Determination of Particle Size Distribution For Particle Sizes between 40 and 1 or 2 Microns W. 0. HINKLEY Raymond Pulverizer Division, Combustion Engineering Company, Inc., Chicago, Ill.
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ITH the increasing demand from the arts and industries for finer and finer grinding i t becomes essential to have a simple method of determining the fineness of pulverized material where the particle size is beyond the range of the standard testing screens-i. e., finer than 38 microns. A number of methods have been proposed to accomplish this, most of them involving the use of expensive apparatus, and many of them taking a day or more for one determination. There are three general methods of making quantitative particle size determinations in the subscreen sizes: microscopic, elutriation, and sedimentation.
Like all other methods using sedimentation, the present one depends upon Stokes’ law, which in effect states that small spheres falling freely through a viscous medium maintain a velocity, which if other conditions are equal is proportional to the square of their diameter. If we take a liquid with which the substance being investigated will not react, determine its specific gravity, and in a known quantity suspend a known quantity of the solid, we can by determining the specific gravity of the suspension derive the specific gravity of the solid. Knowing the specific gravity of the solid and of the liquid, we can by transposing the same equation find the amount of solid material in a given quantity of the suspension at any time. From Stokes’ law we can obtain the time at which the last particle of a given diameter will settle below a given plane. If we determine the amount of solid material in a given volume of suspension before any settling has taken place, and then take a sample at some plane a t the instant that the last particle of a given size settles past it, and determine the amount of solids in the same volume of suspension as previously used, the ratio of the second value to the first, multiplied by 100, is the per cent of material finer than the size under investigation at that point and time.
The microscope is capable of giving accurate results in skilled hands and with considerable expenditure of time. It has the inherent disadvantage of using an extremely minute sample which may not be a t all representative of the product as a whole. On the other hand, it gives an actual visual picture of the individual particles, their distribution, and their shape, which latter may be very important. The elutriation methods which separate out the particle sizes by means of currents, usually of air, moving with various velocities, are not very familiar to the author, but appear to give very accurate results. They involve considerable expensive apparatus, a skilled operator, and an exacting technique. The sedimentation methods, on a whole, appear to be the best adapted to use where rapid determinations are essential and an unskilled operator must be used.
Most sedimentation methods use this ratio of the amount
of solids in a given volume before settling takes place and at a given depth after a calculated time. The difference in the means used t o make these determinations constitutes the differences between the various methods.
In developing the method presented here, several conditions were considered essential:
The more elaborate apparatus utilizes a beam of light and a photoelectric cell, determining the density of the suspension by its light absorption (Wagner turbidimeter and Central Scientific pLotelometir). The densities may also be obtained with a hydrometer (2). Since the densitv of the sumension varies throughout the entire depth of the hydrometer, complicated figuring aGd some assumptions are necessary. Another method is to suspend a weight from a scale beam and measure the change in displacement, but here, unless the weight is withdrawn each time and cleaned, the values may be thrown so far out by material settling on it as to be absolutely worthless, and if the weight is withdrawn and cleaned the method becomes a little more cumbersome than the pipet method described here. Others take a slightly different approach, and instead of measuring the densities, either weigh or measure (3) the sediment as it settles. This involves much more intricate calculations, and in the case of measurements the increments are so small as to make accurate readings extremely difficult.
The method must be adaptable to a wide range of materials without any calibration of equipment. It must rapidly give a sufficient number of determinations at different points to lot a curve. It must be capatle of giving at least closely corresponding results, whether used by an experienced operator in New York or a novice in Timbuctoo, and it must give a reasonably close check with other methods. The apparatus should be compact and preferably not too costly. The sedimentation methods using Stokes’ law seemed to offer the best chance of satisfying these conditions. In investigating the best way t o use this law, the author had no knowledge of methods used by others, except a very general idea of the photoelectric processes, and so had no hesitation in discarding one method if a better one appeared possible. A considerable number of methods were considered, and most of them were tried. After the method presented here had been perfected far enough t o be p u t t o practical use, i t developed that a good many of the discarded methods were being used by others, and a description of some of them had been published. This method is a variation of the pipet method, discussed by Oden ( I ) , which was actually used by the author for a time without knowing t h a t a description of i t was in print. The difference is that previously the pipetted sample was evaporated to dryness and the residue weighed, while the present method determines the amount of solids by the use of the specific gravity bottle. The older method is mathematically more accurate, but i t takes a good deal more time and effort, the practical difficulties are greater, and i t is very difficult, if not impossible, to use with many suspension mediums, such as kerosene.
