Aerosol Filtration by Fibrous Filter Mats Velocity-Dependent Relationships William S. Magee, Jr., Leonard A. Jonas,’ and Wendell L. Anderson’ Edgewood Arsenal, Aberdeen Proving Ground, Md. 21 010 Naval Weapons Laboratory, Dahlgren, Va. 22448
The physical properties and aerosol filtration characteristics of randomly formed fibrous filter mats were studied. Filter bulk densities ranged from 0.205-0.309 g/cm3 and fractional void volumes from 0.774-0.8i9. Pressure drop per unit thickness of filter was a linear function of superficial linear velocity and conformed with Darcy’s equation for fluid flow through porous media. Unique relationships between the filter penetration by a dioctylphthalate (DOP) aerosol and flow velocity permitted calculation of VL,the discrete velocity at which maximum penetration occurred. Mathematical equations, derived from the original Dorman aerosol equations, provided analytical methods for calculating the relative contributions of diffusion, interception, and inertia to aerosol filtration. In a previous paper Jonas and coworkers (1972) had initiated the study of aerosol filtration by the fibrous filter mats Types 5 , 6. 7 , and 8. The flow velocity range covered in that study, which should be considered Part I in a series, was 0.83-13.33 cm/sec (50-800 cm/min). Tentative success was reported in visually determining VL,the velocity a t which maximum aerosol penetration occurred, applying the semiempirical equations of Dorman (1960a,b; 1966) in a slightly modified form, and quantifying the contributions of diffusion, interception, and inertia to the overall filter penetration. Problems inherent in the theoretical interpretation of the data were only partially resolved in Part I and differences in the values for and Dorman parameters between the Part I and present paper must be noted. These differences are believed to result from three factors: one, the existence of a nonlinear systematic error in the calibration of the volumetric flowmeter, since corrected; two, the change to the present use of cgs units for all parameters; and three, the change from V L to~ V L in~ the velocity term associated with the Dorman inertia parameter which resulted from our further extension of the mathematical equations. This paper, Part I1 in the series, investigates the velocity dependent relationships inherent in aerosol filtration. The purpose of this work was to study aerosol penetration through fibrous filter mats over a wide velocity range, and to develop mathematical equations in accord with present theory which, in the self-consistent cgs system, denote the velocity dependencies of aerosol filtration.
tributions of inertia, diffusion, and interception to filtration of aerosols by fibrous filter mats. With the assumption of simple additivity of these contributions, the percentage penetration of dioctylphthalate (DOP) is expressed by log DOP % penetration
=
-(kRXVLr
+
hJVL-’
+KIA)
+2
(1)
where k R , k D , and k r are inertial, diffusional, and interception filtration parameters, respectively; VL is the superficial linear velocity; and h is the thickness of the filter. Values for x and 3 are assigned either from fundamental theoretical considerations for each contribution or from fitting actual filtration data. Equation 1 predicts, and experimental data bear out, that there is a velocity ( VL)for which a maximum occurs in plots of log DOP % penetration vs. VL.From the mathematical condition at a maximum that the derivative is equal to zero, we obtain
kD= kR
(:) vL(””
With this we transform Equation 1to the form log DOP yi penetration =
v~
Theory
As stated in I, Dorman (1960a,b; 1966) developed a semiempirical formulation for expressing the relative conTo whom correspondence should be addressed. This manuscript is a joint publication from Edgewood Arsenal
and Saval Weapons Laboratory. W.L.A. represents the latter.
