684
C. G. DODD, J. W. DAVIS AND F. D. PIDGEON
MEASUREMENT OF SPECIFIC SURFACE AREAS OF XONPOROC'S POWDERS BY -4 PRESSURE-DECLINE LIQCIDPERMEABILITY METHOD' CHARLES G. DODD, JdJIES R. DAVIS,
AX'U
FIiAKCES D. PIDGEOX
Surface Chemistry Laboratory, Petioleuin Ezperiinent Station, Bureau of Maneo, Bartlesuz'lle, Oklahoma Receaved June 16, 1060 INTRODUCTION
Numerous investigators have demonstrated the validity of applying permeability methods to the measurement of specific surface areas of nonporous powders. Most such methods have been based on the Kozeny equation (12) as applied by Carman (5, 6 , 7), who used liquids as his permeating fluids in :I constant-head apparatus. Lea and Nurse (13) and others haye applied the method by using gases instead of liquids.2 Rigden (16) and Arne11 (2) have pointed out that it is convenient to use a pressure-decline (or decay) technique for gas measurements with fine powders, because this procedure permits low rates of flow to be measured with adequate precision. Furthermore, it pressuredecline apparatus may be designed 85 a completely closed and isolated system, a fact which aids in eliminating plugging of the powder bed by foreign particles suspended in liquids. The pressure-decline technique, whereby the pressure drop across a porous membrane decreases continually, has been applied to liquid-permeability measurements by Meinzer and Fishel (l$, Terznghi (20), and Calhoun and Yuster (4);but, except for the work of Rigden (17) discussed below, no cxample of the application of the method to the measurement of specific surface area has come to the writers' attention. This paper describes such an apparatus, the design of which incorporates the following features: (1) The operating procedure requires only measurement of the position of one falling meniscus in a precision-bore tube, from which the instantaneous pressure drop across the packed sand and the instantaneous rate of flow may be calculated. (2) The resistance to flow of the packed powder under test may be separated from the resistance of a supporting disk and layer of identical or similar material. (3) The apparatus may be employed in a modified form designed for precise measurements of low rates of flow wherein the powder membrane and the prefiltered liquid are completely enclosed and protected from contamination, thus aiding elimination of such difficulties as plugging of beds of subsieve powders, or i t may b.e used in a simple form especially 1 Presented before the Division of Colloid Chemistry at the 116th Meeting of the .4merican Chemical Society, which was held at Atlantic City, New Jersey, September 18-23, 1949. 2 In this paper the writers do not plan to discuss the relative merits of gas-permeability and liquid-permeability procedures for the measurement of specific surface area. Rnther, the theory, technique, and spplication of an improved liquid method are presented.
SURFACE AREAS O F NONPOROUS POWDERS
685
adapted for convenient (but sufficiently precise) measurements of higher rates of flow through coarse powders in the sieve size range. The specific surface area of a powder sample may be calculated from the slopes of logarithmic plots of fluid-head loss across the bed verms time for the blank run and the sample run. The apparatus has been used for measuring specific surface areas of nonporous powders ranging in magnitude from about 3 X lo2 to 4 X lo4 cm.2/cm.8 of solid material. THEORETICAL
The Kozeny equation as used by Carman ( 5 ) may be expressed as:
where the symbols are defined below in consistent
Q
C.G.S.
units:3
= volume rate of flow of liquid through the bed of powder in cubic
centimeters per second, k = the dimensionless Kozeny constant (discussed below), A = cross-sectional area of the bed of powder in the cell in square centimeters, p = viscosity of the flowing liquid in poises, So = specific surface area of the powder in square centimeters per cubic centimeter (in terms of volume of solids rather than apparent or bulk volume), c = fractional porosity of the packed powder bed, p = density of liquid in grams per cubic centimeter, g = acceleration of gravity (980 cm./sec?), h = drop in fluid head across the bed of powder, in centimeters of liquid flowing,‘ and L = depth of packed powder bed in centimeters. The Kozeny constant may be determined empirically for most powder-liquid systems. Kozeny (12) and Fair and Hatch (9) considered that it involved the shapes of the cross-sections of the channels through which fluid flows in the packed bed. Carman ( 5 ) and Fowler and Hertel (IO) pointed out that the cons The Koreny equation, in effect, is an expansion of Darcy’s law for isothermal, liquid, streamline flow through porous media:
Ak‘
Q---.r
pgh
L
in which k‘ is defined as the “permeability coefficient,” or simply as the “permeability.” The other symbols in this equation have the same meaning ss in equation 1. 4 For the purpose of the present work, the term ph is identical with the pressure differential across the packed powder bed, A P , as used by other investigators. In all permeability equations i t should be emphssised that the pressure differential or fluid-head loss is mewured only under dynamic flow conditions.
