Multifilter Technique for Examination of the Size Distribution of the Natural Aerosol in the Submicrometer Size Range Sean A. Twomey” and Richard A. Zalabskyt Institute of Atmospheric Physics, University of Arizona, Tucson, Arizona 8572 1
A set of Nuclepore filterlflow-rate combinations, used in a transmission mode by measuring the particle concentrations emerging from each, provides data from which particle size distribution can be inferred. The procedure is described, and applications of the method to natural aerosol samples and to some artificial aerosols are presented. In recent years, greater attention has been given to the question of “typical” size distributions of natural aerosols, and demand has arisen for practical methods for obtaining size distributions in natural and artificial aerosols. Direct sampling and observation of particles individually, whether by optical or electron microscopy, is a time-consuming process, and, for submicrometer particles observable only by electron microscopy, possible evaporation of collected particles before and during observations poses a question which as yet is not fully resolved. Uncertainty about size distribution exists particularly in the submicrometer region-an inspection of the rather sparse literature suggests that even the position of the maximum of the size distribution of number concentration (i.e., the modal radius) is uncertain. It has been estimated to be as high as 0.1 pm cm) by some workers ( I ) , while others (2) have published data which indicate a modal radius closer to 0.001 pm cm), results differing in radius by 2 orders of magnitude (6 orders in mass). Even though the contrasting results just cited were obtained in different geographic regions, one can hardly conclude that there is general agreement concerning even the gross features and general shape of the particle size distribution in natural atmospheric aerosols, especially in the size range below 0.1 pm. The concept of employing multiple filters to obtain optical spectra is a very old one, and naturally analogous concepts have been introduced for obtaining size distributions in aerosols. A heterogeneous aerosol passing through any tube, hole, or array of such elements loses particles by diffusive and inertial effects, and, since the fraction lost depends on particle size, the process is analogous to optical filtering. The emerging particle concentration is given by
an equation which equally well would describe the energy transmitted by an optical filter with spectral transmission K ( x ) and spectrum f(x). In the case of an aerosol, x is any suitable measure of particle size (radius, log radius, etc.); f(x) is the size distribution function in that variable; and K ( x ) is the size-dependent transmission. The idea of measuring emerging concentrations nl, nz, . . . for different transmission functions K l ( x ) , K&), . . . and therefrom, by suitable f
mathematical manipulation, obtaining the size distribution goes back a t least to Pollak and Metnieks (3) and to Fuchs, Stechkina, and Starosselskii ( 4 ) ,who (in 1957 and 1962, respectively) discussed it in the specific context of diffusion batteries (ie., K&) would be the transmission of a diffusion battery, each value of i representing a concentration measurement made with some specific battery geometry and flow rate). Since diffusion battery transmission functions, and aerosol filter transmission generally, are far from the narrow-band filters which can be obtained for optical measurements, the problem of mathematically inverting the data set nl, n2, . . . , n, to obtain f(x) is much more difficult; in fact, in any strict sense, one cannot obtain a unique f(x)-there will be many which give essentially the same set of n’s, and one must in some way select a most acceptable solution from many possibilities. Such a solution will therefore be a somewhat distorted and smoothed-out version of the true f(x). In the application of diffusion batteries, neither Pollak nor Fuchs was apparently able successfully to extract size distributions; a few years later, one of the present authors made and inverted diffusion battery measurements (51,but the inversion scheme used gave somewhat unstable solutions which tended to exhibit spurious oscillations. Fuchs and Sutugin (6) later questioned the practicability of such inversion. The advent of Nuclepore filters and multiple hole structures introduced commercial products which were compact and possessed well-defined geometry, and the multiple-filter technique then became more attractive, practicable, and portable. The use of such devices as filters, combined with a suitable mathematical inversion scheme, provided a practicable sizing method which was especially useful in the size regions below 1pm. The purpose of this paper is to describe in t o t o experimental and numerical procedures which we have used to study atmospheric aerosols in relatively unpolluted locations in Arizona and Australia. Some of the results and the mathematical inversion scheme have already been published elsewhere. I t is hardly necessary to remark that there are other filtering devices and other mathematical inversion schemes which may work equally well. Principles of the Technique A sample of the aerosol being studied is passed through a Nuclepore filter (Nuclepore Corp., Pleasanton, CA 94566), and the concentration of particles after filtration, gl,is measured by a Pollak counter. The measurement is repeated for several filters by using several flow rates through each and obtaining thereby a set of concentrations gz,g3, . . . ,g M . By definition, those concentrations are related to the size distribution f(x) by
Present affiliation: University of Missouri, Rolla, MO.
