a t lower bridging liquid contents. The above conclusions regarding the bridging liquid requirements for sphere formation are applicable only to systems VOL.
6
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149
Table II.
Bridging liquid Contents for Satisfactory Sphere Formation
Suspending Liquid
Sand Used
104- 124-micron (closely sized) 62- 149-micron (wide size distribution) 44- 53-micron (closely sized) (p (p
CC14 ccl4 CCl4 = 1.60 g./cc.) CsHsC1 = ;:1 ; g./cc.)
Bridging Liquid Concentrations W h e n a F e w Large Plastic W h e n Spheres First Formed Agglomerates Formed Fraction of Fraction o f close-packhd close-packid Cc./g. sand aoid volume Cc./g. sand void volume 0.10 0.33 0.18 0.60 0.09 0.41 0.18 0.82
0.15
0.44
0.28
0.82
0.15
0.44
0.29
0.85
0.28
0.82 0.76 0.80
-"--"
(p =
10- 70-micron (wide size distribution)
15- 31-micron (closely sized)
0.88 g./cc.)
CCla CCl4 Collecting liquid, water Speed, 300 r.p.m.
in which the bridging and suspending liquids are mutually insoluble and the particles are inert to the bridging liquid, are not porous, and are not plate-like or fibrous in shape. Hence Sutherland (73) agglomerated graphite from aqueous suspension with an immiscible oil as collector (a system which apparently obeys the above restrictions) and found that the bridging liquid occupied 55% of the void space in the agglomerates, well within the range suggested by the present work. On the other hand, a study of 20 different solids ( 6 ) ,many of which did not obey the restrictions imposed above, showed a wide variation in the amount of bridging liquid required for spherical agglomeration to take place. Factors Affecting Sphere Size
I t is generally accepted (3, 8, 70, 75) that the final size reached by an agglomerate represents a balance between the inertial or disruptive forces acting on the agglomerate and the cohesive forces which resist the destructive forces and hold the agglomerate together. No systematic work has been done on the factors which affect sphere size in the spherical agglomeration process carried out in a reciprocating shaker. However, experience in the authors' laboratory has shown that when the cohesive strength of agglomerates is lowered by adding suitable alcohols to organic-aqueous phase systems, or when the suspended solid is imperfectly wetted (because of the presence of trace contaminants), smaller sphere sizes generally result. Regarding the destructive forces acting on the agglomerates, Smith and Puddington (72) recognized that the intensity and type of agitation were important in determining sphere size and shape, while Sutherland (73), who studied agglomeration from suspensions tumbled in a rotating drum, showed that sphere size was affected by the solids concentration and the drum loading among other factors. Considerable work has been done with regard to the factors which determine floc size in the flocculation of powders in suspension. This work may be considered here, for spherical agglomeration is, in fact, a rather special type of flocculation. For example, the work of Reich and Vold (70), who investigated the degree of flocculation of aqueous suspensions of ferric oxide and carbon as a function of concentration, time, and intensity of agitation, is highly relevant. The average floc size always increased with increasing concentration and with decreasing intensity of agitation. A striking ramification of these conclusions is found in the work of Yusa and Gaudin (75) who studied flocculation in kaolinite pulps to which 150
l & E C PROCESS D E S I G N A N D DEVELOPMENT
0.47 0.09 0.43 0.16 0.43 10 grams of sand 75 cc. of suspending liquid 2-hour shaking 0.16
0.16
0.28
polymeric flocculants were added. The pulps were agitated in stoppered graduates which were rotated slowly; large, compact pellet-like flocs were formed when the graduates were completely filled with the suspension, in contrast to the smaller, voluminous flocs produced when the tube was partially filled with air-that is, when the degree of agitation was much larger. Four factors which one would expect to be very important in determining sphere size in the spherical agglomeration process have been studied : 1 . Interfacial tension between the bridging and suspending liquid 2. Speed of shaking 3. Solids concentration in suspension 4. Fractional filling of the vessel by the suspension