f336
C. 0. DODD, J. W. DAVIS AND F. D. PIDGEON
stant k #alsoinvolves an “orientation factor” in addition to the “shape factor” already mentioned. The orientation factor depends on the tortuosity of the streamline channels of flow, which in turn depends on the morphology of the solid particles, the orientation of the particles with respect to the axis of the packed bed, and the compactness or porosity of the bed. Carman ( 5 ) found empirically that the Kozeny constant, k, is equal to 5.0 ( A 1 0 per cent) for a large variety of powders. Sullivan and Hertel (18) found that a value of 4.5 was applicable to flow through a compact bed of glass spheres. In the present work, the former value was used in the computations for quartz powders and the latter value for microscopic glass spheres. In the derivation of equation 1, the flow is assumed to be isothermal and the fluid viscosity and density are taken as constants; moreover, A , SO,e, and L ATMQSPHCRIC PRESSURE
FIQ.1. Schematic diagram for evaluation of the drop in fluid head corresponding to friction loss a t the solid surface.
are properties of the bed of powder, so that they too are constants. It follows that equation 1 may be converted to the simplified form Q
=
Kph
(2)
in which the constant K is given by
Figure 1 has been prepared to show how the writers applied the foregoing equations to determine specific surface areas. That figure depicts an imaginary system, consisting of a tube of constant internal diameter, standing in a vertical position with its lower end just barely immersed in a large body of the test liquid of density p. The lower part of the tube is packed with a test specimen
687
SURFACE AREAS OF NONPOROUS POWDERS
of powder for a distance L above the free surface of the large body of liquid. At any particular instant, the liquid meniscus in the tube is a distance h above the foregoing free surface, which is taken as the datum of elevation, and a distance H above the top of the packed bed of powder. Consider the calculation of the instantaneous energy loss across the bed of powder as liquid flows down through the powder. It is important to emphasize that the diference in energy at transverse s e c t i a s 1 and 2 i n jigure 1 i s the result of energy dissipated as friction un the surface of the solid powder. The fluid-head loss corresponding to the loss of energy as friction would be indicated experimentally if manometers were attached at points 1 and 2. For a pressure-decline apparatus it is necessary to calculate this pressure differential rather than read it on manometers. A mechanical-energy balance may he set up by equating the energy in the flowing liquid at points 1 and 2 located at the top of the packed bed and the surface of the liquid, respectively. (Electrical, magnetic, and other miscellaneous minor energy effects are neglected, and the liquid is assumed to be incompressible.) z1pg
+ p1g +
pu:
- 2F.g
=
zzpg
+ p2g +
pu:
(4)
where z1and 22 represent the height in centimeters at points 1 and 2, respectively, from the reference level taken at the free surface of the liquid (for the system discussed, z2 = 0 ) , pl and p2 represent the static pressure in grams per square centimeter at points 1 and 2 , respectively, u, and uz represent the velocities in centimeters per second at points 1 and 2, respectively, p and g have the same meaning as above, and ZF represents the loss in pressure in grams per square centimeter due to friction. (Each term in equation 4 has the dimensions of pressure in dynes per square centimeter.) Equation 4 may he rearranged and simplified by considering that z1- 2 2 = L , p l - p , = H , and that the kinetic energy terms cancel, since the internal diameter of the tube is assumed to he constant, thus making the two velocities equal. Equation 4 then reduces to
+
ZF = (L H ) p = hp (5) Thus it is evident that h represents the instantaneous drop in fluid head which is applicable to permeability calculations. The above analysis is included to clarify a subtle point which apparently has been misunderstood by at least one other worker. In his liquid-permeability work Rigden (17) considered h to be equal to H ( L / 2 ) instead of H L. In certain experimental arrangements the resulting error may be appreciable.
