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INDUSTRIAL A N D ENGINEERING CHEMISTRY
have been made is that such linings should give protection under any condition where iron hydroxide tends to precipitate. Thus in tuberculating water such pipe is excellent. Cement-lined pipe has been found good in other water, however-as, for example, in salt water and sulfur water, where the tendency toward tuberculation is not so marked. At the same time it has been found that steam return lines high in carbon dioxide, which have a solvent action on both iron and calcium salts, attack and destroy some cement linings. Other steam return lines have little action, but the conditions of balance are evidently quite delicate. A cement for pipe lining based on the principles above has been developed, which is high in iron and silica and low in lime. Figure 3 shows the appearance of a lining of this type. The rate of solution of lime from the lining is also a sub-
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ject of great interest, which has been carefully studied, but which will not be discussed in the present connection. It is expected later to present data on the solution rates of various compositions of cement in natural water of various kinds, and also to discuss the necessary conditions for obtaining satisfactory physical qualities, such as resistance to shrinkage and necessary physical strength. Literature Cited END.CABM.,19, 777 (1927). (1) Baylis, IND. (2) Carson, Ibid., 19, 781 (1927). (3) Committee on Cement-Lined Pipe, J . Naw Engl. Water Works Assoon., (4) (5)
(6) (7)
42, 492 (1928). Forbes, Ibid., 14, 44 (1900). Gibson, Engineering News, 89,378 (1922); J. Ant. Watn Workr A ~ J O C W . , 16, 427 (1926). Metcalf, J. New Engl. Water Works Assocn., 13, 1 (1909). Sherman, Ibid., 40, 98 (1926).
The Bulking Properties of Microscopic Particles* Paul S. Roller NONMETALLIC MINERALS EXPERIMENT STATION, U. S. BUREAUOF M I N E S ,N E W BRUNSWICK, N. J
By means of an air analyzer for fine powders, a n anhydrite, gypsum, Portland cement, and chrome-yellow powder were separated into homogeneous fractions above 1 micron surface mean diameter. The bulkiness, or volume per unit weight, was found to increase with decrease in particle size below a critical diameter; for particle sizes greater t h a n the critical diameter the bulkiness was constant. For all the powders the same functional relationship was found to hold between the voids per gram and the surface mean diameter. The differences'in the value of the constants for the different powders appear to depend chiefly on the particle shape, whether cubic, prismatic, basal, etc.
As would be expected from a consideration of packing of small particles in the voids of larger particles, the surface mean diameters of the Portland cement and chrome-yellow microscopic powders calculated from the bulkiness of the powder were found to average several tenths of a micron higher than the true mean diameters. With this correction in mind, for powders above 1 micron surface mean diameter, a rapid method presents itself of estimating the mean particle size of the microscopic powder from a knowledge of its curve of bulkiness vs. particle diameter, but no knowledge as to the distribution of the particle sizes in the powder is thus obtained.
K CONNECTION with the development of an air ana-
precipitation. I n this connection he devised a useful apparatus on the principle of a tilt hammer for automatically tapping the cylinder which contained the powder whose bulkiness was to be tested. Work (4) measured the bulkiness of silica powder by handtapping a cylinder containing the powder. He found that the weight per unit volume, which originally was 1.710, after 30 minutes' grinding reached a value of 1.805 and then dropped continuously until after 14 hours it was 1.205.