The 44- to 53-micron uniformly sized sand was used exclusively in this part of the work, with a bridging liquid concentration of 0.2 cc. per gram of sand. This concentration corresponds to the middle of the bridging liquid content range over which satisfactory spherical agglomerates are formed for this sand. The other operating conditions were set as follows: System Shaking speed Shaking time Volume of suspending liquid Weight of sand
Carbon tetrachloridesand-water
300 r.p.m. 2 hours
75 cc. 10 grams
All the variables except the one whose effect on sphere size was being studied were kept a t the levels stated above. The weight mean sphere diameter for each run was calculated from a sieve analysis of the product. T o study the effect of decreasing interfacial tension on the formation of spheres, varying amounts of methanol were added to the carbon tetrachloride-water system. The mixtures were made up in fairly large quantities, shaken together, and allowed to settle for 3 hours to ensure that equilibrium conditions existed. The mixtures were then separated into aqueous and organic phases, and the required amounts were used in the agglomeration experiments. Simultaneously, the interfacial tension for each pair of phases was measured using a du Nouy interfacial tensiometer (supplied by the Central Scientific Co.) equipped with a platinum ring. The make-up of the mixtures used, together with the measured interfacial tension data, and the interfacial tension data for the same system from the literature (74) are listed in Table 111. Valentine and Heideger (74)found that methanol
Table 111.
Data on Mixtures Used to Study the Effect of Interfacial Tension on Sphere Size Interfacial Tension, DyneslCm. Data of Valentine Mole % and Methanol This Heideger Weight of COm!Onents, Grams in Aqueous work (l f ) (26’ C.) (20 C.) cc11 Water Methanol Phase 1500 5 00 0 0 44.2 43 ~. .. 90 9.2 28.8 27 1500 500 222 20 19.6 17 1500 500 11.3 444 40 1500 500
is essentially nondistributive in the system carbon tetrachloride-water and this was assumed in calculating the mole per cent methanol in the aqueous phase in Table 111. The measured interfacial tensions agree reasonably well with those of Valentine and Heideger, but are consistently higher. However, Davies and Rideal ( 4 ) give the interfacial tension for the binary system carbon tetrachloride-water as 45.1 dynes per cm. a t 20’ C., which is also higher than the corresponding value of 43 dynes per cm. found by Valentine and Heideger (74).
T o supplment the data on the effect of interfacial tension on sphere size, the effect of interfacial tension on sphere strength was studied. The agglomerates were crushed between two parallel flat plates, the lmver one of which was the pan of a spring balance. A steadily increasing load was applied to the granule and the maximum value before collapse (as registered by a “follower” on the dial of the spring balance) was taken as the breaking load. Prior to crushing, the spheres were photographed to allow their diameters to be determined later. Provision was made so that spheres could be crushed either in air, or under a blanket of liquid immiscible with the aqueous binding liquid. Hence, interfacial tensions of 72.0 dynes per cm. (crushed in air), 45.1 dynes per cm. (crushed under carbon tetrachloride), and 26.0 dynes per cm. (crushed under nitrobenzene) were operative in determining sphere strength. Results
Crushing strength tests were performed on spheres formed from the 44-to 53-micron sand, with a bridging liquid concentration of 0.2 cc. per gram of sand, suspended in carbon tetrachloride, and produced with various shaker speeds, solids loadings, and suspending liquid loadings. The load required to crush each granule was divided by the square of its diameter (LID2). Agglomerates ranging in size from about 4 to 12 mm. were tested, and it was found that the factor (LID2) for spheres crushed in the same environment-that is, in air or under the same liquid-was independent of the operating conditions under which the spheres were formed, within the limits of accuracy of the tests. The strength factors obtained in air, and under carbon tetrachloride and nitrobenzene, are plotted in Figure 7 as a function of the ratio of interfacial tension to particle diameter. Each point represents the average of a large number (>50) strength determinations. Included in Figure 7 are data for agglomerates produced by conventional granulation taken from the work of Newitt and Conway-Jones ( 9 ) and Capes ( 2 ) . These strength factors are for agglomerates produced from uniformly sized sands with water as binding liquid and crushed in air. The strength factors are all correlated by the same straight line whose equation is:
where L = crushing load, grams
.