+
+
ss8
C. G. DODD, J. W. DAVIS AND
F. D. PIDGEON
If the constant internal cross-sectional area of the tube in figure 1 is designated as A o , the instantaneous volumetric rate of flow as measured by the drop of the liquid meniscus is -Ao(dh/dt), t being the time variable; hence, equation 2 may be put in the form: (6)
Integrating between limits and converting natural logarithms to common logwith,
in which ho = h at t = 0. Equation 7 indicates that a straight line of slope ( - K p / 2 . 3 0 3 & ) = m will result if log h is plotted against t . As p and A. are easily measurable constants, K may be evaluated by a graphical determination of the slope. Then, equation 3 , when rearranged, may be applied to solve directly for the specific surface area :
Ip summary, determinations of specific surface area made by the pressuredecline liquid-permeability method require that the Kozeny constant k be MIsumed, that the constant properties of the powder bed and test liquid ( A , L , e , and p ) be known, MI well as the apparatus constant Ao, and that, during an experiment, h be recorded as a function of t. APPARATUS FOR MEASURING PERMEABILITY OF COARSE POWDERS
The simple equipment developed for flow through sieve-size sands or powders is illustrated in figure 2 . The powder sample is contained in a cylindrical Pyrex glass tube specified by the manufacturer to have an internal bore of 1 in. constant to f 0.0002 in. At the lower end of the cell, a sintered-glass disk is sealed into the tube to support the powder bed. Below the sintered disk, ordinary Pyrex glass tubing is used. Sealing the disk in the precision-bore tubing destroys the constancy of the internal diameter for about t in. above the disc. If the sample were placed directly on top of the sintered disk, variations in the internal diameter would not permit the porosity of the packed bed to be determined with sufficient precision, and the rate of flow of liquid through the bed would be increased at the point of constriction. To avoid these difficulties, a thin bed of powder is placed on the disk so that the top of this supporting membrane is within the portion of the tube where the internal diameter is known precisely. The resistance to flow of the blank membrane may be deducted from the resistance of the blank plus the sample, as shown below. It is convenient to use the same powder for the blank as is used for the sample.6 6 Recently a technique has been developed by which a sintered-glass disk may be cemented in a piece of precision-bore tubing without constricting the tube.
689
SURFACE AREAS OF NONPOROUS POWDERS
A sealed-in sintered-glass disk used to support the powder bed haa several advantages over a metal gauze of negligible resistance to flow held in place by a loosely wound spiral, as employed by Carman (6). The writers found it difficult to find suitable types of metal gauze having the properties described by Carman, ‘I. . a gauze which waa sufficient to retain the bed efficiently, but gave no meaaurable resistance when tested a t the same rate of flow without the bed.” Furthermore, the necessity for cleanliness in surface chemistry experiments is easily met by cleaning the entire all-Pyrex-glass sample cell in warm chromic acid cleaning solution.
.