I
lyzer for fine powders (8) and for the determination of chemical reactivity as a function of particle size (S), a number of microscopic powders2were fractionated into homogeneous particle-size groups above 1 micron surface mean diameter. It was a t once noticed that the finest fractions bulked enormously and that the bulkiness, or space occupied by the unit mass of the powder, decreased rapidly as the mean particle size of the different fractions increased. To see if any relationship existed between the particle diameter and the bulkiness, the latter quantity was measured for various fractions of four different powders for which the mean diameter of each fraction had been accurately determined under the microscope. The powders studied were (1) a laboratory ground crystalline anhydrite, (2) a laboratory ground c. P. gypsum, (3) a commercial Portland cement, and (4)a commercial chrome-yellow pigment. Previous Results
It is known in an empirical way that the more finely ground a powder is the greater it bulks. Cocking (1) utilized this property in standardizing pharmaceutical products formed by Received July 30, 1930. Publis'hed by permission of t h e Director, U, S. Bureau of Mines. (Not subject to copyright.) 1 Here, as elsewhere, a microscopic powder is defined as a powder whose largest particles average 100 microns in size-i. e., t h a t portion of a powder passing through t h e 200-mesh sieve. 1
Experimental Procedure The size of the particles of the well-defined fractions was determined microscopically as the mean of the length and width, or length, width, and depth in the case of the cement and pigment. From these measurements in duplicate the surface mean diameter of the fraction-i. e., the diameter of a sphere or cube of equal surface per gram-was calculated from the equation
a.
=
Zd3 Zd2
-
(1)
In Equation 1, d, the diameter of a particle, is summed for all the particles measured; d, is the surface mean diameter Of the fraction. The surface mean diameter, which is a measure Of the 'pcific surface of the powder, is of greater significance than the
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INDUSTRIA L AND ENGIAVEERINGCHEMISTRY
usual arithmetic mean diameter. The latter merely accentuates the fact that the smaller particles are more abundant by number, consequently the arithmetic mean is closely the same for a variety of powders. Values of the surface mean are greater than the arithmetic mean, so that, while the latter may amount to but a few tenths of a micron, the surface mean may, for the same powder, be several microns. T h e s u r f a c e mean diameters of the 30 Portland cement and chrome-yellow mi25 croscopic powders were determined from knowledge of the weight of the different so fractions in one gram of the sample ( 2 ) . The bulkiness was measured by add,, ing the powder to a cylinder and handtapping until no more would fill a given volume. AP in some instances less than a gram of the fraction was at hand. a o8 small glass tube was used, 4 mm. i. d. and o, 32 mrn. between the closed end and a level marked with an etched ring. Pow- vCc der was added through a small funnel .d, connected to the tube with rubber tubing. o.4 35 The volume of the tube TVRS determined O3 by weighing it with and without mercury. As Cocking (1) points out, the bulki.25 ness depends on the impact imparted o2 to the vessel containing the powder. I n these experiments vigorous hand-tapping until no more powder would fill the tube gave reproducible results. In order to determine the effect of varying the container, particularly its size, the bulkiness of the chrome-yellow powder was determined under different conditions. The results are shown in Table I. Table I-Bulkiness No. 1 2 3
of Chrome-YeIlow Pigment with Different Containers CONTAINER
4-mm. tube, 32 mm. high 100-cc. measuring cylinder (25 cm.i. d.): ( a ) Filled t o 93 cc. illed to 83 cc. Filled to 8 3 cc. 100-cc. volumetric Bask
BULKINESS Cc. per gram 0.712 0.717 0.709 0.784 0.642
The values for the bulkiness obtained with the 4-mm. tube check those obtained with containers 2a and 2b. The results with container 2c are too high, and with container 3 too low. With container 2c the ratio of height of powder to the diameter of the cylinder was 2.2. On tapping, the powder charge appeared to joggle along its length; this effect was obliterated with containers 2a and 2b, for which the ratio of height of powder to diameter was 6.2 and 5.5, respectively. About 6 would seem to be the minimum ratio of height t o diameter necessary to avoid a dispersive joggling effect in tapping the powder charge. The ratio in the case of the 4-mm. tube was 8. b'ith container 3 there is obviouslv an added Dackine: effect due to the pear-shape of the volumeiric flask. -Owing-to uncertainties introduced by the contour, a cylindrical vessel is most desirable for measurements of bulkiness.
