Calibration of Air Permeability Particle Sizers BERNARD DUBROW, Pyrotechnics Chemical Research Laboratory, Picatinny Arsenal, Dover, N. J.
A method of calibrating the subsieve sizer, a commercially available air permeability apparatus for determining the average particle size of fine powders, consists of two experimental procedures employing fritted-glass diffusion tubes as standards. In one procedure, the air flow resistance offered by the glass diffusion tube is measured directly as a deflection of the manometer. The second procedure utilizes a wet-test meter to determine the air conductance through both the diffusion tube and the capillary flowmeters. With the aid of an equation, relating the variables associated with each of the two procedures, the manometric deflections of different subsieve sizers can be calibrated by independently measuring the resistance and conductance of the fritted-glass diffusion tube. The validity of the equation has been checked by comparing observed and calculated manometric deflections. Results are reported for glass diffusion tubes having porosities corresponding to nominal pore sizes from 0.9 to 60 microns.
0
F T H E methods available for particle size determination ( 11, the permeability method offers the advantages of rapid and simple operation. The Fisher subsieve sizer, a commercially available air-permeability apparatus, therefore, has become widely adopted for routine control measurements of average particle size. The subsieve sizer was developed by Gooden and Smith ( 3 ) in their investigations of the effect of particle size in the production of powders for insecticides. In the determination of the average particle size, considerable discrepancies between the values obtained with different subsieve sizers were found to exist for identical samples. As a survey of the available literature failed to disclose a method to compare the values obtained with different instruments, the development of a calibration method was undertaken.
applies to the flow of air through the subsieve sizer. C" is the permeability constant of the diffusion disk. The flow of air through the subsieve sizer can be visualized with the aid of the simplified schematic drawing (Figure 1). Air a t an initial manometric pressure, P I , flows through a packed bed of permeability C1. (In this discussion C1 refers to the permeability of the fritted-glass diffusion tube.) The resistance offered by the packing causes the initial pressure to drop. This lower pressure, P,, is indicated by a deflection of the water in the flowmeter manometer. Air under the manometric head, P,, then flows through the flownieter resistance tube, the permeability of which is equal to CZ. Once the air passes through the flowmeter tube, its pressure is equal t o atmoPpheric pressure, PA. By applying Equation 2 to the flow system of the subsieve sizer, the flow of air, Qz,of viscosity q , and pressure P,, passing through the flowmeter resistance tube, is given by
czP m
Qz = 7
If the diffusion disk and flowmeter resistance tube are considered as individual units, the permeability constant of the combined units in series is equal to the harmonic mean of the permeabilities of the individual units,
c1 = G1 + -Cz1 The flow of air, QI,a t the initial manometric pressure, PI,therefore, is given by DT
As the rate of flow of air through the system is constant-Le.,
Q1 = Qz-then Equations 2a and 2b can be combined:to give (3)
THEORY AIR-
The measurement of the average particle size of powdered materials with the subsieve sizer is based on the relation b e k e e n the rate of flow of air a t low pressure through packed beds and either the external surface or the average particle size of the packing. Investigation ( 4 ) of the lams governing the flow of fluids through packed beds indicates that the rate of flow is very nearly proportional to the pressure drop per unit length of packing, as represented by Equation 1.
FRITTED GLASS, DIFFUSION DISK (PERMEABILITY, Ci)
where Q is the volume of fluid, of viscosity q, flowing per unit time through a bed of cross-sectional area .4 and depth H , A P is the pressure drop across the bed, and C' is defined as the permeability of the bed; it is equal to the volume of fluid of unit viscosity which passes through a unit cross section of the packing in unit time under the action of unit hydraulic gradient. For calibrating the subsieve sizer, a fritted-glass diffusion disk can be substituted for the sample. As the cross-sectional area, A , and depth, H , of the disk are constant, the equation
FLOWMETER RESISTA NC E TUBE (PERMEABILITYC
v
Figure 1. 1242
JJ
Pm
-A
FLOWMETER MANOMETER
I1
Flow of Air through Subsieve Sizer
V O L U M E 25, NO. 8, A U G U S T 1 9 5 3
1243 reading, designated by V Z and tz, respectively, are recorded. To determine the permeability constant for the single-range flowmeter, the range control indicator, located in the upper right corner of the apparatus, is turned to the right or “read directly” scale. To determine the permeability constant for the doublerange flowmeter, the range control indicator IS turned to the left or “read double” scale. The permeability constant, K F , of the flowCALCULATION. meter capillary tube is calculated by means of Eqtiation 4,
-FLOWMETER
K p = 1.263 X 1 0 3 d 6 where CF is the rate of f l o ~of air of unit hydraulic gradient, cubic feet per minute per centimeter through the capillary flovimeter. C F is calculated from the experimental variables by means of the folloiving equation:
...