PRECISION CAP
BORE
TUBING
STANDARD TAPER
GLASS JOINT
P R E C I S I O N BORE
TUBING
FOR
SAMPLE S U P P O R T I N G MEMBRANE ( B L A N K ) SINTERED GLASS DISK (SEALED
FIG.2. .4pparatus for
use
IN 1
with coarse powders
The top of the permeability cell is connected to a straight vertical piece of precision-bore tubing having a length of about 1 m. The column of the flowing liquid which stands in this tube constitutes the head which drives the liquid through the packed powder in the cell. Below the sintered-glass disk is sealed a U-tube of ordinary Pyrex tubing, carrying a stopcock directly below the sintered disk and terminating in an overflow device. The latter is designed so that the overflowing liquid level may be read precisely with a cathetometer. The foregoing equations applicable to the imaginary apparatus of figure 1 also are applicable to the apparatus shown in figure 2. The constant K , as defined by equation 3, may be considered to be analogous
690
C. G. DODD, J. W. DAVIS AND F. D . PIDGEON
to the concept of specific conductivity which is used in electricity and applied to both electronic conduction in metals and electrolytic conduction in ionic solutions. Similarly, the reciprocal of K may be considered to be the resistance of the bed. The resistance of the bed of sample may be separated from the resistance of the sample and supporting bed by considering the analogy to two electrical resistances in series. In symbolic form let: = resistance to flow of sintered-glass disk and supporting bed of
powder (blank)
E2
=
resistance to flow of the sample being tested
E%- - resistance
to flow of the combination
It is possible to obtain experimental values for K1 and K12 from the slopes of the straight lines obtained from log h versus t plots for the two experimental runs, using only the supporting bed (blank) and the supporting bed plus sample, respectively. The value of K Z can be calculated by adding resistances in series:
Finally, the specific surface area of the powder under test can be calculated by replacing K by K2 in equation 8.
Experimental procedure: coarse-powder apparatus Before starting a determination of surface area, the glass apparatus was cleaned thoroughly with warm chromic acid cleaning solution, then rinsed copiously with distilled water, dried at 110°C. (if permeating liquids other than water were to be used), and the stopcock (selected for precision grinding and lubricated with the liquid used) inserted in the cell. The cell was filled with deaerated liquid, and all air was removed from the pores of the glass disk. Enough dry powder or slurry for the blank membrane was washed into the cell, allowed to settle on the glass disk, and compacted by tapping the outside of the cell gently with a rubber mallet. The upper liquid-head tube was assembled and liquid allowed to permeate through the cell until steady-state conditions were obtained. This procedure was found sufficient to remove any entrapped air remaining in the membrane. After recording h as a function of t for the blank run, the upper tube was disassembled, and the weighed sample of pre-wet and deaerated powder washed carefully into the cell and allowed to settle on top of the blank bed. In this operation, it was necessary to take care to avoid disturbing the supporting mat. After compacting gently with a rubber mallet, further settling and removal of traces of air from the powder were accomplished by
691
SURFACE AREAS O F NONPOROUS POWDERS
flowing liquid through the bed, as in the case of the blank bed described above. When powder samples of low density or fine particle size were used, it w m necessary to carry out introduction and packing of the powder in increments. In the latter case, sedimentation of the bed was expedited by pulling a partial vacuum through the overflow cap while liquid was standing to the top of the cell. Whenever powder samples having a considerable range of particle size are used, it is necessary to pack in increments to avoid stratification, which would result in variable porosity in a vertical direction through the bed. Such stratification introduces an unknown error in the procedure for which corrections are difficult to apply. TABLE 1 SpeciJtc surface area of 70- to 100-mesh glass spheres determined by microscopic and permeability methods YKT‘HOD
Microscopic methods: Kenrick projection a r e a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diameter of particle of average area.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diameter of particle of average volume., . . . . . . . . . . . . . . . . . . . . . . . . . . . . Martin’s “diameter”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mean microscopic value.. . . .
328 339 334 332
..................................
Permeability methods:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gas permeability : Air (atmospheric pressure) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Helium (atmospheric pressure) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
334
331 325
Mean gas-permeability value
328
Liquid permeability: Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isoiictane (2,2,4-trimethylpentane) ........................... Water-Silane-treated glass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mean liquid-permeability value. . . . . . . . . .
325 325 324
.................
325
Experimental results obtained with the coarse-powder apparatus are shown plotted in figure 4,and the specific surface areas calculated therefrom in table 1. APPARATUS FOR MEASURING PERMEABILITY O F FINE POWDERS
The apparatus that has been found most suitable for subsieve powders is shown in figure 3. As a result of the greater resistance to flow of packed beds of finer powders, it is convenient to use higher pressure differentials across the beds. Sufficiently high pressure differentials may be obtained by using a mercury-filled U-tube, wherein a head of mercury drives the permeating liquid through the cell. The design shown also permits the system to be enclosed.
