SEDIMENTATION IN THE LABORATORY Design Data from Laboratory Experimentation HENRY T. WARD AND KARL KAMMERMEYER Drexel Institute of Technology, Philadelphia, Penna.
FIGURE1. ASSEMBLY OF EXPERIMENTAL EQUIPMENT, SHOWIXG SETTLING TUBES,P A R T I C L E SIZE APPARATUS,AXD STORMER VISCOMETER
HE analysis of sedimentation processes is usually undertaken by applying the Stokes law or a modification of the Stokes equation. The Stokes law deals with spherical particles falling under viscous resistance with the viscosity of the suspending medium as a controlling factor. Industrial sedimentation processes generally fulfill the requirement of viscous resistance settling. The particles, however, rarely approach spherical shape, nor is the viscosity of the suspending medium that of the liquid. Experimental evidence indicates that suspensions have a viscosity greater than that of the fluid (specifically, water) as soon as the weight concentration of the solid reaches about 3 per cent. Since the increase in viscosity of the suspensions with increasing concentration of solids is relatively slow at first, serious errors probably would not be introduced by using the viscosity of water up to about 5 per cent solids by weight.
influenced greatly by physical factors and the use of various flocculating agents (6),and the structure of the final floc which is produced therefore depends on a considerable number of conditions over v-hich only limited control can be exercised. The complexity of sedimentation problems suggests the use of experimentation on the laboratory scale to develop the necessary basic information for each individual case. Experimental equipment of simple construction can be built at low cost and will serve to determine the characteristic factors of suspensions of solids with a relatively wide range of particle size. Frequently it will be possible to evaluate the properties in experiments with comparatively dilute suspensions in a period of 24 to 48 hours.
T
Equipment Required The equipment used to determine the settling rate of suspeiisions consisted of vertically mounted glass tubes with a diameter of about 4 cm. and an approximate height of 60 cm. A series of six tubes mounted together with suitable measuring scales on a board was used in this work. Temperature control was exercised only in so far as the room temperature was kept reasonably constant. This arrangement permitted the determination of the settling rate of six different concentrations of the suspensions and a t the same time gave the ultimate height to which each suspension would settle. Our experiments showed that many suspensions containing up to 15 per cent by weight of solids settled almost completely in about 10 hours. Particle size can be determined within certain limits by microscopic examination, and this method may give a satisfactory answer if the size range is not too wide. It will generally be found that for solids with a particle size range from a few microns
Factors Involved in Sedimentation Process The problem of primary importance in process design is that of plant capacity. To arrive a t a reliable estimate of the capacity of a settling unit, the rate of sedimentation must be known. This requires the knowledge of the ultimate height to which a suspension settles, the size or size range of particles, and the viscosities of the suspensions. The latter factor is of importance also in so far as it affects the pumping equipment and pipe sizes. The degree and type of flocculation produced influence the rate of sedimentation and the ultimate height more than any other single factor (4). Flocculation, in turn, may be 622
MAY, 1940
SEPARATION OPERATIONS
to about 100 microns, a hydraulic settling method will give more reliable results. The suspension used for the test should be flocculated prior to the particle size determination under conditions which approach those of the actual settling process. The method described by Kelly (8) makes use of the difference in the density of the suspension roper and that of the SUS?ending medium. A suspension ofsuch concentration that the btokes law is valid-that is, 0.5 to 1.5 per cent of solids-is settled in a tube with a small-bore side arm, the side arm itself being filled with the suspending medium. The difference in density between the suspension and the fluid results in a higher reading in the side arm, amplified by an inclined manometer arrangement ; this higher reading will gradually decrease as the particles in the suspension settle out past the level of the side-arm connection. The determination of the viscosity of a suspension is a factor which presents certain difficulties, since ordinary fluid methods involve the danger of settling during the period required for making the measurements. To eliminate this difficulty as far as possible, a Stormer viscometer was used. This instrument measures the time necessary for 100 revolutions of a cylinder rotating in the medium. It was found that the rotating motion of the submerged cylinder kept the suspension well stirred so that consistent readings could be obtained. The viscosities are expressed relative t o some standard fluid such as water. Figure 1 shows an assembly of equipment necessary to carry out all the tests involved.