The method presented here is not intended to replace the expensive turbidimeter and photelometer methods, which may make a dozen determinations between 7.5 and 60 microns in half an hour, but to make possible rapid determination of particle size distribution at as many as six different points from a single sample, which is sufficient t o plot a smooth curve and for most cases is plenty. It has been found to give results which check with different operators and with other far more elaborate, costly, and time-consuming apparatus. The equipment required is available in almost any laboratory, or can be purchased from any chemical supply house, at a cost, excluding the balance, of less than five dollars. The balance will cost about thirty dollars, since i t need weigh only to 1 mg., although a more sensitive one is preferable. MATERIAL REQUIRED.One balance, sensitive to 1 mg., or less. One pipet of 10 CC.
One specific gravity bottle, 10-cc. adjusted. 10
ANALYTICAL EDITION
January 15, 1942
11
or more (not calibrated). One cylindrical graduate of 250 cc. or more, preferably at least 500 cc. with ground-glass stopper. A thermometer, a watch, and a viscometer (Ostwald or similar). I
The calculations are very simple, and the procedure is not a t all laborious, requiring much less care than most quantitative determinations. The time required varies with the specific gravity of the material and the fineness a t which the determinations are being made. With ordinary materials (specific gravity 2 or more) determinations to as low as 5 microns may be made in about an hour, with readings, say, a t 20, 10, and 5 microns. To obtain the reading at 2.5 microns will probably take another 2 hours. For any smaller sizes the time increases rapidly and disturbing influences become more important. However, there is no need for using fixed depths, and the graduate may stand overnight for the finer sizes and the depbh may be figured for any given time.
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Dispersing Agents The solid must be thoroughly dispersed in the settling medium, so that the particles settle individually and not as agglomerates. This will ordinarily not be possible without the addition of a small amount of dispersing agent to the fluid. Sodium metaphosphate, or tetrasodium pyrophosphate, will disperse a great many mineral materials, such as clay, limestone, etc., in water. A lignin compound, lignin dispersing agent 4-A put out by the Marathon Chemical Co., Rothschild, Wis., will disperse carbon products, such as coal, graphite, or the ashes of these products in water. Dispersing agents 7027C and 7027D put out by Palo Myers, Inc., New York, N. Y . , will disperse coal and many carbon products. Oleic acid may be used to disperse cement in kerosene. Other dispersing agents for special materials may be obtained from the chemical manufacturers, and considerable experimentation is sometimes necessary to obtain satisfactory dispersion. Only a fraction of a per cent of any of these agents need be added for satisfactory dispersion. Too much may be detrimental. With any material or any dispersing agent considerable agitation is necessary to ensure dispersion. For ground materials, which are the present author's main problem, a couple of minutes' violent shaking in the graduate is usually sufficient, but if a n attempt is being made to disperse a filter cake or a dried material to its ultimate particle size, nothing short of prolonged agitation with a high-speed mixer such as a malted milk mixer should be considered. When starting with a new material it is often advisable to try several dispersing agents. If all give approximately the same results it seems reasonable to assume that dispersion is complete, or if different results are obtained that the finer values indicate the more nearly complete dispersion. Only in a very unusual material, with a n extremely steep particle distribution curve, will the suspension settle with a visible line of demarcation, between a clearer portion above and a denser portion below, if dispersion is complete. Such a line, which often occurs, definitely indicates an incomplete suspension. An incomplete suspension is also indicated by a flocculent appearance of the suspension, or by small agglomerates adhering to the sides of the graduate. Another way to check the suspension, and the accuracy of the work as a whole, is to plot a curve of values on semilog paper, plotting the particle size on the log scale and the per cent of the material by weight greater (or less) than that particle size on the linear scale. These points should result in a regular curve which takes the form of a straight line through the central portion, curving off toward a tangent with the 0 and 100 per cent lines a t the bottom and top (Figure 1). If the straight-line portion shows a change of more than 40
PARTICLE DMP,?ET€R IN MICFON.5
FIGURE 1 . PARTICLE SIZE DISTRIBUTION CURVE FOR IRON
OXIDE
points for a doubling of the size of the particle, it should be looked on with suspicion. (It will usually be between 20 and
35.)