0013-936X/81/0915-0177$01.00/0
@ 1981 American Chemical Society
gl =
Jm
K ( x ) f(x) dx
(2)
Volume 15, Number 2,February 1981 177
where f(x) is the number concentration distribution as a function of size x and K , ( x ) is the filter transmission during the ith measurement for particles of size x . ( x can be of any unique measure of size; we have chosen here to use logarithm of particle radius to cover the several decades in radius in a reasonably even way, using x: = log (radius) 4.) Since Nuclepore filters have a well-defined pore geometry, mathematical computations of filter transmission, allowing for diffusive and inertial capture, can be applied with more confidence than could be done for filters with more tortuous and variable geometries. Spurny, Lodge, Frank, and Sheesley (7) compared such theoretical calculations with experimentally determined values and concluded that there was close agreement. Extensive tabulations of Nuclepore transmissions have been published (8). When one is given an accurate counter to measure the g , concentrations and accurate values for the filter transmission functions, K , ( x ) , the possibilities for inference of f(x) via measurements of gi become promising. To obtain f(x), however, one needs a mathematical inversion, and, for experimental values of g, and smooth transmission functions, the inversion problem is unstable and no unique solution exists in an exact sense. Nevertheless, by means of suitable constraints, one can find solutions which are acceptable in that, if substituted back into the integral on the right side of eq 2, they give values g,’ which are very close to the measured g, values on the left. However, oscillatory features in any such solutions can be entirely spurious, and it is important to examine the question of resolution specifically for any inversion procedure before any features are accepted as real. We will return to that point in a later section. The algorithm which we used to invert eq 2 has been discussed elsewhere (9); for completeness, a brief description has been given in the Appendix.
+
Experimental Arrangement The arrangement shown in Figure 1was used. A large (200 L ) air sample was brought into an aluminized mylar bag which acted as a storage reservoir (A) from which smaller samples were passed into the Pollak counter (C) via a multiple-filter holder (B), which could hold five Nuclepore pads. However, one holder was left empty to allow several “blank” or unfiltered measurements to be made during the sequence of filtered measurements. Table I shows the raw data of a typical set of measurements; it will be seen that the measured concentrations after filtration ranged over approximately two decades in particle number concentration. Figure 2 shows the set of filter transmission curves applicable to these measure200 I Mylar B a g
ments, computed from the known filter geometries and meastued flow rates by employing the same equations as were used by Spurny et al. (loc. cit.). Inspection of Figure 2 suggests that a useful separation of sizes was being produced from 0.1 pm down almost to 0.001 pm when that set of filters was used. (Since a change in flow rate produces a change in transmission function for a given Nuclepore, it is more logical to use the Table 1. Typical Set of Filter Data and Volumetric Flow Rates Used in a Set of Measurements measurement
no. (1)
liltel
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
A A A A B B B B
C C C C D D D D
volumetrlc flow 0, cm3 S-1
tlme since reserv oi r filled, min
Pollak count 91, cm-3
171.6 85.8 42.9 24.2 171.6 85.8 42.9 24.2 171.6 85.8 42.9 24.2 171.6 85.8 42.9 24.2
1 6 11 17 2 7 12 19 3 8 13 21 4 9 14 23
9866 7849 6074 4527 9044 6793 4763 3209 6291 4176 2571 1592 983 622 235 118
0 5 10 15 25
11877 10268 9288 8571 6247
Unfiltered
filter data
A
pore diam (pm) pore density (cm-2) thickness (Pm)
.E
0.95 2X
C
B
2.7
lo7
11
1.8X
D
7.0
lo6
10
1.0 X
4.5
lo5
7.5
3.7 X 8.0
.6
.Y)
E
i .4 t
Pollak Counter and Flowmeter
.2
F---@+Sampling Pump
n ”
10’8
Figure 1. Experimental arrangement used to obtain aerosol size distributions with the Nuclepore filters (schematic). 178
Environmental Science & Technology
10”
IO*
IO’*
10-4
10.3
r(crn)
Figure 2. A typical set of filter transmission curves.