By Equation 3 we see that plots of [2-l0g DOP 9’0 penetration] vs. [ VL. (x/y) x-2) V L - ~ are ] straight lines from the slope of which k n and k u are determined and from the intercept k l . This in essence constitutes the Dorman procedure. In actual practice two difficulties are encountered. First, it is often difficult to obtain a reliable value for VL, upon which all subsequent calculations depend. Usually it is chosen visually from plots of log DOP % penetration vs. VL.This “eyeball” estimate is subjective at best and virtually useless for filter mats displaying broad penetration curves rather than relatively sharply peaked curves. Second, the linearity for plots of [2-log DOP % penetration] vs. [VLx (x/>) VL~x+.\lVL-\]are relatively insensitive to moderate changes in the values used for x and/or 3 , To circumvent these difficulties a standardized procedure was devised. By means of the identity
+
v~
+
Equation 3 can be transformed to the following expression: log DOP % penetration = Volume 7, Number 13, December 1973
1131
Taking the derivative with respect to V L -we ~ obtain
d log DOP % penetration dVI,-'
= hRX
():
[ V I ~ ( x' ?vL(x '
'"I
(6) Hence: by plotting
d log DOP % penetration
were developed by Edgewood Arsenal in the 1940's, and are composed of aerosol filtering fibers (Blue Bolivian crocidilite asbestos) and coarse matrix fibers (cotton floc, viscose, hemp, and esparto). The N series of six mats were developed by the Naval Research Laboratory, each consisting of a n 84.1/15.9 mixture of viscose and B.B. asbestos. These mats differ from one another in physical properties because of variations in the beating time of the asbestos fiber clumps. The remaining six mats were specially fabricated by the Naval Research Laboratory for aerosol filtration study and were composed entirely of their fiber designations.
Results and Discussion
vs. VLX*\
dVL-' we obtain straight lines (for the proper choice of x and 3 ) which cross the abscissa (i.e., ordinate equal to zero) when V L equals VL. This uniquely and systematically determines ~ L ' ~ + J 'from ) which can be obtained. Also, once a value for y is chosen (usually from theoretical considerations), this method uniquely determines x. In actual practice the derivative of Equation 6 is approximated by finite differences in the aerosol penetration and superficial linear velocity data. The functional relationship sought for these finite differences resides in the mean of the velocity range. Thus, Equation 6 is shown
v~
as A log DOP % penetration
Weight per unit area and mat thickness values were determined for each of the filter mat types. From these data physical properties, such as bulk density, fiber density (or weighted mean fiber density where mixtures of fibers were used), volume fiber fraction, and volume void fraction (porosity) were determined. The porosity t of the filter mat is conceived as e =
(bulk density-') -(fiber density-') (bulk density-')
since the reciprocal of the bulk density represented the specific volume (cm3/g) of the filter mat which included both the specific volume of the filter fibers and their interfiber space volumes. For ease of computation, Equation 9 was used in the form
AVL-' e = 1-
(7) and the LHS of Equation 7 is plotted vs. the x plus yth power of the mean velocity ( V L , , , , * +for ~ ) the appropriate velocity interval. For consistency this mean velocity is defined by the relationship (Wang, 1973):
where the V L , ,bracket , the finite velocity difference.
Equipment The equipment used to test the filtration characteristics of the filter mats was essentially the same DOP aerosol test apparatus as that described in the Part I paper except for the following changes: The aerosol was generated by a NRL-E3 generator; the DOP liquid temperature was set at 168°C to produce a n aerosol concentration of 80 pg DOP per liter of air; the newly generated 0.3 p diameter DOP was stored in a 8-gal reservior; and the aerosol penetration was measured with a NRL-EX smoke penetration meter. All experimental tests of the DOP penetration of filter mats were performed a t the Naval Research Laboratory, Washington, D.C.
Procedure The procedures for obtaining the operating temperature of 168"C, the aerosol concentration of 80 pg DOP per liter of air, and the pressure manometer and NRL penetrometer readings were the same as those described in the Part I paper. All sample flow velocities were established by means of a National Bureau of Standards calibrated orifice plate.
Materials The 16 filter mats studied represented a wide range of fiber type and composition. The filter mats Types 5-8 1132
Environmental Science & Technology
(9)
The fiber fraction volume
bulk density fiber density
(10)
( u ) was
0 =
1-€
(11)
The physical properties of the filter mats are shown in Table I. The pressure drop across unit thickness of the filter, resulting from forced airflow through the filter, was determined as a function of the superficial linear velocity for the various filter mats. Pressure drops were obtained in millimeters of water a t 25°C over the velocity range 7.2 to 141 cm/sec. Pressure drop per unit thickness values l P / h ( m m water per cm thickness) were shown to be a linear
Table I. Filter Mat Physical Properties Filter type
5 6 7 8A N11 N12 N 13 N 15 N 16 N17 Esparto Visc. 1.5D Visc. 3.OD A AA AAA
Wtlarea, g/cm?
