Determination of Specific Surface by Permeability Measurements WILLIAM F. KEYES, California Portland Cement Company, Colton, Calif. 2.64 X 10-6. Correction was made for the resistance of the cell membrane, which was of the order of 1 % of the resistance of the bed of powder, in the calculation of the ratio of hl/ht. For any given powder and cell S,, pl, A , L,and C in Equation 2 may all be considered constant. Then Equation 2 may be written
The effect of varying porosity on air permeability of powders has been investigated. The present experimental data indicate that the relation between permeability, specific surface, and porosity may be represented by the following modification of Kozeny'r equation:
For certain pulverized materials, such as ground limestone, quartz; and portland cement,
' a was found to be approximately 0.1 1.
1f a
If the porosity function holds and Equations 2 and 3 are valid, a plot of (h2/h1)'/3(1 - 4 3 1 3 versus e should yicld a straight line intersecting both axes at the origin. The data obtained on pulverized quartz powder of varying fineness are plotted in Figure l, and the data obtained on several other materials are plotted in Figure 2. In general the points fall in straight lines intersecting the z-axis to the right of the origin. I n the case of the pulverized quartz the intercept is independent of the fineness. These plots are entirely equivalent to those of Powers (IO), who plotted Q' / 3 X
T
H E industrial importance of the state of subdivision of many substances has led to the development of various methods of determining particle size. The permeability of beds of powdered materials has recently been investigated as a property by which the particle size or specific surface of such materials may conveniently be measured. Carman (5) utilized the permeability to liquids, while Gooden and Smith (6), Lea and Nurse ( 9 ) , and Blaine (3) used air as the permeating fluid. . The relationship, developed by Kozeny ( 7 ) and Carman, upon which this work is based is
IO
1
1
I
1
0.9
0.8 0.7
whereK = permeability of the porous medium or apparent linear rate of flow (volume rate divided by bed area) per unit pressure drop (expressed as grams per sq. cm. per cm.) across the bed ( ~ mper . ~gram sec.) g = acceleration due to gravity, cm. per sec.2 E = porosity or fractional void of bed (dimensionless) q = absolute viscosity of fluid, grams per em. sec. SO= specific surface of powder, cm.2 per cmS3
vE 0.6 u)
I
0.5 -in
--
e 0.4 1
v
Lea and Nurse (9) developed an apparatus for measuring the air permeability of powdered materials and modified Equation 1 to express specific surface directly in terms of the apparatus copstants and the manometer readings:
sw
0.3 0.2
14 e 3 Ah, x[(l - E ) ~ L C ~ ~ ] ~ "
0. I
where 8, = specific surface, sq. cm. per gram p, = density of material t,ested A = cross-sectional area of bed of material L = depth of bed C = constant for flowmeter capillary hl = manometer reading across bed hz = manomet,er reading across capillary
0.1
Figure
Although Carman has presented rvidence tending t o show that these equations are valid, and that variations of permeability with porosity are represented by the porosity function,
€3
*I"
~
(1 - E ) 2 ' over a wide range, the work of Blaine (3)and t,hat of the Working Committee on Fineness of A.S.T.M. Committee C-1 on Cement (8) as well as preliminary tests made in this laboratory have indicated that for fine powders the permeability changes disproportionately with the porosity function. Experiments were made to determine the effect of varying porosity on the air permeability. The apparatus used was essentially similar to that described by Lea and Nurse (9). The permeability cell had an inside diameter of 1.69 cm., and was filled to a depth of 3.00 cm. The capillary tube had a constant C = 1
O5
0.2 0.3 0 . A POROSITY
1
1
0.1
0 2
1 '
I
I
0 4
0.5
I
1
I
08
09
t
Figure
33
0.6
I. Permeability of Pulverized Quartz
OS
POROSITY
Present address, Johns-Nanville Products Corp., Lompoc, Calif.
05
0 6
0.7
E.