N
E
0
INTERFACIAL TENSION =_I_ , PARTICLE DIAMETER d
Figure
dynes cm,rnicron
7. Crushing strength data
Spheres formed in present work, crushed under various liquids or air 0 Crushed in air 0 Crushed under carbon tetrachloride A Crushed under nitrobenzene Agglomerates formed b y conventional granulation, crushed in air
-$-
Data of Newitt and Conwoy-Jones (9)
0 Data of Capes (2)
D T d
= = =
agglomerate diameter, cm. interfacial tension, dynes per cm. particle diameter, microns
The results of the experiments on the effect of the various operating and system variables on sphere size are shown in Figures 8 to 11, inclusive. I n each case the weight mean granule diameter is plotted as a function of the variable being studied. Each weight mean sphere diameter represents the average of three or four runs under the conditions indicated. The weight mean sphere diameter was found to: Vary directly (approximately) with interfacial tension, as shown in Figure 8 Vary inversely with shaker speed raised, approximately, to the 8/10 power (as shown in Figure 9) for shaker speeds between 150 and 550 r.p.m. The sphere diameter falls very rapidly to a relatively small value as the speed is raised further to 600 r.p.m.
Y
3
INTERFACIAL TENSION PARTICLE DIAMETER
Figure 8. Effect of sand particle size and interfacial tension on sphere size 10 grams of sand 2 cc. of bridging liquid 75 CC. of suspending liquid 3 0 0 r.p.m. 2-hour shaking 0 4 4 - to 53-micron sand, organic-aqueous liquid pairs listed in Table 111 22-, 49-, and 114-micron sands; watercarbon tetrachloride system
VOL 6
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JANUARY
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151
Increase linearly as the weight of sand being agglomerated is increased, as shown in Figure 10 Be independent of the volume of suspending liquid (as shown in Figure 11) for volumes between 40 and 180 cc. The sphere diameter increases significantly as the volume of suspending liquid is raised to 225 cc. Discussion
100
200 300 400 500 600 SHAKER SPEED, r.p.m.
Figure 9. size
Effect of shaking speed on sphere 44. to 53-micron sand
FD
10 grams of sand 2 cc. of water 75 CC. of carbon tetrachloride 2-hour shaking
E- 14
The final size reached by an agglomerate is determined by a balance between the destructive forces and the cohesive forces acting on the agglomerate. The destructive forces arise from collisions between agglomerates and collisions with the container walls. Disruptive forces due to gravity will be considered negligible in comparison to those arising from impacts. Qualitatively these destructive forces will be proportional to the mass of the agglomerates-that is, to the sphere diameter cubed (8, 70). Thus :
,
1
= f(S,W8,pS,
VL,etc.) D3
(1)
where FD are the destructive or (inertial) forces D is the agglomerate diameter f(S, Jl’s, p s , VL, etc.) indicates that the constant of proportionality is a function of the shaking speed, S, the weight of solids being agglomerated, W,, the density of the ultimate particles, p s , the volume of suspending liquid, V L ,etc. The cohesive forces associated with the interfacial tension between the bridging and suspending liquids have been examined by Newitt and Conway-Jones ( 9 ) . They found that the breaking load is proportional to the agglomerate diameter squared-that is,
L = kD2 w
3
o
IO
20
30
40
50
AMOUNT of SAND C H A R G E D , gm.