0.0128 0.0214 0.0245 0.0205 0.0288 0.0247 0.0263 0.0265 0.0241 0.0257 0.0204 0.0274 0.0112 0.0180 0.0185 0.0069
TAPPI T-411 M e t h o d .
Thickness, ern"
0.048 0.086 0.089 0.100 0.112 0.080 0.089 0.122 0.102 0.117 0.068 0.095 0.050 0.071 0.075 0.028
Porosity
(vol.
Bulk denFiber sity, density g/crn? gjcrnzh'
Fiber fraction, u
void fraction), e
0.267 0.249 0.275 0.205 0.257 0.309 0.296 0.217 0.236 0.220 0.300 0.288 0.224 0.254 0.247 0.246
0.171 0.141 0.176 0.150 0.144 0.173 0.165 0.121 0.132 0.123 0.226 0.191 0.148 0.203 0.198 0.197
0.829 0.859 0.824 0.850 0.856 0.827 0.835 0.879 0.868 0.877 '0.774 0.809 0.852 0.797 0.802 0.803
From Hail (1965).
1.565~ 1.772c 1.561~ 1.369~ 1.787< 1.787c 1.787c 1.787c 1.787c 1.787c 1.33 1.51 1.51 1.25 1.25 1.25 c
Weighted m e a n .
function of the superficial linear velocity VL (cm/sec) in accordance with the general equation form
APIA
=
k,VL
in which the pressure drop AP is in dyn/cm2, the thickness X in cm, the fluid viscosity g in g/cm sec, the material permeability K in cm2, and the superficial linear velocity VL in cm/sec. To convert the Table I1 AP/X units of mm water/cm to centimeter gram sec (cgs) units, the values should be multiplied by 98.06. The aerosol filtration characteristics of the various filter mats were studied using a DOP aerosol with a mean diameter of 0.3 g and measuring the percent penetration of the DOP through the mats over the velocity range 7.2-141 cm/sec. These data are plotted in Figures 1 and 2, showing that for all filter mats the DOP % penetration vs. linear velocity shows a maximum. It can be seen that VL varies both in absolute value and discreteness depending upon the filter mat composition. By use of experimental data of DOP % penetration as a function of superficial linear velocity, values of Alog DOP % penetration/A V L - ~ were calculated for nine sequential velocity intervals. If we assign x = 1 and y = 2/3 (Dorman, 1966), Equation 7 can be shown as
AVL-"~
Coeff. of correlation, r
(12)
The values of the coefficient kl [units of ( m m water.sec)/cm2] for the 16 fibrous filter mats tested were obtained by regression analyses on the Hewlett-Packard Model 35 computer, assuming the greater dispersion of values to exist in AP/X, the y or dependent variable of Equation 11. The regression equations for the 16 filter mats, together with their correlation coefficients (Spiegel, 1961) which range from 0.9975 to 0.9999, are shown in Table 11. The form of the equations is in accord with Darcy's equation (Collins, 1961) for the flow of an incompressible fluid through a porous media
Alog DOP % p e n e t r a t i o n
Table II. Regression Analysis Equations for Pressure Drop-Velocity Relationship
= 1.5 M&'~c~,5'~- VLsi31(14)
Regression analyses of Y on X in the form Y = aX + b were made on the basis of Equation 14 for each of the filter mats, using Slog DOP % penetration/AVL-2 as the