Ultimate Settling - Height The ultimate height, H,, to which suspensions will settle without agitation is a function of the concentration of the suspension, the particle size, and t o some extent of the initial height, Hoe It has been possible t o correlate experimental data obtained on aqueous suspensions of calcium carbonate, barium sulfate, and silica with the weight concentrations.
6olC -Coco3
A V E R A G E PARTICLE S I Z E i 2 6 M I C R O N S TEMPERATURE 80-F.
FIGURE 2. WEIGHTCONCENTRATION OF SnsPENSION a's. HEIGHT RATIO
Figure 2 shows t h a t the relation between weight concentration and initial relative concentration can be represented by straight lines on log-log paper for a definite particle size when the initial height is kept constant. The term "relative concentration" as introduced by Robinson (9) is the ratio of ultimate height t o initial height. The accuracy of the correlation was surprisingly good. In 93 per cent of all cases the deviation of the calculated from the actual values was less than 5 per cent of the actual value, and the maximum deviation for any one value was only 6.6 per cent. Such curves can be established from one set of experiments comprising about six concentrations, and it is then possible to
623
Experimental equipment and technique have been developed suitable for the plant laboratory and for instructional purposes in the chemical engineering laboratory. The equipment permits the determination of settling data without agitation, as well as particle size of the solid and viscosities of suspensions. A relatively simple correlation is developed between the ratio of ultimate to initial settling height of suspensions of several solids and the weight concentration of the suspensions. A number of viscosity data for suspensions of varying concentrations are presented. An attempt is made to analyze the relative degree of accuracy of the methods of Robinson and of Egolf and McCabe for the reconstruction of settling curves. Modifications of these methods are suggested which improve their utility.
predict the ultimate height for any given weight concentration by multiplying the initial height by the relative concentration factor. The curves apply only t o a solid of a definite average particle size, with the possibility that a different size distribution for the same average particle size may have further modifying effects. It was found possible to plot most of the data presented by Egolf and McCabe (6) in the same manner as shown by Figure 3. The degree of correlation on the whole was good. This was particularly true of silica data a t 86" F. (30" C.) for average particle radii of 5.13 and 16.7 microns, respectively. The deviation of these points from straight lines was small, and the lines for the two particle sizes were parallel to each other and also parallel to the line determined by the authors for silica particles having an average radius of 40 microns. The latter line was determined at 80" F. (26.7" C.) as indicated in Figure 2. Suspensions of the same solid with a given weight concentration will show a decrease in the degree of packing-that is, an increase in the ratio H,,/Ho-as the average particle size decreases. For instance, the H.,/Ho ratios at a weight concentration of 30 per cent silica are 0.302, 0.383, and 0.432 for average particle radii of 40, 16, and 5 microns, respectively; this means that the 40-micron fraction settled t o 30.2 per cent of the initial volume, whereas the µn fraction settled to only 43.2 per cent of the initial volume. The straight lines on log-log paper (Figure 2) represent functions of the type, y = ax"
where n log a
= =
slope intercept at x
=
1
Applied to the present correlation the equation can be written: where C
=
HJHo o~C" weight per cent of solid
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The exponent n would be the same for any one solid in question for a definite initial height, and the factor a would be proportional to the average particle size. This correlation should permit the determination of average particle sizes from comparative ultimate height data if the particle size of two material fractions is known,
Viscosity of Suspensions The suspensions used in this experimental work were made up with water as the suspending medium. All viscosities were determined in a Stormer viscometer. The observed values are shown in Figure 4 as a function of the weight concentration. The temperatures a t which the viscosities were measured correspond to those of the settling experiments as given in Figure 2. The viscosity plot clearly shows that with suspensions of low weight concentrations the viscosity of the suspending medium can be used without introducing appreciable errors. Stewart and Roberts (IO) discuss the factors which influence what they term “effective viscosity”. From the information in Figures 2 and 4 it is possible to construct plots giving the variation of viscosity with the relative concentration. Such plots will be useful for computing settling curves by the Robinson method. Particle Size Measurement of the particle size of the solids with the microscope was found rather difficult, since the variation in size was too great to permit a reliable estimate for the average particle radius. Therefore particle size was determined in the Kelly tube. This hydraulic settling method could be used with good success. The experimental data can be evaluated either by a graphical or an analytical method. The
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if the degree of asymmetry is not too great ( I I ) , and for the problems in question it should be possible to apply the Stokes law in this form.