C. G. DODD, J. W. DAVIS AND F. D. PIDGEON
FIG.3. Apparatus for use with fine powders
FIG.4. Pressure-decline runs with coarse-p3wder appnratus
SURFACE AREAS OF NONPOROUS POWDERS
693
Precision-bore Pyrex-glass tubing was used in making those portions of the U-tube where the mercury menisci travel. Thus, the head of mercury may be calculated from the level of only one meniscus, provided the equilibrium level has been established previously with nothing but mercury in the U-tube. If the head of mercury measured from the equilibrium level to the top of either mercury meniscus is designated as 7 , and the vertical distance from the equilibrium level to the top of the overflow tube as X, the drop in fluid head, h, across the cell due to friction can be shown to be h = v
rT-
1)
+x
in which pHg is the density of mercury and p is the density of the permeating liquid. Equation 11 may be combined with equation 6 if dh,'dt in equation 6 is first replaced by dq/dt. Integration of the resulting equation leads to
in which A o , in this case, represents the internal cross-sectional area in the precision-bore tubing in the U-tube arms. Equation 12 is similar to equation 7, and is used in the same manner. Experimental procedure: $ne-powder apparatus The apparatus shown in figure 3 was designed so that it might be taken apart and completely submerged in warm cleaning solution before a determination was made. The necessity for having clean glass surfaces is more important in the case of the fine-powder apparatus, because surface-active contaminants are more readily adsorbed on the greater exposed surfaces of the finer samples, such adsorbed impurities may anomalously affect the observed rate of permeation, and, in addition, the mercury menisci in the glass V-tube may stick to dirty spots on the inner walls of the U-tube. The clean dried U-tube was filled with redistilled mercury approximately to a reference scratch mark on the outside of the U-tube and placed in an air-bath thermostat (held constant to +O.l"C.) before the permeating liquid was added. After thermal equilibrium was attained, the distance from the equilibrium mercury level to the reference scratch mark was determined. The cell mas filled in the same manner as described for the coarse-powder apparatus, and the apparatus was assembled &s shown in figure 3 . After thermal equilibrium was attained in the air bath, the blank and sample runs were made in the same manner as those with the coarse-powder apparatus. Typical plots of experimental observations are shown in figure 5 and corresponding specific surface areas in table 2. PREPARATION OF MATERIALS
The glass spheres used in the work with the coarse-powder apparatus were purchased from an artists' supply dealer where the spheres were designated as
694
C. G. DODD, J. W. DAVIS AND F. D. PIDGEON
0
10
FIQ.5 . Pressure-decline runs with fine-powder apparatus TABLE 2 Specijic surface area o j j i n e quartz powder determined by light and electron microscopy and by the liquid-permeability method
Light microscopy: Amberg’s method.. .................................... Martin’s “diameter”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 x 104 1.7 X 10‘
Electron microscopy: Martin’s “diameter”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 X 10‘
Liquid permeability: Water: Run 6A.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Run 6B .................................... Mean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.00X lo4 3.50 x 104
3.8
x
104
2.7
x
104
Isoiictane (2,2,4-trimethylpentane):
..................................
2.65 X lo4
“crystal frosting, clear finish.” The smallest-size glass beads available were purchased for this work. The spheres were screened with care, and the sample that passed a 70-mesh but was retained on a 100-mesh U. S. Standard screen
SURFACE AREAS OF NONPOROUS POWDERS
695
was reserved for experimental use. After screening, the spheres were cleaned in warm chromic acid cleaning solution, rinsed copiously with de-ionized water, and dried at 110OC. One portion of the cleaned-glass spheres was treated with General Electric No. 9987 Silane to render the glass surface water-repellent. The quartz powder used in the work with the he-powder apparatus was an elutriated fraction of commercially available material. The desired particlesize distribution was in the range from 1 to 7 microns. After elutriation the powder was cleaned by washing and by treatment with warm chromic acid cleaning solution, as were the glass spheres. Washing with de-ionized water was done by decantation, followed by repeated mashing on a Biichner funnel; then the material was dried at 110°C. Distilled or de-ionized water was used as the water phase in the liquid-permeability experiments. The 2,2,4-trimeth~lpentane~ was used without further purification. Immediately preceding an experiment the permeating liquid was deaerated and quickly brought to the experimental temperature.