Regression equation
Fibrous filter mat
0.9991 0.9994 0.9999 0.9999 0.9993 0.9999 0.9991 0.9992 0.9999 0.9999 0.9992 0.9992 0.9981 0.9995 0.9983 0.9975
APIA = 17.709 V L = 74.367 V L = 74.788 V L = 69.649 V L = 50.873 VL = 66.874 V L
Type 5 Type 6 Type 7 Type 8A
APIA AP/A APIA APIA APIA APIA APIA
N11 N12 N13 N15 N 16 N17
APIA APIA APIA APIA
Esparto Visc. 1.5D Visc. 3.OD
APIA
A AA AAA
APIA
APIA APIA
= 74.259 V L = 52.778 V L = 44.957 V L = 63.518 V L = 52.748 V L = 8.227 V L = 7.345 V L = 37.547 V L = 88.522 V L = 261.36 V L ~
~
Table 111. Regression Analysis Equations for Filter Penetration-Velocity Relationship Max. penetration velocity, V L ,cm/sec
Fibrous filter mat
Type TY Pe Type Type
Calculated
Regression equation"
5 6 7 8A
N11 N 12 N 13 N 15 N16 N17
Y = 0.004216 X Y = 0.035625 X Y = 0.063605 X Y = 0.029174 X Y = 0.045290 X Y = 0.039815 X Y = 0.044660 X
- 0.8647
= 0.025086 = 0.033846 = 0.007813 = 0.000571 = 0.000700 Y = 0.011810 Y = 0.013994 Y = 0.018768
- 5.9712
Y Y Y Y Y
Esparto Visc. 1.5D Visc. 3.OD A AA AAA
X X X X X X X X
24.4 18.8 22.0 33.0 22.5 9.2 7.2
- 4.7434
- 10.9803 - 9.9014
- 8.1299 - 1.6084 - 1.2070
Experimentalb
25.0 26.0 26.0 32.0 26.7 57.2 57.2
26.7 20.0 17.4 50.7 43.6 32.9 33.1 17.0
- 4.9718 - 0.9172 - 0.3936 - 0.3777 - 3.9834 - 4.7649 - 2.1153
26.7 20.5 21.0 44.0d 44.0d 32.0 35.3 16.0
= A log DOP%~p e n e t r a t lon A V L - ~3 = VL{,,,,5'3 O b t a i n e d b y graphical interpolation of experimental values. c N o equation possible since all DOP penetrations were 0.000%. d Mean of Dlateau f r o m 18-70 c m l s e c .
*
x
c -
1
>-
--
.. 1 -
i-
. Linear Velocity
cmrsec
~
.. '.
3:
:I
:.
,
7.
5;-
;.
-
Linear Veloclty c m / s e c
Figure 1 . DOP penetration as function of linear flow velocity for various filter mats
Figure 2. DOP penetration as function of linear flow velocity for various filter mats
Arrows indicate velocity for maximum penetration
Arrows indicate velocity for maximum penetration
Volume 7, Number 13, December 1973
1133
Table IV. Dorman Parameters for Aerosol Filter Mats Dorman parameter Diffusional Inertial I n , cm-1 sec
Filter type
TY Pe 5 Type 6 Type 7 Type 8A N 11 N12 N13 N15a N 16 N17
Esparto Visc. 1.5D Visc. 3.OD
RD,
cm-1 3 sec-? 3
Interception kr, cm-1
0.1
18.0
0.3 0.5 0.2 0.3 0.3 0.3
55.2 123.4 72.6 20.1 13.6
7.3 23.2 16.7 20.1 22.0 44.2 33.7
0.2 0.2 0.1 0.0 0.0 0.1 0.1 0.4
58.5 42.5 13.5 4.1 7.6 56.1 63.5 75.5
20.1 22.8 3.5 0.2 -0.4* 8.2 36.4 131.0
99.0
A AA AAA N o values calculable since DOP penetration was 0.000% a t all veloci-
*
t i e s tested. Negative value probably occurred owing t o a n artifact. However, since only t h r e e d a t a p o i n t s were calculable for t h e viscose 3.0 D m a t , t h e value is presented as obtained.