The permeDetermination of K1, Kz, K.v. PROCEDURE. ability constants, K,, K z , . K.v, of the fritted-glass diffusion tubes supplied by Corning Glass Vorks are determined by substituting the diffusion tubes for the floametrr capillary tubes in the subsieve sizer. Figure 3 illustrates the insertion of a diffusion tube in the sizer.
Figure 2. Assembly €or Flowmeter Calibration
It is advisable that the permeability constants, Cl, Cz . . . , C,V, be consistent with the permeability constant associated with particle size measurements-Le., the constant K,, KO, . ., K N , given by the Gooden and Smith equation. The relationship between the two constants is:
With the diffusion tube in place in the instrument, the permeability constant, K.v, is determined in accordance with the procedure for the determination of K F . The diffusion disks must be clean and dry if accurate results are to be attained. The disks are cleaned by washing with hot 1 to 1 hydrochloric acid and rinsing thoroughly with distilled water. The tubes are dried a t 110” C. for 4 hours in an oven and stored in a desiccator. Determination of PI. PROCEDURE.An empty sample tube is inserted in the subsieve sizer. With air flowing through the apparatus, the deflection of the water in the manometer on the front panel is measured directly with a centimeter wale to fO.05 cm. The reading multiplied by 2 is equal t o the manometric deflection, P I , equivalent to the air pressure entel ing the apparatus.
.
K N = 1.263 X 1 0 3 d z 7
(4)
By combining Equations 3 and 4 one ultimately obtains:
where Kp is the permeability constant of the subsieve sizer flowmeter. Since P I and Kp are constants for any one subsieve sizer, diffusion tubes having experimentally determined permeability constants, K,, K,, . . K N , can be used t o determine, and therefore calibrate the manometric deflections of different subsieve sizers.
.
EXPERIMENTAL
Determination of KF. APPARATUS.The apparatus used was the Fisher subsieve sizer ( 2 ) . A Precision-Sargent wet-test meter was used t o measure the rate of flow of air per unit hydraulic gradient froin which the permeability constants, Kp, of the flovmeter capillary tubes in the Fisher subsieve sizer can be calculated. PROCEDURE. As shown in Figure 2, the wet-test meter is connected to the bottom end of the flowmeter tubes; care is taken not to damage the fine wires extending from the capillaries nor to block the holes on the side of the flowmeter. With the empty sample tube inserted in the subsieve sizer, air is passed through the apparatus. When air is observed to pass through the wettest meter a t a constant rate, the initial volume reading, VI, and the time of the reading, t l , are recorded. The deflection of the water in the manometer on the front panel of the subsieve sizer is measured directly with a centimeter scale to A0.05 em. Twice the manometer reading is equal to the hydraulic gradient, P . After 1 hour the volume reading and time of the second
Figure 3. Insertion of Diffusion Tube i n Subsieve Sizer
....
For determination of 4,Kz, Kn A . Single-range capillary flowmeter tube A - B . Double-range capillary flowmeter tubes C. Fritted-glass diffusion tube D . Manometer tube E. Clamp F. Rubber tube G. Range control switch (open) H . T o wet-test meter
Determination of P,. PROCEDURE. The manometric deflection, P,, indicating the resistance of the fritted-glass diffusion tube, is determined by substituting a clean, dry diffusion tjube for the sample tube of the subsieve sizer. This is done by disconnecting the inlet and outlet rubber tubes which extend from
ANALYTICAL CHEMISTRY
1244 Table I. Comparison of Calculated and Observed Manometer Deflections for Two Subsieve Sizers Diffuaion Tube Designation
Max. Pore Size, Microns
Gltrafine Fine Medium Ace Coarse
0.9-1.4 4 -5.5 10 -15
Ultrafine Fine Medium Ace Coarse
0.9-1.4 4 -5.5 10 -15
Manometric Deflections, P m ,Cm. Single-Range Double-Range Flowmeter _ _Flowmeter _~_ Calcd. Obsd. Calcd. Obsd. Xfachine 1 12 00 29,50 43 55 47.16 48.87
Nonegiven
40 -GO
11.84 29.72 43.52 46 92 48.98
3.68 13.51 32.13 41.29 46.91
3.60 13.80 32.58 41.42 47.10
13.04 31.22 44.66 47.72 49 46
4.09 14.98 33.63 42.57 47.81
4.00 14.62 33.66 42.46 47.82
.Machine 2
None given
40 -GO
13.38 31.83 44.70 47 98 49.47
Table 11. Equation of Manometric Deflections of Two Subsieve Sixers Diffusion Tube Designation Ultrafine
Flowmeter Range Single Double
Manoriietric Deflection, Pm. Column Cm. Cor4 X Column 3Machine hfachine rection Column Column 6, 1 2 Factora 5. Cm.b Cm. 12.00 3.68
13.38 4.09
0,8782 0.870
11.75 3.56
-0.25 -0.12
Fine
Single Double
29.50 13.51
31.85 14.98
0.9287 0.9152
29.58 13.71
+0.08 +0.20
RIediiitri
Single Double
43.55 32.13
44.70 33.63
0.969 0,957
43.31 32.17
-0.24 4-0.04
Ace
Single Double
47.16 41.29
47.98 42.57
0 979 0.972
46.99 41.38
-0.17 +0.09
Coarse
Single Double
48.87 46.91
49 47 47 81
0 984 0.984
48.70 47.02
-0.17 +0.11
a
Correction factor obtained by solving radiral
+ +
[(KN)* (KF,)' P 2 ] . ( K N 2 ( K F ~ ) " Pi2
Corrected value of calculated manunietric value of machine 2.