Microscopical measurements of surface area and particle size Glass spheres: The specific surface area and particle size of the 70- to 100mesh sample of glass spheres was determined with the light microscope, using four independent methods: (1) The projected-area method or Kenrick method (11, 21,22) was employed to determine the specific surface directly. This method is based on the principle that the mean projected area of particles having no reentrant surfaces is one-quarter of the total surface area. (8) The diameter of the sphere of average area mas calculated from the projected areas of 379 particles, as determined in the first method. (3) The diameter of the sphere of average volume was calculated from the particle volumes as determined in the first method. For this measurement, it was necessary to count 20,520 particles contained on three slides in order to obtain the desired precision. ( 4 ) The method employing Martin’s “diameter” (8, 14) was used to measure the mean diameter of three samples mounted in a medium of optimum contrast and maximum definition. A total of 677 particles was measured for this determination. Since the shape factor of the glass spheres was known with sufficient certainty, it was possible to use the above four independent microscopic methods. Specific surface areas determined by each of the four methods are given in table 1. The mean value of the specific surface area of the glass spheres was found to be 334 ~ m ? / c m The . ~ probable error of the mean is believed to be less than 4 per cent. Quartz powder: Two methods employing the light microscope were used to determine the specific surface area of the quartz powder: (1) Amberg’s method (1) was used to make three counts of approximately 500 particles each. The mean specific surface area thus was determined t o be 4 X IO4 cm.*/cm.s (8) The method of Martin’s “diameter” (8, 14) mas used to measure 539 separate particles. A shape factor of 10 as used for the calculation of surface area. A value of 1.7 X lo4 ~ m . ~ / c m was . ~obtained by this method. This was puiest grade “isooctniie,” obtained fiom the Rohm and Hnas Company.
696
C. G. DODD, J. W. DAVIS AND F. D. PIDOEON
An estimate of the range of particle size present in the quartz-powder sample was obtained by examination with an electron microscope at a magnification of about 3500X, using polystyrene spheres of known particle size interspersed with the quartz particles. The plates were enlarged and 651 particles were measured by Martin’s “diameter” method. A mean specific surface area of 2.8 X lo4 cm.*/cm? was calculated, a value which is believed to be more accurate than the results with the light microscope. It was found that particles ranged in siae from less than 0.1 micron up to 7.6 microns. About 44 per cent of the particles by number were below 0.1 microns, but these fines contributed less than 0.05 per cent of the calculated total specific surface area of the powder. Neither of the measurements made on the quartz powder with the light microscope is believed to approach the accuracy of those on the glass spheres. The particles below 0.1 micron in diameter would not have been resolved by the light microscope. Furthermore, the irregular shapes of the quartz particles necessitated assumption of an approximate shape factor for area calculations from Martin’s “diameter” data. DISCUSSION
Results obtained with glass spheres The precision of the experimental results with the 70- to 100-mesh glass spheres is indicated by the excellent linearity of all the plots shown in figure 4. A comparison of the specific surface areas of the glass spheres as determined by microscopic and permeability methods is presented in table 1. The specific surface areas determined by the pressure-decline liquid-permeability apparatus are in excellent agreement with similar measurements made by more widely accepted gas-permeability techniques (19) and by independent microscopic methods. The latter are considered to give reliable accurate values of true specific surface area. One of the more interesting results of this work is the excellent-in fact, fortuitous-agreement between the specific surface areas calculated by the liquidpermeability method for different samples, even when the solid-liquid adhesion characteristics were varied. As shown by the liquid-permeability specific surface areas in table 1, almost identical values were obtained for the clean glass-water, clean glass-isoijctane, and Silane-coated glass-water systems. A separate portion of glass spheres was used for each run. Water and n-heptane are known to wet silica surfaces without forming a finite contact angle (3). Water and benzene behave similarly on glass (23), and isooctane would be expected to do the same. However, while both water and n-heptane form zero contact angles on glass, the free energies of adsorption and of adhesion of water are stated to be about five times those of n-heptane (3). The corresponding free energies of the glass-water and glass-isooctane systems would be expected to have the same relative orders of magnitude as those for the silica-water and silica-n-heptane systems. On a Silane-treated glass surface water forms a contact angle of about go”, and the free energies of adsorption and adhesion would be expected to be low as compared with the other two systems. Thus, in spite of the variations in the free energies for the three systems, no