Symbols Used t = time, seconds h = depth of fall, cm. q = viscosity of medium, poises (water = 0.01 at 20" C.) p l = density of solid material, grams per cc. p a = density of medium and dispersing agent (suspending medium), grams per cc. g = acceleration due t o gravity, 980 cm. per second er second d = average diameter of particle, microns (actuallye!t reciprocal of the mean of the reciprocals of the diameters) T = tare weight of specific gravity bottle, grams B = gross weight of bottle, filled with suspending medium, grams m = grams of solid in specific gravity bottle filled with dispersion before settling takes place M = gross weight of bottle filled with dispersion before material has started t o settle, grams Ch= gross weight of bottle filled with dispersion pipetted from depth h at time t, grams W = weight of sample used, grams Q = volume of dispersion after solid has been added and dispersed, ml. V = volume of specific gravity bottle, ml.
Calculations Stokes' law may be stated mathematically as:
or: The time of fall of a particle in a viscous medium varies directly as the depth of fall, directly as the viscosity of the fluid, inversely as the difference between the specific gravities of the solid and fluid, and inversely as the square of the particle size. STEPSIN DnTERmNATIoN. 1. Determine the tare weight of the specific gravity bottle, T . This need be determined only once during the life of the bottle, although an occasional check is advisable to guard against loss of weight from chipping or gain of weight from insoluble deposits.
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1NDUSTRIAL.AND ENGINEERING CHEMISTRY
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2. Dissolve from a 0.25 to 0.5 per cent of dispersing agent in the fluid which is to be used. Bring to room temperature and weigh for B. 3. Determine the viscosity of the dispersing medium-i. e., fluid plus dispersing agent. If distilled water is used at 20" C. this value is 0.01 poise. The difference in using ordinary tap water is usually very slight but should be occasionally checked. A difference in temperature, however, may make a considerable difference in viscosity. The temperature should not be allowed t o change more than 2" C. during the test. Viscosities may be determined rapidly and accurately enough for this purpose with a very reasonably priced viscometer. 4. From (1) and (2) det'ermine the specific gravity of the solid, B - T -
v 5. 'm =
p2.
W V / Q . l17hen a 25-gram sample is dispersed to form 500 cc. of dispersion and a 10-ml. specific gravity bottle is used, m = 0.5. 6. Accurately weigh quantity of material W and thoroughly agitate with settling medium until complet'e dispersion is obtained. It is best to make a little more than Q dispersing medium and keep some in the specific gravity bottle, so that the graduate may be filled up to quantity Q after the solid is added. Thoroughly disperse the solid in the dispersing medium (see remarks under Dispersing Agents). 7. Before material has time to start settling, draw off sample in pipet, fill specific gravity bot'tle, and weigh for M . This, like all other samples withdrsimn for weighing, is discarded after weighing. 8. From the values determined above determine p1 (density equals mnss/volume). pi =
mP2 (B - T ) - (M - T
- m)
9. We now have all the quantities necessary for substituting in the formula for Stokes' law. It is only necessary to substitute in this formula for one depth and particle size. Other particle sizes can be found by simple proportions. It is convenient to use for the substitution in the formula 10 microns at 10 cm. Then: (18)(10)(0.01)(108) - 1835 t1o = ( P l - P2)(980)(100) Pl - P2 If some other fluid than water is used at 20' C., the suitable viscosity will have to be inserted in the above equation. Other convenient depths are 20 cm. for 20-micron particles, 7.5 cm. for 5-micron particles, and 5 cm. for 2.5-micron particles. If these values are used the figuring is very simple: tZ0for 20 microns a t 20 cm. is one-half of tlo. t b for 5 microns at 7.5 cm ~ microns at 5 cm. is eight times t l ~ . i s three times tlo. f ~ for. 2.5 It is well to take samples for larger particles at deeper depths than for small particles, partially for increased accuracy and timesaving due to the long time it takes small-sized particles t o settle, and partially to avoid removing any of the fluid above the point where a sample is to be taken, which would introduce a slight error. 10. Obtain samples with the pipet a t the depths and times figured, fill specific gravity bottle, using precautions suggested later, and weigh. Obtain the quantities c h - B for each of these positions. 11. Get the quantity M - B. This is 100 per cent. 12. Divide each c h - B by M - B. The result multiplied by 100 is the percentage by weight smaller than the particle size under consideration at that particular point. Stokes' law is valid only over a certain range of particle size a n d no attempt should be made to use it outside this range. Particles larger than about 44 microns (325-mesh screen) settle with turbulent or partially turbulent Aow, instead of the viscous flow as postulated by Stokes' law, and their fall is slower. Particles smaller than 1 or 2 microns begin to feel the effect of the random molecular movement of the suspending fluid (Brownian movement) and may move in any direction. I n this size, too, the slightest convection current will disturb the settling. If particles larger than the 325-mesh screen or at very most the 200-mesh screen (74 microns) are present, they should be screened out and the settling test run on the material through the screen. The actual particle distribution on the original
material can then be figured, knowing the percentage of large particles which remained on the screen.