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The density of the various fractions of the industrial powders showed a small variation and was also determined. I n each case the densities of the fractions increased progressively from fine t,o coarse, with a maximum variation from the mean of 0.11 for the cement and 0.35 for the pigment. The measured density was used in all calculations.
d,,uica>hls
I n Table I1 the results of the measurement of the bulkiness of the fractions of anhydrite, gypsum, Portland cement, and chrome-yellow powders are shown, respectively. Table 11-Bulkiness of Fractions of Various Powders SURPACE BULKINESS SPECIFIC VOIDS PER 1/+ VOLUME,l / p GRAM,V Microns Cc./gram CC. CC.
LIEANDIAMETER, da
A N H Y D R I T E POWDER
1.96 3.17 7.56 14.1 25.8 66.9
1.520 1.122 0.738 0.611 0,590 0.593
1.12 2.21 9.58 18.8 41.7 65.2
2.140 1.219 0.890 0.791 0,755 0.726
0,344 0.344 0.344 0.344 0,344 0.344
1.176 0.778 0,394 0.267 0.216 0.246
.
GYPSUM POWDER
0.429 0.429 0,429 0.429 0.429 0.429
1.711 0.793 0.461 0.362 0.326 0,297
P O R T L A X D C E M E N T POWDER
2.4 8.3 15.3 30.2 49.2 81.6 9 . 6 (powder)
1.520 0.780 0,590
0.564 0.574 0.574 0.678
0.336 0,328 0.321 0.317 0.314 0.314 0.322
1.184 0 452 0 269 0 217 0 260 0 260 0.356
C H R O M E - Y E L L O W POTVDER
2.3 10.4 20.1 40.6 4 . 8 (powder)
0 . sa2 0.648 0.561 0.558 0.712
0.278 0.259 0.248 0.254 0.272
0 601 0.389 0 313 0.334 0.440
The voids per gram, V , is the difference between the values of the second and third columns, and is defined by the equation
Results
The densities determined with a pycnometer were found t o be 2.91 for the anhydrite and 2.33 for the gypsum; the mean density of the cement %-as3.11 and of the pigment, 3.68.
where 1/7 is the bulkiness, and 1 / p is the specific volume of the substance, both in cubic centimeters per gram. It is readily calculated from the last column that for 1 cc. of solids
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in the powder the voids range from a constant value of about 0.7 cc. for large particles to 4 cc. for a particle about 1 micron in size. Analysis of Results
It was found that the voids per gram, V , is related to the diameter of the particle in the same functional way for all the powders. Figure 1 is a plot for each of the four powders studied, of the voids per gram defined by Equation 2 against the surface mean diameter, d,, defined by Equation 1. It is seen that in each case, with the exception of one point at 1.12microns for gypsum, the curve is a sloping straight line up to a diameter of 14.3-28.5 microns. For larger particles the curve is horizontal. We may express the relationship between V and d, by the equation: (3)
I n these equations K , n, and C are constants, d,, is the diameter a t which the curves given by Equation 3 and 4 intersect, or d,,=
({);
1
(5)
The values of these constants for the different powders are given in Table 111. Table 111-Bulkiness Constants of Different Powders POWDER K n c dao Anhydrite 2.15 0.818 0.245 14.3 1.05 Gypsum 0.360 0.315 28 5 2.52 Portland cement 0.826 0,255 16.2 Chrome yellow 0.77 0.306 0.305 21.4
Discussion The bulkiness of a given powder, as Cocking has pointed out, depends on the manner in which it ‘is packed in the container, and, as shown above, on the form and dimensions of the container. By suitable means these variables may be kept constant so that the results obtained will be strictly comparative. Under these circumstances the bulkiness would depend on (1)the superincumbent weight of powder in the measuring container, (2)the general electrostatic forces of repulsion, and (3)the specific properties of the powder grains, such as shape, hardness, and nature of the surface. I n Equation 3 the basis of comparison is unit weight of the powder. Furthermore, I/& is proportional to the specific surface or, since the total electrostatic charge may be taken as proportional to the surface, l/d, is proportional to the charge. Causes (1) and (2) which affect the bulkiness are thus accounted for in Equation 3,which governs the bulkiness relationships of the different powders. Above a critical diameter, d,,, the electrostatic effects become negligible and, as represented in Equation 4,the voids become a constant independent of the particle size, and for different powders a function only of the specific properties of the grains. The latter determine the magnitude of the constant C in Equation 4, and also the constants K and n in Equation 3. Comparing the results for the different powders, it appears that the most significant of the specific properties is the shape of the grains. I n Figure 1 curves A and C for the anhydrite and Portland cement powders and curves B and D for the gypsum and chrome yellow are related to each other with respect to the slope of the line, the ordinate of the constant portion for diameters above do,or in general with respect to the