FIGURE4.
VISCOSITIES OF SUSPENSIONS vs. WEIGHT CONCENTRATION OF SUSPEXSIONS
The distribution curve for barium sulfate obtained with the Kelly method is shown in Figure 5, and from this curve an average particle radius of 18 microns was calculated. The following table gives the average particle size for the solids used in the experimental work:
Bas04 CaCOa SiOa Milk of magnesia
Equivalent Radius Microns 18 12.6 40
10
Actual Density Dry-Bulk Density ,-.Grams/cc.-4.16 1.320 2.60 0.495 2.58 1.600 2.38
0.631
A-40 Mu 902 26.7.C
80 8 0 B - l B M u So2 C 5Mu Slop
30’C 30’G
1
1 I
Density
60 50
y
4
3 2 1.5
I
I 15 2 3 4 .5 .6 FINAL H E I G H T ~ I N I ~ I A‘HEIGHT L
.06 .08
0
I.
FIGURE3. DATA OF EGOLFAND MCCABEPLOTTEDHEIGHTRATIOus. CONCENTRATION OF SUSPENSION
graphical method is shorter than hut perhaps not quite so accurate as the analytical method. Descriptions of these methods are given by Holmes (7), Calbeck and Harner @), and Svedberg (11). The value of the average particle radius which is actually determined in this manner is the “equivalent radius”, since the particles will not, in general, approach a spherical shape. The inaccuracy introduced by using the Stokes equation for spherical particles is negligible, however,
The actual densities of the solids were determined with the pycnometer. Dry-bulk densities were determined for some of the solids by taking a known weight of the material and tapping it to a constant volume in a graduated cylinder. The actual densities and dry-bulk densities for some of the materials used are given in the above table. I n the discussion of the t h e o r y of s e d i m e n t a t i o n , Badger and McCabe (9) desigO: nate the bulk density as that obtained in the settling of the particles a t the end of the sedi50 mentation process. This value, which could be termed “wetbulk density”, however, is not a constant value since it changes 4 with the weight concentration $10 of the suspension. Egolf and McCabe bring out this fact in their discussion of the “compression” lone. The bulk 0 0 20 40 60 80 density to be used in the S I Z E OF P A R T I C L E S MICRONS Robinson equation for the prediction of settling curves could be the dry- or the wet-bulk ~ ~ D’,”;. ~ density. The former will be a BARIUM SULFATE constant but the latter will vary with different conditions of settling. It was to be expected that the wet-bulk density would result in a better agreement of the calculated settling curve with the actual settling curve, and trials have borne out this
gi&
~
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SEPARATION OPERATIONS
theory. The value of the wet-bulk density for a definite weight concentration can be calculated from the ultimate height obtainable from Figure 2.
Types of Settling Curves
A number of authors, specifically Egolf and hfcCabe, have mentioned that apparently two types of settling curves exist. Type I shows an initial constant-rate period followed by a compression zone. Type I1 shows an initial constant-rate period followed by a secondary constant-rate period, with a subsequent compression period. If the initial flocculation zone were taken into account, two additional types of settling curves would have to be accounted for; however, they would simply be modifications of types I and 11. 100
625
Flocculation was not observed with the calcium carbonate suspensions. As in the case of the barium sulfate suspensions, type I curves seem t o be the rule a t low and high concentrations of solids, whereas a few of the intermediate concentrations-that is, 8 to 10 per cent-definitely gave type I1 curves. The silica suspensions were preflocculated in accordance with directions given by Egolf and IlfcCabe, and all of the suspensions seemed to give type I1 settling.