2. Permeability of Various Materials
IO
INDUSTRIAL AND ENGINEERING CHEMISTRY
34
(1 versus E , as Q, the volume rate, is proportional to the linear rate, and in the case of sedimentation the hydraulic gradient is proportional to the solids content (1 - E ) . Powers found that the bleeding of portland cement pastes may be represented by a relationship based on Kozeny’s equation if it is assumed that part of the fluid is immobile and does not flow. Steinour ( I S ) has also demonstrated that the same relationship holds in the case of nonflocculated suspensions of emery powders and has shown the probable explanation of this phenomenoii to be simple stagnation of fluid behind angular particles-that is, failure of fluid stream to trace out angularities of particles. I n view of the similarity of these plots with those of Powers it would appear reasonable to assume that the same inferences apply to the flow of a fluid through a bed of powder as apply t o the sedimentation of powdered materials suspended in a fluid. Then, following the work of Steinour, if it is considered that the immobile fluid E< is proportional to the volume of solids-that is, E< = a(1 - €)-then E - a(1 E) may be substituted for e in Equation 1 to yield
-
(4) Similar substitution in Equation 2 yields
If, as before, it is considered that
(x)’” (I$)’”= k, C PIS,
Equation 5 may be written
A plot of the experimental valuesfor (h21h1)lP(l-
versus k (1 +
e should yield a straight line. The slope of the line, m = a)1/3,the intercept is a / ( l a ) , and the specific surface,
+
s, = 14(1 + P1
1
(7)
The specific surface calculated in this manner represents the surface of the envelope separating the flowing from the immobile fluid. This surface may be somewhat greater than the true surface in the case of particles possessing no interior angles, or it may be substantially less in the case of particles possessing internal angles, pores, or fissures. It will be seen that in the case of spherical zinc dust the intercept with the z-axis is the origin. This confirms Steinour’s finding of no immobile fluid in the sedimentation of spherical particles, and indicates that in this special case Kozeny’s equation is valid. In the case of certain pulverized materials, such as ground limestone, quartz, and portland cement, the intercept is E = 0.11 a p proximately. I t is apparent that variations in shape of this class of particles are sufficiently small to have a negligible effect on the proportion of immobile fluid, and that differences in fineness have no effect. However, in the case of materials of high porosity, the intercept is greater than c = 0.11 and is varying. I t is probable that in addition to immobile fluid due’to the angularity of the particles there is also immobile fluid contained in those internal pores and fissures which communicated with the surface. The practical consequence of these variations of intercept is to require that permeability measurements on a given powder be made a t sufficient porosities to establish the intercept unless it is already known. Rigden (11) and Lea (8) believe nonuniform packing of the bed of powder to be the cause of the observed disproportionality of permeability to the porosity function. Although no proof to the contrary is available from the air-permeability experiments reported here, it is improbable that nonuniformity was a factor in Steinour’s nonflocculated emery powder suspension. In addition, comparative fineness tests on portland cements using the apparatus described here and using the Blaine (4) apparatus gave excellent agreement when calculated by Equation 5 and the
Vol. 18, No. 1
Table 1. Specific Surface of Various Materials Material Surface sq. c n . / g .
Pulverized quartz Pulverized quartz Pulverized quartz Pulverized quartz Pulverized quartz Zinc dust Portland cement Ground limestone Hydrated lime Diatomite Table
626 958 1430 5000 6330 1400 2570 5800 5800 6340
1 2 3 4 5
II. Comparison of Methods of Calculating Surface of Portland Cement
Method
--
Wagner turbidimeter Equation 2,e 0.47 Equation 2,e 0.60 Equation 2,e = 0.53 Equation 2,c = 0.56 Equation 7
Surface
Ratio to Wagner Surface
SQ.cm./o. 1870 3670 3510 3410 3350 2570
...
1.96 1.88 1.82 1.79 1.33
equivalent equation for the Blaine apparatus, regardless of the porosity of test. It is thought improbable that if nonuniform packing were present to m y effective degree its magnitude should be dependent only on the porosity and not on the dimensions of the cell. The possibility that the observed phenomena might result from simple adsorption of fluid on the surface of the particles is thought to be eliminated by the fact that the ratio of immobile fluid to solid volume was observed not to increase with increasing surface area and by the fact that the fluid layer of any reasonable thickness can be calculated to possess a volume too small to be detected by the methods used. Capillary attraction in the interstices may likewise be eliminated by the fact that no increase is observed with increasing surface area and by the absence of the effect in the case of spherical particles. The specific surfaces of the materials shown in Figures 1 and 2 were calculated by Equation 7 and are given in Table I. The surface of the portland cement calculated from the data a t each porosity by Equation 2 and that determined by the Wagner turbidimeter (1) is compared with that calculated by Equation 7 in Table 11. Surfaces obtained by other sedimentation and elutriation methods by Roller and Roundy (12) and others are usually higher than those given by the Wagner turbidimeter by factors of from 1.2 t o 1.5, and application of Equation 5 or.7 yields similar values. ACKNOWLEDGMENT
The author is indebted to W. C. Hanna, chief chemist, and t o Harry E. Kaiser for their interest and advice, and to the California Portland Cement Co. for making this investigation possible. LITERATURE CITED
(1) Am. SOC.Testing Materials, Designation C115-42. (2) Bates, P. H., et al., Am. SOC.Testing Materials, Bull. 118, 31-6 (1942). (3) Blaine, R. L., I b i d . , 108, 17-20 (1941). (4) Ibid., 123, 51-5 (1943). (5) Carinan, P. C., J . SOC.Chem. Ind., 57, 225-34 (1938); 58, 1-7 (1939). (6) Gooden, E. L., and Smith, C. M . , IND. ENG.CHEM.,ANAL.ED., 12, 479-82 (1940). (7) Kozeny, J., Ber. Wien. A k a d . , 136a, 271 (1927). (8) Lea, F. M., Am. SOC.Testing Materials, Bull. 123, 50 (1943). (9) Lea, F. M . , and Nurse, R . W., J . SOC.Chem. Ind., 58, 277-83 (1939). (10) Powers, T. C., “Bleeding of Portland Cement Pastes, Mortars, and Concrete”, Research Laboratory, Portland Cement Association, Chicago, Ill., Bull. 2 (July, 1939). (11) Rigden, P. J., Am. SOC.Testing Materials, Bull. 123, 49 (1943). (12) Roller, P. S., and Roundy, P. V., Jr., A.S.T.M. Symposium on Particle Size, pp. 3 6 4 9 , 1941. (13) Steinour, H. H., IND.ENQ.CHEW,36, 840-7 (1944).