Figure 10. Effect of amount of solid being agglomerated on sphere size
(2)
where the strength factor, k, for spheres made from uniformly sized sands in which the pores were slightly less than saturated with the bridging liquid which completely wets the solid is given by : (3)
44- to 53-micron sand 0.2 cc. of water per gram of sand 75 cc. of carbon tetrachloride
where K = constant e = sand porosity T = interfacial (or surface) tension d = diameter of sand particles
3 0 0 r.p.m. 2-hour shaking
From Equations 2 and 3, the cohesive force, Fc, is given by:
Fc=C
3
AMOUNT of CARBON TETRACHLORIDE, cm3
Figure 1 1 . Effect of amount pending liquid on sphere size
of
SUS-
44- to 53-micron sand 10 grams of sand 2 cc. of water 3 0 0 r.p.m. 2-hour shaking
152
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
-
(I
:
-0’
(4)
where C is a constant. Equation 4 has been found (2, 9 ) to apply for granules formed by conventional granulation from uniformly sized sands of different sizes and bound with liquids of various surface tensions when the granules were crushed in air. It is seen in Figure 7 that Equation 4 also applies to spheres formed in the present process when they are crushed under various liquids of different interfacial tensions with water. [The factor (1 - c)/e was ignored in plotting the crushing strength data in Figure 7. In fact, the porosity varied between about 0.41 and 0.45 for the various sands for which data are plotted, and this variation probably accounts for some of the scatter of the data in Figure 7.1 The crushing strength data in Figure 7 from ( 2 ) and ( 9 ) apply to agglomerates whose voids are filled with the bridging liquid (plus some air), whereas the data
from the present work apply to agglomerates whose voids are about 70y0 filled with bridging liquid, while the remaining pore space is filled with the suspending liquid (plus some air). However, the crushing strength of all these agglomerates may be correlated by the same equation. I t may be concluded that the suspending liquid held within the spheres produced by the present process is completely surrounded by bridging liquid, and the strength characteristics of the agglomerates, which depend on the capillary pressure developed when the surface liquid is withdrawn into the pores, are therefore the same as those of spheres whose voids are occupied by only a single wetting liquid. The final sphere size reached in the spherical agglomeration process is given when FDis set equal to Fc-that is, using Equations l and 4
This equation is consistent with the experimental results cited above. The mean sphere diameter varies approximately directly with the interfacial tension. I n addition, factors which would be expected to increase the function j ( S , W,, p s , V L ,etc.), such as increased speed of shaking or decreased solids loading, were found to decrease the mean sphere size. (Decreasing the solids loading, I$;, apparently increases the distance agglomerates travel between impacts, thus leading to more energetic collisons.) These findings are in agreement with the work of Reich and Vold (70) regarding the behavior of agitated suspensions of flocs. One would also expect the agglomerates to grow larger as the volume of suspension is increased because the collisions which the spheres undergo should become less violent as the movements of the agglomerates become more constrained with decreasing amounts of air in the vessel. However, the sphere size remains independent of the volume of suspension until the vessel becomes about 7oy0 filled (volume of vessel = 280 cc.), after which this effect becomes noticeable and the sphere size begins to increase. Equation 5 also indicates that sphere size should be inversely proportional to the sand particle diameter. The effect of sand particle size on the size of spheres produced from uniformly sized sands can be seen in Figure 8. T h e data plotted along with those which indicate the effect of interfacial tension were taken from the experiments described earlier, in which the 22-, 49-, and 114-micron average diameter sands were agglomerated (see Figure 5 ) . The sphere size may be considered to be inversely proportional to sand particle size, as well as directly proportional to interfacial tension, for values of T/d less than about 1 dyne/cm.