SAMPLE CALCULATION. Sample, red iron oxide (25 grams used). Medium, tap water at 72" F. Dispersing agent, sodium metaphosphate (Calgon). Tare weight of bottle, T , 8.021 Gross weight of bottle, water, and dispersing agent, B, 18.022 Gross weight of bottle with dispersion, M ,18.401 Amount of solid in 10-ml. dispersion, -(10)(25) , m, 0.5 500 B 18.022 M 18.401 T 8.021 8.021 B - T 10.001 271-T 10.380 m 0.5 M - T - m 9.880
Hence for 10 p at 10 cm. substituting in Stokes' equation M - B = 0.379 = 100 per cent Material screens 99.98 per cent through 400
For 40 p a t 20 cm.5 b o = 9.75/9 = 1.2 minutes B a t PO cm. tzo = 9.75/2 = 4.9 minutes For 10 LI a t 15 cm. tio = (1.5) (9.75) = 14.6 minutes For 5 r a t 10 cm. t 5 = (4) (9 75) = 39 minutes For 2.5 r a t 7.5 em. t 2 . 5 = (3) (39) = 117 minutes For 1.25 p a t 5 cm. ti.*) = (8) (39) = 312 minutes a Sample returned t o graduate and graduate shaken again before taking reading for 20 microns.
For 20
The sample for determining the specific gravity of the material is usually also returned to the graduate and reshaken before proceeding. This reduces the chances of getting below the area of free fall on the 20-cm. readings. p
h
40 20 10 6 2.5 1.25
20 20 15 10 7.5 5
t (min.)
C
1 . 2 18.401 4 . 9 18.381 14.6 18.281 39.0 18.190 117 18.081 312 18.034
C-B 0.379 0.359 0.259 0.168 0.059 0,012
0.379/0.379 0.359/0,379 0.259/0.379 0.168/0.379 0.059/0.379 0.012/0.379
= = = = = =
In actual routine work the calculations can be so condensed that two complete tests can be readily recorded on a sheet of 4 X 7 inch notebook paper. Precautions Most of these precautions would be automatically adopted by a n y one used to this type of work, and should not be regarded as burdensome. After two or three determinations they become automatic. The graduate or other vessel must have a diameter large enough to enable the pipet to draw all its charge from approximately the same plane, and it must be deep enough to give satisfactory depths without getting below the range of free fall. When the specific gravity bottle containing the suspended material is filled, an excess should be drawn from the graduate in the pipet and used to rinse out the bottle. This washes out any sediment from previous weighings. The top of the pipet should always be kept closed when being inserted, until the bottom reaches the correct level. The top of the stopper should be wiped immediately after inserting, but if the warmth of the hand forces out more fluid, this should not be wiped away. Otherwise the bottle must be perfectly dry before weighing, and some effort should be made to keep the elapsed times from filling the bottle to reading the weight approximately equal, in order to equalize evaporation. Although a known specific gravity of material may be used for figuring time of settlement, it should never be used for figuring M . The sample should never be drawn from so close t o the bottom of the container that the free fall of the particles has begun to be checked. The longer the material has settled, the greater this distance should be. Seven or 8 cm. is the minimum for the first reading after about 7 or 8 minutes, and should be increased for the succeeding readings. If any weight i s greater than the origi-
January 15, 1942
ANALYTICAL EDITION
nal weight before settling started and no mistake has been made in either weighing, it is proof positive that samples are being taken from too close to the bottom. The graduate should not sit in it position where hot or cold air can strike part of it t o set up convection currents, nor should the temperature change more than 2" C. during the course of the test. Distilled water may increase the accuracy slightly, and if distilled water at 20" c. is used with a weighed quantity of dispersing agent, the first weighing of the specific gravity bottle with the clear solution may be omitted, since under those conditions this weight will always be the same. ,
If care is used, this method is just as accurate and as rapid (probably a great deal more rapid) as with equipment costing hundreds of dollars, where not more than four or five different sizes are wanted from one sample. A 500-ml. graduat,e is not snt,isfactory for more than this number of determinations. Using a larger sample and a deeper settling container additional determinations could be obtained.
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Great cleanliness of the containers is not necessary, as in methods measuring the transmission of light through the suspension. Calculations of percentages should not be carried into fractions of a per cent, since the accuracy of this method (or any other method) probably does not warrant it. Where some other material than water must be used for t h e settling medium, its viscosity may be determined with a cheap viscometer (Ostwald or similar). The specific gravity is readily obtained with the specific gravity bottle.
