THE PERMEABILITY METHOD FOR THE MEASUREMENT OF SURFACE AREAS OF FINE POWDERS I. A. ALLEN and C. I. HAIGH The University of Tasmania, Tasmania, Australia
ALTHOUGH the measuremeut of the surface area or particle size of a moderately fine powder is frequently an important procedure in industrial laboratories, it is seldom included in laboratory courses in physical chemistry in universities and technical colleges. Of the large number of methods available (1) some form of the permeability method based on the measurement of the rate of flow of air or other suitable fluid through a plug of the powder is, perhaps, the one most frequently employed industrially. A commercially made apparatus in common use, although very convenient for routine work in that the desired answer is given directly, is unsatisfactory for teaching purposes, since its operation reqnires no knowledge of the theory on which the measurement depends. In this contribution the theorolical background of the ~ermeabilitvmethod is brieflv reviewed. A simole. . , inexpensive apparatns which requires a minimum of constructional skill, but which has proved its reliability, is described. A useful comparison is made between the resnlts of a large number of measurements on nickel oxalate precipitates carried out with this apparatus and by means of a fiimplc optical method. Some importa.nt limitations for very fine powders are indicated.
where U = & / A = linear rate of flow through tho l ~ e d ; AP = pressure drop across the bed; g = acceleration due to gravity; S = surface area of particles in unit volume of the bed; K = constant, which by experiment is equal to 5.0; q = viscosity of the fluid; c = porosity of the bed, defined as the total volume of voids divided by the gross volume of the bed. Mathematically the porosity function is defined by the equation,
THEORY AND APPARATUS
where SS' = surface area in cm.=per g.; So = specific surface of the particles, i.e., the total surface divided by the total volume; Q = rate of flow in ml. per sec.; and the other quantities are as previously defined. , A second method employs a steadily diminishing pressure head, measurements being made simultaneously of the pressure drop across the bed and the rate of flow. While this requires a more complex modified Carman equation, i t permits the use of a very simple apparatus &itable for student use. A sketch of the apparatus based on the design of ~ i (7) is~showndin ~i~~~~ ~ 1. ~ The two ends of the U-tube of uniform bore, 2 cm., and about 30 cm. in length, half-filled with ethylene sealed to an oblique-bore 2-way stopglycol, are is connected to a cock. onebore from each demountable glass tube in which the powder plug is packed. ~h~ second bore from each of the two stopcocks is open to the atmosphere drying tube, ~h~ ,vhole apparatus is mounted on a wooden stand which carries a graph paper scale behind the Utube. ~h~ liquid in the u.tube serves the triple purpose of ~rovidinethe means of drivine the air throueh the bei, of ind;ating the pressure drop across the ced a t any instrant, and of measuring the rate of.flow.
Permeability methods are based on the measurement of the rate of flow of a gas or other suitable fluid through a plug of the powder being investigated. The fundamental relationship is contained in Darcy's equation (81,
where Q = volume rate of flow through the plug; A = area of the plug: L = length of the plug; AP = Pressure drop across the plug; and K , = constant. The original equation was deduced from measurements of the flow of water through porous beds of sand, but has been extended and treated theoretically, notably by Kozeny (3). He considered the flow of a fluid through s. porous medium as equivalent to that through a group of parallel channels, for which the total internal surface and the total internal volume were equal, respectively, to the particle surface and pore volume in the medium. Kozeny's equation is
u = APg .-I. =
KL?Sa
(2)
where W = weight of material iu the bed; p = density (bulk) of the material comprising the bed; and A and L are as defined for equation (1). All permeability methods involve some modified form of equation (2). There are two general methods of utilizing the Kozeny equation. In the first, used by Carman (4) and others (5, 6), a fluid, usually a gas, is driven through the powder bed under a constant pressure head. The appropriate equation is
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JULY, 1994
355
Rigden modified Carman's equa,tion for an apparatus of this kind and obtained the following expression: S. =
2Agdt c' (K(1 - e)$~'aL[log.hdh,1
(5)
correct for the two thicknesses of brass and filter paper. The calculation of the results is illustrated below: a = ares of cross section of U-tube = 3.142 ern.% A = ama of cross section of bed = 1.88 cm.% p =
density of nickel oxalate dihydrate = 2.235 g. per
v = viscosity of air = 180.8 X 10dpoise where d = density of the liquid in the U-tube; a = area Equilibrium level in U-tube = 11.92 om. on scale of cross section of the U-tube; K = constant = 5.0; h, = 9.92 em,; = 3.92 om, t = time in seconds for the liquid in the U-tube to fall Sm reduces between two marks, h and h2 cm., respectively, above With these 'gures the the equilibrium value. Other symbols have the same s, = (1 - s ) ~ L3.122 x 106)"' meaning as before. This equation may be simplified when the constants of the apparatus are known, viz., and Sa' = ktrS/(1 - e)*plL (6) e = 1 - W/4.202L
( z
where k = 2Agd/Kna lag, h,/b
(7)
(6)
(7)
Measurements of W, L, and t enable S, t o be evaluated.