-micron. However, there is apparently a gross deviation from Equation 5 for higher values of T/d. I t appears that Equation 5 is an oversimplified representation of the forces acting in the process. The equation is useful, however, in indicating how various factors would be expected to affect the final sphere size. In the above discussion, the sphere size finally obtained has been treated as resulting from an equilibrium between disruptive and cohesive forces acting on the agglomerates. One might ask whether the process is completely reversible-that is, whether the sphere size obtained is independent of the path which has been followed to reach the final state. Experiments indicate that the process is only partially reversible-for example, spheres having a mean diameter of about 10 mm. were produced from the 44- to 53-micron sand under standard conditions a t 200 r.p.m. The speed was then increased to
600 r.p.m., and after 2 hours, spheres 2 to 3 mm. in diameter had formed, whereas spheres formed in a single operation a t 600 r.p.m. should be about 1 mm. in diameter. When the speed was then reduced back to 200 r.p.m., larger spheres (approximately 7 to 8 mm. in diameter) were formed, but were smaller than those which had been produced originally. Reich and Vold (70), in studying agitated suspensions of flocs, found that the dispersion process was not completely reversible. Conclusions
When a particulate solid is suspended in a liquid and a second liquid, which preferentially wets the solid and is immiscible with the first liquid, is added and the mixture is shaken in an appropriate vessel, the solid becomes agglomerated. Using sands of narrow and wide size distribution suspended in various organic liquids, it has been shown that compact spherical agglomerates are formed if the amount of the second (or bridging) liquid is sufficient to fill between approximately 44 and 81 yoof the voids between the sand particles when highly compacted. With lower bridging liquid contents, a bulky flocculated mass is formed. With higher bridging liquid contents, irregular easily deformable agglomerates which stick readily to each other are formed. The final sphere size reached in the spherical agglomeration process may be treated as representing a balance between the destructive and the cohesive forces acting on the agglomerates. T h e following equation for the final sphere size results:
One would expect the proportionality constant, j ( S , W,, p,, V L , etc.), to be related directly to the speed of shaking and inversely to the weight of solids being agglomerated and the fractional filling of the vessel by the suspension. The experimental results are roughly consistent with the proposed equation. T h e final sphere size varies approximately directly with the ratio of the interfacial tension to the sand particle diameter, varies inversely with (speed)o.*, increases linearly with the weight of sand being agglomerated, and increases significantly when the vessel becomes more than 70% filled with suspension. Acknowledgment
A. E. McIlhinney performed many of the early experiments which resulted in the development of the apparatus used in this study. T h e help of J. P. Kolody in performing the experimental work is also acknowledged. The authors thank I. E. Puddington for his interest and encouragement. Nomenclature
C d
D
j ( ,. . , , ) FD FC
k K L S T VL JV8
e Pa
Pa
= = = = = = = = = =
= = = = = =
a constant in Equation 4 particle diameter, microns agglomerate diameter, cm. function of quantities within brackets destructive or inertial force, consistent units cohesive force, consistent units strength factor, g./sq. cm. a constant in Equation 3 breaking load, g. shaking speed, r.p.m. of drive wheel interfacial tension, dynes/cm. volume of suspending liquid, cc. weight of solids being agglomerated, g. sand porosity, dimensionless apparent density of sands, g./cc. particle density, g./cc. VOL. 6
NO.
1
JANUARY 1967
153
literature Cited
(1) Bob+ J. E., Mattax, c. c.2 Denekas, M. o., Petrol. Trans. A I M E 213,155 (1958). (2) Capes, c. E., ‘‘Formation of Granules from Powders,” Ph.D. thesis, University of Cambridge, 1964. (3) Capes, c. E., Danckwerts, p. v., Trans. h t . Chem. Engrs. 43, 116 (1965). (4) Davits, J. T.,Rideal, E. K., ‘‘Interfacial Phenomena,” 2nd ed., p. 17, Academic Press, New York, 1963. (5) Farnand, J. R., Meadus, F. W., Tymchuk, P., Puddington, I. E., Can. Met. Quart. 3, 124 (1964). (6) Farnand, J. R., Smith, H. M., Puddington, I. E., Can. J . Chem. Eng. 39,94 (1961). ( 7 ) Meadus, F. W., MacLeod, W. D., Mykytiuk, A., Puddington, I. E., Can. Mining Met. Bull. 59, 968 (1966).