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bulkiness constants of Table 111. I n spite of these mutual similarities the hardness of the cement is 4.5 and of the anhydrite 3.5;the hardness of the pigment is 2.5-3.0 against 1.5-2.0 for the gypsum. On the other hand, the two sets of substances are obviously related in respect to the shape of the grains. Anhydrite tends to cleave in cubes, and also a t least one of the important constituents of cement, tricalcium aluminate. Likewise the gypsum crystals and the constituents of the pigment tend to cleave in the form of flat, elongated prisms. These resemblances are brought out by observation under the microscope and with the camera lucida. Thus, although the hardness and nature of the surface no doubt influence the bulkiness constants of a powder, the shape of the grains seems to be of greatest importance. I n Figure 1 the point at 1.12 microns for gypsum falls off the curve and almost on a continuation of the curve for anhydrite. On the basis of the above considerations as to the influence of the geometric shape, bhe gypsum crystal bulks as though it were cubic. This may be due to a greater uniformity of the electrostatic field with decrease in particle size, and possibly also to the fact that the bulkiness for this grain size is such that the average distance between crystals is more than 0.8 of the grain diameter. With further subdivision of the gypsum crystals below 1.12 microns one might therefore expect the points to fall along a continuation of the curve which would obtain if the crystals were cubic. Surface Mean Diameter of Microscopic Powder
If for the microscopic powder the relationship between bulkiness and mean particle diameter were the same as that for the pure fractions, a determination of the bulkiness curve of the powder as in Figure 1 would offer an easy means of estimating quantitatively the fineness of the powder. However, owing to the wide distribution of particle sizes, it is not likely that the powder will behave like a pure fraction. The fine particles will tend to fill the voids of the larger grains and thus give rise to a packing effect. For a given mean particle size of the microscopic powder the bulkiness will therefore be low with respect to the pure fractions. I n Table I1 the voids per gram of the Portland cement and chrome-yellow powders were found to be 0.356 and 0.440,respectively. From Figure 1, curves C and D, the corresponding particle diameters are 10.7and 6.4 microns, respectively. The actual surface mean diameters of the powders are 9.6 and 6.1,respectively. As we would expect, these values are lower than those determined from the bulkiness of the powder, the differencesbeing 1.1 and 0.3 microns, respectively. These differences will be the same in sign for all powders. The smaller error for the pigment is probably connected with the fact that it is more homogeneous than the Portland cement with a surface dispersion (2) of 6.1against 13.3. From a knowledge of its bulkiness a rapid determination may be made of the degree of fineness of a microscopic powder by the use of an experimentally determined curve for the particular powder of V , the voids per gram, vs. d,, the surface mean diameter. The value for the surface mean diameter of the microscopic powder thus obtained from bulkiness measurements is less than the true value by several tenths of a micron, This error decreases with increase in the degree of homogeneity of the powder, Obviously from considerations of the bulkiness of the powder no information as to the distribution of the particle sizes is yielded. Literature Cited (1) Cocking, Pharm. J.,107,226 (1921). (2) Roller, Bureau of Mines, Tech. Pager, t o be published. (3) Roller, J. Phys. Chem., to be published. (4) Work, Proc. A m . SOC.Testing Maferials, as, 771 (1928).