Construction of Settling Curves At present the two most useful methods for the estimation of the settling rate curves are those of Robinson, based on the work of Adams and Glasson (1) and of Egolf and McCabe. The latter method was developed for flocculated particles, but i t seems reasonable to assume that Robinson’s method likewise should be applied to the sedimentation process after flocculation has been completed. The Robinson equation can be written as follows:
90
eo
where X
= height of suspension, cm. 0 = time, sec. D = average particle diameter, cm. p‘ = density of particles, grams/cc.
density of suspension, grams/cc. viscosity of suspension, centipoises k = experimental factor
pa = fi =
The viscosity of the suspension can be related to the relative concentration which is expressed as:
where Xo
initial height of suspension, cm. c0 -= initial concentration, cc. solids/cc. sludge p: =
MILK OF MAGNESIA-TOTAL SOLIDS
7.6%
T I M E , MINUTES
CURVESOF MILK OF MAGNESIA FIGURE6. SETTLING AT VARIOUSDEGREES OF DILUTION
An example of settling curves with initial flocculation zone is shown in Figure 6 which presents the behavior of suspensions of milk of magnesia a t various dilutions. (The sample of milk of magnesia was a product of the Philadelphia Magnesia Company.) The commercial suspension itself did not exhibit any settling tendency. With increasing dilution, settling became more and more pronounced, and i t is of interest to note that the flocculation period decreased with progressing dilution. The flocculation which took place in this instance was due to “autoflocculation”, and the phenomenon could be reproduced by shaking the settled suspensions and observing the settling behavior a second time. In the case of the barium sulfate suspensions the following observations were made: At relatively high weight concentrations of solids it was not possible to discern a flocculation period, probably because of the extremely slow settling rate. At concentrations of about 10 to 30 per cent solids by weight, flocculation was noticed but the trend of the flocculating period with increasing dilutions was not definite. Below 10 per cent solids a flocculating period did not seem to exist. Most of the settling curves of the barium sulfate suspensions were of type 11, but type I curves were observed a t concentrations below 5 per cent and above about 30 per cent by weight. In either case, however, the respective settling rates may have been too great or too low to permit observation of a secondary constant-rate period.
bulk density, grams/cc.
The use of the wet-bulk density will give better agreement than can be obtained with the dry-bulk density. I n order to apply the Robinson equation, factor k has to be evaluated from experimental data on suspensions of the material in question, This factor is usually referred to as a constant, but this was not the case when different settling times were used for its determination. When the Egolf and McCabe equation is employed for constructing the settling curve, the initial settling rate is obtained from a plot relating this rate with the following function: (4)
where r
average particle radius, microns density of medium, grams/cc. Z = viscosity of suspending medium, centipoiaes HO = initial height of suspension, cm. H, = ultimate height of suspension, cm. Vu = volume concentration of solids, cc./cc. of suspension at ultimate height =
p =
When the values of this function for the various solids were correlated with the initial settling rates, the points did not fall on the plot presented by Egolf and McCabe. Therefore individual plots were prepared for each solid in question and were used in the application of the equation. The compression part of the curve was constructed as outlined by Egolf and McCabe, except that a somewhat different procedure was used to obtain the value of B in the equation necessary for the construction of the compression period. This equation is:
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so
40
30
20 0
TIME,
40
80
I20
160
200
240
260
MINUTES
FIGURE7. ACTUALSETTLINGCURVESOF 13 PER CENT BY WEIGHTSUSPENSIONS OF CALCIUM CARBONATE AND BARIUM SULFATE,AND CURVESRECONSTRUCTED BY METHODS OF ROBINSON AND EGOLFAND MCCABE
