Atmospheric Environment Vol. 16, No. 2, pp. 293-300, 1982 OlW-6981/82/020293-08 SO3.00/0

Printed in Great Britain. 0 1981 Pergsmon Press Ltd.

A COMPARISON OF OPTICAL AND AERODYNAMIC AEROSOL SIZES: THE EFFECTS OF INHOMOGENEOUS

PARTICLES

LEE HARRISON

College of Engineering, FC-05, University of Washington, Seattle, WA 98195, U.S.A.

and

HALSTEAD HARRISON

Department of Atmospheric Sciences, AK-40, University of Washington, Seattle, WA 98195, U.S.A.

(First received 1 December 1980 and infinalform 12 February 1981)

Abstract-We have performed an intercalibration experiment with two common aerosol size measuring instruments: a single particle optical counter and an aerodynamic dichotomous separator. We present results of two test aerosols: uniform spherical particles of a polyethylene glycol, and irregular non-spherical particles of sodium chloride. The two aerosols display very different apparent sixes on the two instruments, which we attribute both to shape influenced aerodynamic drag and to optical inhomogeneities of the salt oarticles. We discuss our results with the aid of Mie scattering calculations for radially inhomogeneous particles. For irregular particles, the inference of conversely, involves uncertainties of factors of two.

aerodynamic sixes from optical measurem&ts, or

1. INTRODUCTION

A variety of methods are commonly used to measure particle size distributions of aerosols, including elec- tron microscopy, electrostatic mobility, light scattering, and aerodynamic inertial separation. In general, electron microscopy is the primary standard, and other methods are calibrated to yield equivalent radii for particular test aerosols, usually spherical homogeneous particles. The several secondary methods infer differences sizes when used on other aerosols. For this reason the secondary methods are usually referred to as producing “optical radii”, or “aerodynamic radii”, for example, to make clear that the sizes referred to may not be geometric. This uncertainty is not always a problem; when the underly- ing concern of a measurement is with lung deposition, for example, then aerodynamic radii measured by inertial separators are sensible and appropriate. For other experiments, however, it may be desirable to compare the results of different sizing methods, or to infer one type of semi-empirical size distribution from another. In this paper we present a comparison of the optical and aerodynamic behavior of two unlike aerosols, measured with two widely used devices, a single particle optical counter* equipped with a multi- channel pulse-amplitude discriminatort and an aero- dynamic dichotomous separator. $

In the following sections we discuss experimental procedures for preparing sodium chloride and Car-

* Royce Model No 200, Royce Inst., Menlo Park, CA, U.S.A.

t Custom built in this laboratory. Instruments Model 240, Carmel Valley, CA,

bowax polydisperse test aerosols and for measuring their transmissions through an aerodynamic dicho- tomous separator, as functions of apparent optical size. We discuss our results in terms of optical scatter- ing by spherically symmetrical but radially inhomo- geneous particles and in terms of the Stokes’ scaling laws to permit estimation of aerodynamic radii from the transmission curve of a single stage impactor. We conclude with a discussion of the inaccuracies and limitations associated with inferences of aerodynamic radii from optical measurements.

2. EXPERIMENTAL PROCEDURES

Sodium chloride test aerosol

A test aerosol of irregular salt particles was generated by passing filtered humidified air through a drawn glass capillary into a 12Y solution of NaCl in deionized and filtered H,O. The rest&g aerosol was dried to less than 20% relaiive humidity by adding filtered dry air, and was passed through the charge neutralizer from a Bergland-Liu single particle generators (Fig. 1.). The resulting aerosol concentration and size distribution could be varied by controlling the air pressure to the capillary. There appear to be two distinct particle generating mechanisms; the size distribution (Fig. 2) is bimodal by mass with one maximum at a radius of 0.4pm and the other at approx. 1.1 pm. The relative contributions of the two modes depend on the pressure and surface tension; low pressures favor the large particles, and high pressures increase the relative concentration of the small ones. We ran the bubbler at 5 psi (34 kPa). The large particle mode seems to depend in some way on the surface tension of the solution. The addition of small amounts of polyethylene glycol or sodium lauryl palmitate suppresses the large particle mode; this addition was not used for the sodium chloride tests.

8 Thermosystems Model 3054 charge neutralizer from Thermosystems Inst. St. Paul, MN, U.S.A.

293

294 LEE HARRISON and HALSTEAD HARRISON

t !t E E c’

The effects of inhomogeneous particles 295

1 I 1 I 1 1

176 .223 ,261 354 445 ,506 ,701 ,000 I 12 I.41 1.76 2.23

mdius, pm

Fig. 2. Volume (third moment) distributions for the two test aerosols as measured by the Royce optical particle counter and assuming spherical particles.

The resulting aerosol size distributions were then measured using the Royce optical counter on single particles, with sixes inferred from pulse amplitudes, compared to calibrations with polyvinyl latex spheres. Total sample flow through the optical counter was 300cm3 min- r, but to reduce sedimen- tation losses a greater flow was passed through the external manifold with diversion to a vent just upstream of the counter, and a recirculating filtered sheath air was added as a modification within the counter (Fig. 1) (Willeke and Liu, 1976).

For measuring the transmissions of the dichotomous separator with NaCl aerosols, we took samples downstream of the supporting mesh for a fine particle filter, but without the filter in place. This mesh produces significant losses which must be corrected for by separate transmission measurements. Both this transmission and that of the dicho- tomous separator itself were made by alternately measuring

the distributions of optical sixes in excess air vented just upstream of the test object, and then in the flow downstream, each averaged over 10min.

The transmission of the fine particle exhaust as a function of optical size was determined by dividing the downstream concentration in each optical size class by the average of the two upstream concentrations measured just before and just after (Table 1). The transmission of the filter support mesh was measured separately (Table 2). Tbe transmission of the aerodynamic stage alone is the total trnasmission divided by that of the filter support mesh (Fig. 3).