For routine work on a single material a standard weight OPTICAL METHOD of which can be compacted to a fixed depth the e w e s As most teaching laboratories have available a photosion reduces t o electric absorvtiometer it is convenient to compare measS, = k,t% (8) where k , is a constant. In general, it is preferable for instructional purposes to use a different weight of powder for each determination and to study changes in the results arising from this and from the use of different values of the porosity function. PREPARATION OF THE PLUGS
H
The glass packing tube of uniform bore (1.55 em.) is snugly F.tted with two perforated brass discs, 0.6 cm. in thickness, through which as many as possible 1/a2-inch holes have been drilled. The central hole is tapped to take a screwed rod by means of which the disc is readily handled. One disc rests on a slight concentric indentation run in on the glass tube with a small sharp flame and is fixed in place with picein wax. A filter paper disc (Whatman No. 1) is placed on the fixed disc; a weighed amount of powder, 6 + 2 g. in our experiments with nickel oxalate, is added to the tube a portion at a time, the tube being gently tapped after each addition. When all the powder has been added a second filter paper disc is inserted and the second brass disc temporarily attached to the screwed rod is used to compress the powder. The ideal bed should have an even packing and the most consistent results are obtained with beds of porosity s = 0.4-0.5. PROCEDURE
When the plug has been prepared and the apparatus axsembled the liquid in the U-tube is raised in one limb by applying a vacuum to that limb, the other limb being open to the atmosphere. The two stopcocks are then adjusted so that the U-tube limbs are connected via the ~ o w d e rbed. The time taken for the liauid t o fall between two marks, hl and h2 em., respectively, above urements of surface areas by the above method with the equilibrium value, is noted. The height of the bed those obtainable with the absorptiometer using the is readily measured by a finely divided scale held against following method: When an opaque powder is dispersed the packing tube. It is convenient t o measure the dis- in a, suitable liquid and a beam of light passed through tanne between the outer edges of the brass discs and to the suspension, the amount of light cut off is related to
JOURNAL OF CHEMICAL EDUCATION
should also be noted that the Lamhert-Beer law of light extinction fails when the particle diameter becomes comparable with the wave length of light,. This limitation is not, serious for powders in which there is little material below 2.5 p in diameter. The formula also fails to take into account ally settling of the suspended material so that if the powder contains particles over a considerable size range, errors are to be expected. Results obtained with this optical method and those derived from sedimentation data have been shown to afford different figures (8),but a correlation exists and hence the calibration of one method in terms of the other is possible. A similar comparison of measurements by the permeability and optical methods for nickel oxalate precipitates is shown in Figure 2. I t is clear that there is a satisfactory correlation over a considerable area range, the optical measurements giving results higher by a factor of -1.8. This factor is of the same order as that given by Sharratt, et al. (8) for a comparison between the optical and sedimentation methods for opaque materials. Agreement between any of these methods cannot, of course, be expected since each is based on a different set of assumptions. I
I
I
I
I
4WO 5WO 6000 7WO 8WO Surface sna oras g m . 7 by air perm. method
I 900(
the surface area of the powder by the relat,iou
where L = length in cm. of the suspension in which the light intensity falls from I, t o I, and W = weight of the powder in g. in V ~ mof .liquid. ~ Since the drum readings of the ahsorptiometer are usually on a logarithmic scale to base 10, the formula simplifies to
where 0, and 8, are the drum readings for the clear liquid and the suspension, respectively. This formula is based on two assumptions: (1) that the particles are spherical, or alternatively that the projected area hears the same relation to the volume of the particle as in the case of a sphere; and (2) that the light obscured by the particles depends only on their projected areas. It Precipitates of Nickel Orelate Group
No. of powders
Range,
n.'per g.
Mean limits,, nn.l per g.
ACCURRCY AND LIMITATIONS OF PERMEABILITY METHOD
The reproducibility of the results can he seen from the data on precipitates of nickel oxalate given in the table. Precipitates in Group I were prepared a t 20°C. and in Group I1 a t 40°C. All powders were measured in quadruplicate with different amounts of material in the range 6 2 g. compressed to different porosities in the range 0.4-0.6. Microscopic examination showed a greater variation in particle size in Group I and this probably accounts for the somewhat larger limits in this group. For certain types of routine work on one substance it is often convenient to use a fixed amount of material compressed t o a definite porosity. Under these circumstances the reproducibility is very high. Finally, we note that for powders of surface area greater than 12,000 cm.= per g. the errors become gross. This is t o be expected since the simple theory of the method no longer holds for particles of this size and appropriate slip correction factors have to be applied. These have been discussed in detail by Carman and Malherbe (9).
*
LITERATURE CITED (1) BRUNAUER, S., "The Adsorption of Gases and Vapours," Oxford University Press, 1945, p. 271. , Fountains Publiques de le Ville de Diion," (2) D ~ R C Y"Les Paris, 1856. J., Rer. Wien Akad., 136a, 271 (1927). (3) KOZENY, (4)CARMAN, P. C., J. Soe. Chem. I d . , 57, 225 (1938); 58, 1 f lO3Q). (5) LLA, F.'M., AND R. W. NURSE,ibid., 58,277 (1939). E. L., AND C. M. SMITH,Ind. Eng. Chm., Anal. (6) GOODEN, Ed., 12,479 (1940). P.J., J. SOC.Chem.I d . , 62, l(1943). (7) RIGDEN, (8) SHARRAT~, E.,E. H. S. VANSOMEREN, AND E. C. ROLLASON, ibid., 63, 73 (1945). P. C., AND P. R. MALHERBE, ibid., 69,134 (1950). (9) CARMAN,