Literature Cited (1) Alexander, Jerome, "Colloid Chemistry", New York, D . Van Nostrsnd Co., 1937. (2) Am SOC.Testing Materials, D-422-39. (3) Travis, P. M..A . 8. T.M . BztZl, 102, 29-32 11940)
Recording Color of Opaque Objects MAURICE E. STANSBY' AND JOHN A. DASSOW U. S. Fish and Wildlife Service. Technological Laboratory, Seattle, Wash.
To compare the colors of opaque objects, such as fish fillets, photographic color transparencies are prepared and their spectral distribution curves obtained, using a photoelectric spectrophotometer. Errors due to variations in illumination during exposure and in processing of the film are eliminated by taking pictures of objects to be compared on the same negative.
C
OLOR of transparent liquids can conveniently be recorded by obtaining a spectral distribution curve, utiliz-
ing equipment which is now available in many chemical laboratories for colorimetric analyses. Opaque objects present more of a problem, and no simple yet entirely satisfactory method is available that does not require special equipment for reflectance measurements. I n connection with studies on changes in color of salmon caused by cooking and by cold storage, a method was developed in which color photographs were taken on Kodachrome film, the transparencies were placed in a Coleman spectrophotometer, and spectral distribution curves n ere obtained. While such curves are not absolute records of the color of the original object, they are very useful in recording relative changes in color-for example, pictures of two identical objects taken on the same negative and processed together will give substantially identical curves. If the two objects-e. g., fish fillets-are subjected t o different treatments, such as storage at different temperatures, the relative change in color of the two objects will be recorded and the effect of the treatment upon the color change can be determined. If the change in color takes place over a relatively short period of time, the photographs of the object before and after the color change has taken place can be made on the same roll of film, and if reproducible illumination and expo1 Present address, U. $. Fish and Wildlife Service, Fishery Products Laboratory, Ketchikan, Alaska.
sure conditions are used the curves can be directly compared. If color changes slowly over a period of weeks or months, t h e original and subsequent photographs must be made on separate film, and slight differences in processing will render a direct comparison unreliable. Even in such a case, however, color changes between a control and one or more variable conditions can be photographed on the same negative, and the relative color change recorded. Photogrflphs \yere takeii using equipnient whereby il1uiiiiii:Lt io11 a n d exposure conditions could be readily duplicated. A 35-nm. camern with f 3.5 anastigmatic lens was mounted on ;I rigid upright attached to a large wooden base, which was p1:icc.d inside :{ light-tight box without a top and of such a height tll:it tlie c:inier;i \vas slightly above the open top of the box. Ttvo lights in metal reflectors were rigidly attaclicd above the camera and pointing inward slightly. Five hundred-watt, clcnr, 3200' Kelvin lnrnps were utilized. These lamps arc corrected for Eastman type L3 film which is available only as cut film in the larger sizes. The type oi film employed with the 33 is desipned for use w i t h photoflood lamps, but can be 3200' Kelvin bulbs ivith only a slight difference in r disadvantage is more than compensated by the f A c t t h x t tlie 31'00' Kelvin lamps have a iar more con.itant illumination o \ w tl:eir liie (30 hours) t h n n the photoflood lamps. The voltage to tl.ese lamps was adjusted to 120 volts by means of an autotrm~fvrnicr. Two square. of opal flysh glass were supported on t1.e top oi the box direcrly beneath the lampj but leaving an opening a t the r r n ter for the cnniera. This resulted i n a fairly uniform i1lumiii:~tion of the object to bc phc,topraphed. The camera \\:I+ niounterl .+o t h a t it could be raised or lonered t o obtain a field of varying dimensions. By adjusting the field of the camera properl),, it wsi pos3ible t o obtain a photoarsph of the object of :t sizc vcr?. slightly lfirger than the exit slit o i the spcctrophot[imc.tr.r. Ir' thcse conditions are fulfilled the color of the entire object \vi11 tie measured; this is an important consideration in obtaiiiinr rcprt,ducible results, if the color oi the object is not uniform tlirourliout.
If the pliotograph of the object is considerably larger than the exit slit of the spectrophotometer, only a portion of the image nil1 be in the path of the light beam, and the color of that portion only will be recorded. If there is considerable variation in color from one part of the object t o another, different results will be obtained, depending upon the portion of the photograph placed in the beam of light. On the other hand, it is imperative t h a t the photograph of the object be a t