REVERSE
(8) Meissner, H. P., Michaels, A. S.,Kaiser, R., IND.ENC. CHEM. PROCESS DESIGN DEVELOP. 3,197 (1964). (9) Newitt, D. M., Conway-Jones, J. M., Trans. ~ n r t Chem. . Engrs. 36, 422 (1958). (10) Reich, I., Vold, R. D., J . Phys. Chem. 63, 1497 (1959). (11) Roller, P. S.,Ind. Eng. Chem. 22, 1206 (1930). (12) Smith, H. M., Puddington, I. E., Can. J . Chem. 38, 1911 (1960). (13) Sutherland, J. P., Can. J . Chem. Eng. 40, 268 (1962). (14) Valentine, R. S.,Heideger, h’.J., J . Chem. Eng. Data 8, 27 (1963). (15) Yusa, M., Gaudin, A. M., Ceram. Bull. 43, 402 (1964).
Issued as NRC No. 9303
RECEIVED for review May 4, 1966 ACCEPTED September 28, 1966
OSMOSIS SEPARATION AND CON=
CENTRATION OF SUCROSE IN AQUEOUS SOLUTIONS USING POROUS CELLULOSE ACETATE MEMBRANES S. S O U R I R A J A N Division of Applied Chemistry, A7aiional Research Council, Ottawa, Canada
The effects of operating pressure and feed concentration on solute separation and product rate for the system sucrose-water were studied, and the data correlated by empirical equations. Some parameters of process design are illustrated from the point of view of developing this separation process as a practical batchwise concentration technique. The variation of product rate as a function of feed concentration was studied at the operating pressure of 1500 p.s.i.g. using three typical films capable of giving more than 99% solute separation in the entire feed concentration range 0.1 to 1.4M. Performance of films was also studied in a month-long continuous test run. On the basis of the experimental results, it i s estimated that the porous cellulose acetate membranes of the type employed may be expected to have actual processing capacities of 20 to 30 gallons of feed solution per day per square foot of film area at an operating pressure of 1500 p.s.i.g. for concentrating aqueous sucrose solutions from 3.3 to 32.4 weight %. A few experiments were conducted with natural maple sap containing 3.76% equivalent sucrose; increases in solute concentration up to 34.6% with reasonable processing capacities for the membrane, and essentially 100% solute recovery were obtained.
THE reverse osmosis membrane separation process has been demonstrated with a wide variety of solution systems (6-77, 73). This paper summarizes some of the characteristics of the recently developed porous cellulose acetate membrane (3, 4, 72) for the separation of sucrose in aqueous S o h tion. This work is of interest from the point of view of the possible Of the process as a practical concentration technique for natural maple sap and other industrial sugar solutions ( 7 , 8). The experimental separation and product rate data for the sucrose-water system also illustrate the extended validity of the empirical correlations developed earlier for systems involving inorganic salts in aqueous solutions ( 2 ) . 154
I & E C PROCESS D E S I G N A N D DEVELOPMENT
Experimental Details
Reagent grade sucrose and porous cellulose acetate membranes (designated here as CA-NRC-18 type films) made in the laboratory, were used. The film details, the apparatus, and the experimental procedure have been reported (7, 72, 73). The aqueous sucrose solution (feed) was pumped under pressure past the surface of the membrane held in a stainless steel pressure chamber provided with two separate outlet openings, one for the flow of the membrane-permeated solution, and the other for that of the concentrated effluent. A porous stainless steel plate, specified to have pores of avenge size equal to 5 to act microns, was mounted between the pump and the as a filter for dust particles which might otherwise clog the on the membrane surface. unless othemise stated, the experiments were of the short-run type, each lasting fof 1
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