lo5
word "filter" to denote a particular Nuclepore/flow-rate combination, and we shall follow that usage from here on.) The connecting lines and sampling tube were of stainless steel, and their lengths were kept as short as possible. The Nuclepore pads were clamped between O-rings in the filter holder which were entered by, and exited to, stainless-steel manifolds, to ensure (so far as possible) identical flow paths. The total length of run was -1 m. While it is difficult to estimate the accuracy of these measurements, their reproducibility was very good: typically better than f0.005 for Pollak counter extinction of the order of 0.2, somewhat larger (on a relative basis) for very small extinctions of the order of 0.02. Storage Losses Equation 2 applies only when f(x) does not change while the measurements of g,, g2, . . . ,gM are being made. In fact it does, since the completion of 20 or more measurements involves a time lapse of at least 20 min, and during that time an appreciable loss in particles occurs (see Figure 3). Losses of this kind are certain to be size dependent, affecting the smallest particles most, so both the magnitude and shape of f(x) must have varied with time. We attempt to minimize the effects by taking first those measurements in which the smallest, most mobile particles were transmitted with the greatest efficiency. This was done by ordering measurements so that the filter which had a transmission cutoff at the smallest size was used first, and the filter for which the transmission cutoff radius was greatest was used last. In spite of this procedure and the reduction of the postpressurization waiting time for the counter to 10 s, as compared with Pollak's original recommendation of 1 min (it having been first verified that 10 s was the shortest waiting period which did not alter the reading), a considerable storage loss still occurred, and it was clearly nedssary to take it into account before any useful size-distribution inferences could be made. When different decay curves were compared, it was noted that the shape of the curves was not greatly influenced by the initial concentration (see Figure 4) , suggesting that coagulation was not the dominant process for the decay in numbers (a conclusion that was supported by detailed calculations of particle coagulation, using the size distributors eventually derived by inversion; the results of one such calculation are included in Figure 4 for comparison). The most likely cause for the decay observed was believed to be diffusion to the walls of the mylar storage bag. Losses as large as those shown in Figures 3-4 could not have been produced if the air sample in the bag had been totally quiescent, since diffusion over a distance of 1 25 cm in lo3 s would imply a diffusion coefficient of -0.3 cm2 s-l, which is larger than that of most molecules. Evidently convective currents within the bag are involved in the transport of particles to the wall. The intensity of convective mixing may sometimes change with time, but, if one can assume constant geometry and constant mixing, the concentration for size x will be represented by a formula of the form
-
+
f(x,t)/f(x,O) = ale-blD(x)t u2e-bzD(x)t + . . .
5t I
0
Figure 3. Decay of
1 5
IO
15 20 T (rnin)
25
35
30
particle concentration with storage time in the mylar
bag.
.21 .I
O'
b'
Ib
Ib
2;
2'5
3b
: 3
T(rnin1 Figure 4. Decay for different initial particle concentrations. The curve labeled "Coagulative Decay" was calculated for the size distribution obtained upon inversion. Initial concentrations as indicated on the curves.
appreciable loss has occurred, the terms beyond the first in such series rapidly become negligible (note the factors m2), and one can approximate the variation with time of particle concentration by means of a single exponential term. When this further approximation is valid, the concentration of particles with diffusion coefficient D follows the relationship In n/no Dt, and, for a heterogeneous population of particles, the total concentration in the storage bag at time ti can be written
(3)
The diffusion coefficient D is, of course, size-dependent, while the parameters ai and b, depend on the container geometry. For example, with a spherical container of radius r and under quiescent conditions, the formula would be (10)
so that, in this case, a,,, = 6 / ( m 2 r 2 )b, ; = (m2.sr2)/r2.Whatever the geometry, the same general form applies, only the actual values of ul, u2, . . . and b l , bz, . . . are altered. Once
7 being an unknown parameter depending on the geometry and convective intensity and f(x) being the size distribution function at t = 0. In eq 1,&(x) represented the transmission of the ith filter; if the measurement through that filter was carried out at time t i , then, in the presence of a decay process that is size-dependent via the diffusion coefficient, the result of the ith measurement can be written
Volume 15, Number 2, February 1981 179