the lower and upper caps that hold the sample tube. The ends of the diffusion tube are connected to the inlet and outlet rubber tubes as shown in Figure 4. With the air pump turned on, the level of the water in the manometer is allowed to rise to Its maximum height. The maximum deflection of the height of the water in the manometer on the front panel of the subsieve sizer is measured directly to +0.05 rm. by means of a centimeter scale. The reading is multiplied by 2 to obtain the manometric deflection, P,. lJ1 SCIJ S SIOh
As indicated in Equation 5, it is necessary to measure P I , K F , and K N in order to calculate the deflection of the water column The calculated values of P , in the flowmeter manometer, P,. can be checked experimentally by using diffusion tubes of known permeabilities, K1,K z , , . K N , as series resistance to the flow of air entering the apparatus. The calculated and observed value9 of P , for the single and double flowmeter ranges of two subqieve sizers are compared in Table I. The values calculated from Equation 5 and the observed values of P , agree within experimental error. Equation 5 also can be used to compare the characteristics of different subsieve sizers. A convenient form for comparison is obtained by combining the values in Equation 5 for two instruments and solving for the manometric deflection of one. The following equation results:
.
Figure 4.
Determination of P , (Observed)
A. B. C. D. E.
Capillary flowmeter t;bes Assembly for calibration of capillary flowmeter tubes Manometer tube Rubber outlet tube Standpipe F. Dryingtube 6. Tube extending from upper cap H . Pressure-reducing valve K . Fritted-glass diffusion tube L . Air pump .M. Manometer level control N. Tube extending from lower cap P. Rubber inlet tube
The reported theory and experimental data are significant because they indicate that it is experimentally feasible to adjust different subsieve sizers to give equivalent manometric deflections. This adjustment or calibration can he achieved by lengthening or shortening the fine resistance wire in the capillary flowmeter of the subsieve sizer until the pernieability constant is equal to an arbitrarily chosen standard value. The method developed in this report also provides for an independent check of the manometric deflections, This check can be made by inserting a diffusion tube in the subsieve siaer in place of the sample tube, and comparing the observed value of P , with the value c.:~lculnted from Equation 5 . ACKNOWLEDG3lENT
Acknowledgment is made t o David Hart, Garry Weingarten, and Saul Gordon, of this laboratory, for their valuable suggestions, and to Rubin Schiffman and Clement Campbell for conducting much of the experimental work. LITERATURE CITED
(1) Am. SOC.Testing Materials, Tech, Pub. 51 (1941). where PI,, KF,, P , are characteristics of machine 1, and PI^, KF2,and P,, are characteristics of machine 2. Table I1 indicates the feasibility of utilizing Equation 6 to equate manometric deflections for different instruments in various pressure ranges. The data in Table I1 show that the manometric, deflections of machine 1 agree within experimental error with the corrected values of the manometric deflections of machine 2.
(2) Fisher Scientific Co., "Directions for Determination of Average Particle Diameters of Powders with t h e Fisher S u b Sieve Siaer." (3) Gooden, E. L., a n d Smith, C. AI,, IND.ENG.CHEM.,Ai-i.4~. ED.,12, 479-82 (1940). (4) Poiseuille, J., "Recherches experimentales sur le m o u v e m e n t des liquides d a m les tubes de trhs-petit diamhtre," Inst. de
France, Acad. des Sei., Meinoires present& par divers savants, 9, 433-543 (1846).
RECEIVED March
10, 1953.
Accepted May 29. 1953.