dependent variable and the mean of the velocity interval VL,,,) to the 513 power as the independent variable. Since the slope of the straight line curve was 1.5 hk* and the Y-axis intercept was -1.5 hkRVL5/3, the calculated value of V L was
‘L
=
(-intercept)3” slope
The calculated values of VL for each of the fibrous filter mats compared closely with the experimental values obtained from the maxima of the penetration vs. velocity plots of Figures 1 and 2. Table I11 shows the regression equations for the various filter mats together with comparative experimental and calculated VL values. Correlation coefficients for these regression equations ranged from 0.939-0.994. When we use VL values calculated from Equation 15, X values from Table I, and Equations 1, 2, and 14 for the conditions x = 1, and y = 213, the three Dorman parameters k*, kD, and kl were determined for the various fibrous filter mats and are shown in Table IV. It is of interest that the kR’s for all filters are generally much smaller than the k u or kl parameters, indicating relatively little contribution from inertial effects to the overall filtration of 0.3 p DOP aerosols over the velocity range test, with relatively high kt’s, in ed. High values of k ~ coupled the ratio range of 3-6 to 1 are characteristic of fibrous filter mats exhibiting excellent DOP aerosol filtration properties. When the ratios are outside this range, the filters exhibit either poor aerosol filtration or good aerosol filtration a t a n unacceptably high pressure drop. The experimental data show that the N15 filter mat showed the highest filtration of the 0.3-p DOP aerosol. Since the actual DOP penetration was below the minimal detectable limit of 0.001% under the conditions of test, and therefore recorded as O.OOO%, it was not possible to calculate Dorman parameters for the N15 filter from our set of equations. In general, the validity of Equations 1 and 7, together with the theoretical justification (Dorman, 1966) for choosing y = 213, provides an independent method of obtaining the value of X based upon the best straight line fit 1134
Environmental Science & Technology
for the relationship of Alog DOP % p e n e t r a t i o n / A V ~ - ~ / ~ as a function of VL!,,, to the X + 213 power. For our data, we believe this to be the case for X = 1. Experimental support for this choice can be derived from the fact that over the velocity range studied, the pressure drop to velocity relationship was that of Darcy’s equation for flow, shown in Equation 13, and for which the exponent on the linear velocity term is identically one. Theoretical support for the choice can be found in the work of Stechkina and coworkers (Stechkina, 1969) who found the inertial parameter to be a function of the superficial linear velocity to the first power. As a consequence of the excellent agreement between the calculated and experimental VL values, and the high correlation coefficients for the regression analyses equations, we propose a simplified analytical procedure to calculate the parameters VL, k*, kD, and k [ for fibrous filter mats from a minimum number of experimental penetration data. We feel that the use of more rigorous numerical techniques, such as interpolating polynominals based on Lagrangian ordinate or Newtonian divided difference expressions, is not warranted. The use of such techniques is partially dictated by the magnitudes of the differences AVL-2/3, which for our intervals are O(10-2). In short, the simplified procedure is adequate if the penetration data pairs are taken from regions where very large changes in log DOP YO penetration do not occur for small changes in linear velocity. It is obvious, however, t h a t the interval chosen should not include a n extremum. The procedural steps are detailed as follows: Determine experimentally the thickness ( A ) of the filter mat and the DOP 70penetration at three successive linear velocities, identifying the values as PI a t V L ~ ~P2, , a t VL,S,,and P3 a t V L , ~ , . Tabulate the values
and
identifying them as Alog DOP YO p e n e t r a t i o n / A V ~ - ~for VLim5 3 and plot in accordance with Equation 14. Determine the slope and intercept (ordinate = 0) of the resulting straight line curve. Calculate VLfrom Equation 15. Calculate k R from the slope of a plot of Equation 14 since the slope = 1.5 X k K . Calculate h~ from Equation 2 using x = 1 and y = 213, forming the equation
kD = 1.5 k R V L 5 l 3 An alternate method of calculation can be derived from the fact that the Y-axis intercept of Equation 14 shows -intercept
kD =
h
(17)
Choose either the value PI at V L , I , , PZa t V L , ~or, ,P3 a t V L ! ~insert ,, it into Equation 1 (for x = 1, y = 213) with the other known and determined parameters, and calculate
ki. This procedure utilizes only three pairs (PL, V L ,) ~of penetration data and represents the minimum number of pairs needed for use in plotting according to Equation 14.
Obviously greater confidence in the results is afforded if a t least one additional ( d o g DOP % penetration/ A V L - ~ / ~V, L ( ~ )point ~ / ~is )used in plotting Equation 14. This requires the use of at least one more pair (P,, V L , , , ) of penetration data.
Spiegel, M. R., “Statistics,” p 243, Schaum Pub., New York, X.Y., 1961. Stechkina, I. B., Kirsch, A. A,, Fuchs, N. A,, Ann. Occup. Hyg., 12,l (1969). Wang, C. s.,private communication (1973).