With this simplification, the problem of accounting for diffusion losses reduces to that of obtaining a value for 7. In quiescent air, 7 could be calculated, but, since one is involved with convection, only an experimental determination of 7 is of any value. There is no guarantee that 7 will remain constant from experiment to experiment, and a determination of 7 during each experiment was the procedure eventually adopted. (Note that the influence of 7 is felt primarily by the smallest particles; the measurements in which these were appreciably transmitted were made first. For larger t,, the filters chosen had Ki values that were very small or zero a t small sizes.) If 17 is known, the factor e - D ( x ) tbecomes i for practical purposes part of the kernel K , ( x ) , and the inversion mathematics are otherwise unaffected. The procedure for inferring 17 was to take a set of values of 7 and carry out a complete inversion for each. The value of 17 giving the best agreement (in a root mean square (rms) sense) between calculated (g,’) and measured (gi)values was adopted as the best estimate for 7, and the corresponding solution was taken as optimum. Quite appreciable changes in 7 were found to be needed to change that “optimum” solution significantly (see Figure 5), and so the precise selection of 7 was not critical. It was nevertheless essential to take the losses into account; by so doing, the “misfit” between measured and calculated values for g was reduced to below 10% rms, compared to -30-40% when decay during storage was ignored. The values of 7 varied by about a factor of 2 either way from experiment to experiment, its typical range of value being 4-8 cm-2. Resolution As mentioned earlier, it is important to test resolution, and to do so for the system as a whole (which includes the particular filters used, as well as the mathematical inversion process itself). Such a test is easily carried out if one notes that an idealized monodisperse distribution of particles of size 4 would give for gl, g2, . . . , gi),i the values K1(4),K z ( [ ) ., . . , K d t ) , which for any 6 can immediately be written down from tabulations or graphs of filter transmission. If now that set of numbers is subjected to the inversion procedure, a perfect (nonexistent) inversion process would return a delta function at x = or, when a finite grid of x values is used, zeros a t all
,:I ‘0250
, , , , ,
,
grid values except a t x = 4. This test was carried out for a number of values (4 = 1,1.7,2,2.7,and 3, which are equivalent t o r = 0.001,0.005,0.01,0.05, and 0.1 pm), and the results are shown in Figure 6, where the “perfect” solutions are the five sharply peaked triangles, while the wider, flatter distributions are the result of inversion applied to the “data”, K I ( [ ) , K2(4), . . . , Ki),i([),using the same set of K, as applied to our real measurements. It is apparent that the resolution of the sygtem was about one-fifth of a decade in radius in the region around O.Ol-km radius, worsening (to about two-fifths) around 0.1 pm. Although the Nuclepore filters show a band-pass type of transmission (see Figure 2), the kinds of size distributions which were found in our observation were such that very little influence was being exerted by the large-.particle (inertial) end of the transmission curves-there is more than a two-decade interval in radius between the half-transmission values, and, in most conditions, the number concentration of the filtered particles will be dominated completely by the smaller end of the transmitted particle spectrum e-qd*Xi(x) f(z), and any change in f(x) or error in K L ( x for ) large sizes is of little consequence. Thus it is diffusion that is important under the actual experimental conditions, and the adequacy of the description of inertial removal processes in the basic formulas is virtually irrelevant; for the same reasons one should discount inversion solutions in the region (r > 0.2 pm) where only inertial removal processes respond to a change in particle size. Relation to Other Sizing Methods Nuclepore filters have been applied to the inference of aerosol size distribution by Melo and Phillips (11),but in that work it was the mass captured by different filters that was measured; in our application, the number transmitted through the filters is the quantity that is measured. The Melo-Phillips technique is therefore weighted in favor of larger particles and primarily involves inertial deposition (i.e., separation of particles by Stokes number) whereas our technique gives greatest weight to small particles and relies predominantly on diffusive removal &e., separation of particles by P6clet number). The basis of the Whitby-Clark (12) technique and of the technique described by Hoppel (13) is separation of particles by electrical mobility. Since mobility is proportional to diffusion coefficient for a singly charged particle, separation by means of diffusion coefficient or mobility is fundamentally equivalent, except for the effects of multiply charged or uncharged particles, which give rise to possible ambiguities in electrical mobility techniques and must be corrected for in some way. The Nuclepore technique
, , , , , , ,
200 400 600 800 1000 7)x 60 (cm-* 1
Variation of the residual E , = [~(gi’-gJ2/~gi2]’’* (which measure the degree of agreement between measurements gi and the solution, gi’ being the result of inserting the solution into the integral in eq 2. For a perfect inversion, the residual would vanish.
r
Figure 5.
180
Environmental Science & Technology
Illustration of the extent to which a monodisperse size distribution could be retrieved. The broader, flatter distributions are those retrieved by inversion. Figure 6.
’
(and also Hoppel's) depends on the Pollak counter calibration to convert the fundamental measurement (extinction) to particle numbers; the Whitby-Liu-Clark technique is based on measurements of current carried by charged particles. Losses of particles during storage introduced an additional uncertainty into our present technique; this is not perhaps a fundamental difficulty, being occasioned by the use of a single Pollak counter to make upward of 20 successive measurements. It is nonetheless a disadvantage, especially in that it increases the uncertanity associated with the effective kernel functions in the basic integral equation.