SURFACE AREAS OF NONPOROUS POWDERS
697
difference was observed in the permeabilities or the specific surface areas calculated from the permeabilities. These observations indicate that surface forces do not affect the flow of liquids through packed beds of glass spheres as large as the 70- to 100-mesh particles used in this work. Results obtained with quartz powder
The excellent linearity of the pressure-decline runs with the quartz-water and quartz-isooctane systems as plotted in figure 5 is fully as satisfactory as that of the results shown in figure 4 for the glass spheres. The straight lines in figure 5 indicate that the design of the fine-powder apparatus and the procedure described herein have eliminated the difficulties encountered by many investigators with the plugging of pores in membranes of powders as fine as the quartz used in this work. If progressive plugging of the membranes had occurred, the plotted results would have shown a noticeable curvature convex to the time axis. The absence of any curvature stands as evidence that the properties of the powder beds remained constant during experimental determinations. The surface-area values calculated from the plots in figure 5 and shown in table 2 are less consistent than those for the glass spheres. The quartz-powder membranes exhibited lower permeability to water than to isooctane, resulting in calculated specific surface areas differing by about 40 per cent. As emphasized above, this difference is not thought to be caused by plugging of the quartz membranes by foreign particles suspended in the liquids. At present the writers prefer to make no attempt to explain the differences in permeability with the two liquids. Research on the general problem of solidfluid interactions which might affect flow through fine pores as small as those of the quartz-powder membranes is under way at this Laboratory. The work described here indicates that no such complications are involved in the case of membranes made up of uniform particles of the size of the 70- to 100-mesh glass spheres. Whether complications are involved wi$h finer powders remains t o be determined. Aside from the above-mentioned difficulties, the results obtained with the glass spheres and the quartz powder are presented as evidence that the analysis and procedure of the pressure-decline liquid-permeability method of measuring surface area presented herein are valid for a wide range of sands and powders. SUMMARY
1. An analysis has been presented of the behavior of a pressure-decline liquidpermeability apparatus, whereby the specific surface area of a packed powder sample may be calculated. 2. Two types of apparatus to which the foregoing analysis applies are described. One modification of the basic design is especially adapted to convenient measurements of relatively high rates of flow of liquids through beds of coarse powders having particles in the sieve size range. The other modification has been adapted for measurements with beds of fine powders in the subsieve size range. The construction and operation of the two modifications are described. 3. Results obtained with a 70- to 100-mesh sample of glass spheres, the spe-
698
C. 0. DODD, J. W. DAVIS AND F. D. PIDGEON
cific surface area of which was determined by independent, precise microscopic measurements, are presented as evidence of the validity of the analysis and of the application of the apparatus. Results obtained with a sample of quartz powder consisting of particles ranging from less than 1 micron to 7 microns in diameter confirm the applicability of the method to the measurement of permeability but raise a question concerning the measurement of specific surface of powders in this size range. 4. It is concluded that surface forces do not affect the flow of liquids through beds of particles as coarse &s the 70- to 100-mesh glass spheres, but anomalies in surface-area measurements on the h e quartz powder require further investigation. The writers are indebted to Dr. J. C. Arne11 of the Defence Research Chemical Laboratories in Ottawa, Canada, to Frank G. Miller of the San Francisco Office of the United States Bureau of Mines, and to R. V. Smith of this Station for valuable discussions and suggestions relating to this work. REFERENCES
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