Egolf and McCabe made use of a plot relating (B).(HJ).(Z)the particle size increases, the ratio H,/HI, decreases a t constant weight concentration, and Vu increases in the same with the concentration. A somewhat better agreement was proportion. For silica i t was estimated that Vu becomes obtained by substituting the term Hu/Hain place of Ho in the equal to 0.415 a t an average particle radius of about 25 mifunction. crons. This estimate neglected the effect of weight concentraThe settling curves of suspensions containing 13 per cent tion upon Vu, since it seemed to be small in the case of silica. by weight of calcium carbonate and 15 per cent by weight of When the Egolf and McCabe equation is to be used, i t is barium sulfate have been reconstructed. I n each case the therefore necessary to make preliminary check calculations to necessary information to use the Robinson and the Egolf and ascertain whether the constant 0.415 will be greater than the McCabe equations was derived from suspensions of various values of V , in question; if the constant is too small, i t will be concentration. necessary to develop a new constant. The reconstructed curve for 13 per cent calcium carbonate Both the Robinson and the Egolf and McCabe equations presented in Figure 7 showed a maximum deviation of 10 to gave fairly good agreement in the examples presented. 15 per cent in the constant-settling-rate period for both equaHowever, their application is apparently limited to the pretions. I n the compression zone, however, the Egolf and Mcdiction of settling curves under conditions which will not vary Cabe equation deviated from the actual settling curve by only greatly from those used to develop the factors involved in the about 2 per cent, while the Robinson equation deviated by equations about 10 per cent. The greater deviation of the Robinson equation in this region is probably due to the fact that an average value of k was used, and the variation of k with Temperature Effects settling time was not taken into account. It is well known that temperature exercises considerable The reconstruction of the settling curve of the 15 per cent influence upon settling behavior (6). All of our work waa barium sulfate suspension was started a t the point where the carried out a t room temperature, since the primary objective flocculation period was completed as shown in Figure 7. It was that of developing the necessary technique and means of gave good agreement for both the Robinson and the Egolf correlating the basic factors. In all experiments i t was posand McCabe equations in the constant-rate settling zone, but sible to maintain the temperature within *2”F. (l.l°C.) and in the secondary constant-rate zone and in the compression the errors introduced by this variation should not greatly zone the Egolf and McCabe equation gave closer agreement affect the validity of the results. than the Robinson method. It was not possible to use a straight line for the secondary constant-rate period. Therefore, in the reconstruction of the settling curve, the curve Literature Cited determined for the Compression period was extended to cover Adams, W. H., Jr., and Glasson, P. S., Mass. Inst. Tech., thesis, the secondary constant-rate period and in this particular 1925. instance gave fairly good agreement. It should be kept in Badger, W. L., and McCabe, W. L., “Elements of Chemical mind that the agreement will probably not always be so good Engineering”, 2nd ed., p. 586, New York, McGraw-Hill Book Co., 1936. as that obtained in these examples, for Egolf and McCabe do Calbeck, J. H., and Harner, H. R., IXD.EKG.CHEM.,19, 58 not claim an accuracy greater than 20 per cent for their (1927). method. Cullen, Wm., and Durant. H. T., Trans. Inst. Chem. Engrs. When we attempted to reconstruct the silica settling curves, (London), 12, 210 (1934). Deane, W. A., Trans. Am. Electrochem. Soc., 37, 71 (1920). we found that the Egolf and McCabe equation could not be Egolf, C. B., and McCabe, W. L., Trans. Am. Inst. Chem. Engra., applied. This was due to the fact that the application of the 33, 620 (1937). equation is limited to conditions where Vu, the concentration Holmes, H. N., “Laboratory Manual of Colloid Chemistry”, of solid a t ultimate height, is less than 0.415. As soon as 2nd ed., p. 3, New York, John Wiley & Sons, 1928. Kelly, W. J., IND.ENG.CHEM.,16, 928 (1924). Vu becomes equal to or greater than 0.415, the term (0.415 Robinson, C. S., Ibid., 18, 869 (1926). will pass through zero to negative values, indicating Stewart, R. E., and Roberts, E. J., Trans. Inst. Chem. Engrs. impossible conditions. (London), 11, 124 (1933). The value of Vu is influenced mainly by the particle size Svedberg, The, “Colloid Chemistry”, A. C . S. Monograph 16, and also by the weight concentration of the suspension. As 2nd ed., New York, Chemical Catalog Co., 1928.