Literature Cited Collins, R. E., “Flow of Fluids through Porous Materials,” pp 10-11, Reinhold, Sew York, N.Y., 1961. Dorman, R. G., “Aerodynamic Capture of Particles,” Permagon Press, Oxford, 1960a. Dorman. R. G., “Aerosol Science,” Academic Press, Xew York, N.Y., 1966. Dorman, R. G., Air Water Pollut., 3,112 (1960b). Hall, A. J.: “The Standard Handbook of Textiles,” p 94, Chemical Pub., New York, N.Y.. 1966. Jonas, L. A., Lochboehler. C. M., Magee, W. S., Enuiron. Sci. Technol., 6,821-6 (1972).
Received for reciew March 21, 1973. Accepted August 9, 2973. Supplementary Material Available. Four tables of data on fibrous filter mats including composition, pressure drop vs. linear flow velocity, DOP 70 penetration vs. linear flow velocity, and DOP 70 penetration vs. velocity slopes will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (106 X 148 mm, 20X reduction, negative) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington D.C. 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number ES&T-73-1131.
Simple Piezoelectric Probe for Detection and Measurement of SO, Michael W. Frechette and James L. Faschingl Department of Chemistry, University of Rhode Island, Kingston; R. I. 02881
A new system for the detection and measurement of sulfur dioxide using a coated piezoelectric crystal has been designed and evaluated. The device is rugged, portable, inexpensive, and should lend itself easily to automation. The detector response was measured as a function of sample size, weight of substrate applied to the crystal, concentration of sulfur dioxide, and sample volume. Sulfur dioxide is often used as an index of general air pollution because of its widespread sources and occurrences. The burning of coal, petroleum, and wood, all of which contain a significant amount of sulfur, is the most widespread source. Most common methods of sulfur dioxide analysis are based on a color change of a solution or paste, although conductometric methods, such as that of Martin and Grant (1965), have been used with some success. The most widely used method is that of West and Gaeke (1956), a colorimetric determination with formaldehyde and acid bleached pararosaniline. Most of these methods give useful results but are troubled by chemical interferences, or lack the ruggedness and portability for “in the field” measurements. The piezoelectric detector developed by King (1964) has been shown to be a promising device for the measurement of gas compositions. The detector employs an electronic oscillator and a vibrating quartz crystal which, when coated with an appropriate compound (substrate), can selectively “sorb” the gaseous component of interest. The change in frequency of the quartz plate can be measured and directly related to the concentration of the gaseous analate. The change in frequency of the vibrating quartz crystal according to the Sauerbrey Equation (1959) is:
AF
F
where P F = frequency change, Hz F = frequency of the quartz plate, MHz A = area of coated electrode, cm2 T = thickness of quartz plate, cm PW = weight of applied coating or “sorbed” substance, g The uniqueness of the piezoelectric sensor is that it can be used both as an integrating weighing device or as a dynamic partition weighing device. King has developed a detector for hydrocarbons using a squalene coated crystal, an integrating detector for hydrogen sulfide using lead acetate and a moisture detector using sulfonated polystyrene as the substrate. To date, the work with coated piezoelectric analyzers has been centered on their use as gas chromatographic detectors-i.e., in a flowing gas stream. The authors have developed and investigated a “static” system for the detection and measurement of sulfur dioxide using a coated piezoelectric crystal.
Experimental Figure 1 shows the schematic block diagram of the piezoelectric sulfur dioxide detection system. The sample chamber is an Erlenmeyer flask modified with glass sidearms to permit gas flushing. A set of these flasks with varying sample volumes was constructed. The crystal probe consists of a 15 X 2 cm glass tube. At one end is located a 9 MHz AT cut quartz crystal obtained from International Crystal Corp., Fort Lee, Okla. The quartz wafer is plated with l/4-in. circular electrodes consisting of nickel
AW A
= -0.38X106X~X--
PROBE
To whom correspondence should be addressed.
Figure 1 . Block
diagram of “static” analyzer system
Volume 7, N u m b e r 13, December 1973 1135