z Q
-1.6
ta
Results Our primary interest was the natural atmospheric aerosol in the free atmosphere, and we did not therefore seek out heavily polluted situations. The results are set out in Figures 8-12 and briefly discussed, according to location, as follows. Tucson, Arizona. Size distributions obtained under fairweather conditions in a somewhat polluted urban environment (samples taken on the roof of a building on the campus of the University of Arizona in Tucson) are shown in Figure 8a. Several distributions taken when the air was filled with dust raised by strong winds are shown in Figure 8b. Although visibility was markedly reduced during these dust episodes, it is interesting to note that the total number of particles did not increase-in fact, over all of our observations, the total number averaged 18 000 ~ m in- blown-dust ~ episodes, compared to 29 500 cm-3 at other times. While the modal radius was essentially unaltered, the distributions in dust episodes tended to contain significantly fewer particles between 0.01 and 0.1 pm than was otherwise the case. These results suggest that the wind-raised dust consists predominantly of relatively few large particles, which modify visibility and mass loading without contributing much to total concentration, which indeed was reduced overall, perhaps because of enhanced diffusive losses of the finer, more mobile particles in the presence of additional particles of larger sizes. Southeastern Australia. Size distributions obtained in southeastern Australia in modified polar maritime air are shown in Figure 9. These samples were taken a t a rural location with no known local pollution sources and regional pollution confined to that occasioned by habitation and agriculture. North Atlantic. Size distributions measured aboard ship in the North Atlantic in May 1977 are shown in Figure 10. In this case, the sampling line was long and the quality of the measurements questionable. No storage bag was available, so
-
I-
2 -1.4.
w
0
z
0 0 -1.2
Electrical Influences In handling a Nuclepore filter, it becomes immediately evident that these filters become highly charged electrically. T o determine whether filter transmissions were influenced seriously by the charge state of the aerosol, we carried out the following experiment. Ambient aerosol was stored in an aluminized mylar bag, and the total particle concentration was monitored as a function of time. After some time, an americium-241 a source (200 pCi) was placed in the flow line between the bag and the particle monitor. The a source was of sufficient strength to guarantee that charge equilibrium was attained during the residence time of the samples in the source holder. The concentration in the bag was changing with time in a (typical) somewhat irregular way, but, as Figure 7 shows, any change due to charge effects was not detectable against that background fluctuation and, to that extent at least, could be discounted; quite clearly any influence of electric charge is less than the uncertainties resulting from particle storage losses. Similar conclusions were reached by Liu and Lee (14) and Smith et al. (15).
i
- 1.8
-
TIME (minutes) Figure 7. Influence of electrical effects. An ionizing source was introduced from t = 22 to t = 42 min. 1
0
IO"
~,
.
,~ , , , ,,,
, , , ,,
IO5
, ,
10-5
r
(cm)
1
(cm)
I
, -,
IO'
Figure 8. (a) Tucson size distributions (clear days). (b) Tucson size distributions (during blown-dust episodes)
Volume 15, Number 2, February 1981
181
S E AUSTRALIA WXIFIED MARITIME
Io3
dN d log r
102
IO IO"
I0'4
r (cm)
r (cm)
Figure 9. Southeastern Australian size distributions in modified maritime : 5 air at a clean rural site.
A[ d log r
I
'4
Figure 10. North Atlantic maritime samples, May 1977.
r (em)
Flgure 11. Size distributions in artificial photochemical aerosol (see text).
samples were taken from outside without storage, subject therefore to natural concentration fluctuations. Comparison of Size Distributions-Continental Locations. Size distributions measured at the two different continental locations (Arizona and southeastern Australia, Figures 8 and 9) show marked similarities. In both sets of samples, the modal radii vary from ca. 0.006 to 0.015 pm. A Junge distribution described quite well the general shape of these distributions down to -0.03-pm radius, but a slower rate of increase was exhibited from there down to the peaks of the 182
O
Environmental Science & Technology
r (crn) Figure 12. (a)Comparison with Whitby instrument (atmospheric aerosol). (b) Comparison with Whitby instrument (artificial aerosol).
distributions. Below the modal radius ( 4 . 0 1 pm), the inferred distributions fell rapidly (at about the fastest rate that could be resolved). Few particles with radii less than 0.005 pm were inferred to be present in either location. A significant feature of these distributions was this apparent absence of significant amounts of aerosol material less than 0.005 pm in radius. The reality of this result depends, of course, on the ability of the Pollak counter to detect particles in that range of size. The work of Nolan and O'Toole (16)and of Pedder (17) suggests that the Pollak counter can detect particles down to cm, so that an instrumental detection threshold would not appear to be capable of influencing the results seriously. For appreciable loss to occur within the counter in the 10-s waiting period in quiescent air, the particle diffusion coefficient would have to be on the order of 0.1 cm2 s-l, which is much larger than even that of particles as small as 0.001-pm radius. Nevertheless, it seemed important to verify that the behavior of our inferred size distribution functions for radii