The Carbowax text aerosol

The principal problem we faced in finding a suitable calibration aerosol for the dichotomous separator was to obtain a reasonable concentration of particles for the sizes larger than 1 pm. All of the organic solutions we tested gave

Table 1. Transmission fraction as a function of optical radius, NaCI test results

Optical radius (pm)

Run No. 0.178 0.223 0.281 0.354 0.445 0.506 0.701 0.800 1.12 1.41 1.78 2.23

1 0.895 2 0.857 3 0.864 4 0.872 5 0.862 6 0.890

X 0.873 0” 0.014

0.876 0.825 0.774 0.705 0.586 0.467 0.372 0.263 0.150 0.084 0.823 0.779 0.739 0.640 0.529 0.418 0.330 0.243 0.158 0.114 0.824 0.790 0.738 0.654 0.542 0.440 0.333 0.245 0.149 0.090 0.847 0.798 0.743 0.652 0.554 0.441 0.338 0.245 0.164 0.133 0.824 0.787 0.741 0.649 0.547 0.445 0.355 0.263 0.168 0.107 0.856 0.814 0.752 0.674 0.560 0.446 0.359 0.260 0.142 0.103

0.841 0.799 0.747 0.662 0.553 0.443 0.348 0.253 0.155 0.105 0.019 0.016 0.013 0.022 0.018 0.014 0.015 0.009 0.009 0.016

0.070 0.092 0.114 0.071

*

0.060

0.069 0.033

l Indicates insufficient counts in this channel to permit a meaningful estimation of transmission.

Table 2. Filter support correction factor measured at 16Pmin-’ flow

Optical radius (pm)

Run No. 0.178 0.223 0.281 0.354 0.445 0.506 0.701 0.800 1.12 1.41 1.78 2.23

1 1.045 1.067 1.093 1.117 1.202 1.267 1.398 1.595 1.789 2.516 3.537 4.290 2 1.076 1.081 1.105 1.136 1.192 1.296 1.453 1.604 1.936 2.368 * * 3 1.071 1.067 1.105 1.137 1.181 1.272 1.352 1.486 1.845 2.224 3.386 3.952 4 1.071 1.077 1.111 1.137 1.196 1.303 1.390 1.527 1.713 2.361 2.912 3.861

X 1.066 1.072 1.104 1.132 1.192 1.284 1.398 1.553 1.821 2.367 3.278 4.036 0. 0.012 0.007 0.007 0.009 0.008 0.015 0.036 0.049 0.081 0.103 0.266 0.184

* Indicates insufficient counts in this channel to permit a meaningful estimation of transmission.

296 LEE HARRISON and HALSTEAD HARRISON

lo----‘----.-__,__ Carbowax

T I T

1 a-

; Y g 6

z 2 G4- :

z

2-

O_ 178 223 281 354 445 506 701 800 I 12 14, I78 2 23

Fig. 3. Fracttonal transmtssion out of the fine particle exhaust of the Sterra model 240 dichotomous separator as a function of optical size for the two test aerosols.

more unimodal size distributions than did our aqueous salt solutions. We finally settled upon a 50% solution of Car- bowax 600 in 2-propanol. Carbowax 600 is a proprietary polyethylene glycol, available from Fischer Scientific Co., Chem Mfg. Div., Fairtown, NJ 07410, U.S.A. Other com- monly used materials for producing uniformly spherical test aerosols include di-octyl phthalate and polyvinyl latex. The aerosol generating apparatus was unmodified, except for the substitution of the different aerosol generating solution and of propanol for water in the “pre-humidifier”.

The size distribution of our Carbowax test aerosol is shown in Fig. 2. The relative scarcity of the larger particles made it necessary for test runs to be l-h long, to obtain reasonable counting statistics. For this reason, we replaced the dicho- tomous separator’s lossy filter-support mesh with a custom fitting which eliminated the losses and made their correction unnecessary. The results of four test runs using Carbowax test aerosols are given in Table 3 and Fig. 3.

3. DISCUSSION

Our Carbowax transmission data are consistent with those reported by others for the same model of dichotomous separator with a similar organic test aerosol of di-octyl phthalate (Loo et al., 1979). For comparison we show this curve also on Fig. 3.

It seems likely to us that the fairly gross discrepancy between the transmissions displayed by the NaCl and the Carbowax aerosols results from two effects.

(1) The NaCl particles are neither spherical nor

uniform, and so the total scattered light phase function (angular distribution of scattered light) depends on the shape of the particles and on their orientation at the time they go through the light beam.

(2) The aerodynamic properties of a NaCl aerosol depend on the shape of the particle and the void fraction.

Natural salt aerosols at humidities below their de- liquescence points will exhibit both behaviors, and the discrepancy between our two sets is a warning that it may be very difficult to interpret results of either optical scattering or aerodynamic separator exper- iments performed on real atmospheric aerosols in terms of true mass or geometric size.

Figure 4 shows electron micrographs of salt particles of approx. 1.6pm radius, made by evaporation from solution droplets. The principal field shows a col- lection of particles made from pure NaCl, and the insert shows an enlarged micrograph of a single particle evaporated from sea water. Clearly, irregula- rities both of fuzzy edges and of hollow cores are possible. We have therefore attempted to estimate the effects of such irregularities upon determinations of optical and aerodynamic sizes by considering the scattering behavior of spherically symmetrical, but radially inhomogeneous particles, and their aerody- namic scaling.

Table 3. Transmission fraction as a function of optical radius, Carbowax test results

Optical radius (pm)

Run No. 0.178 0.223 0.281 0.354 0.445 0.506 0.701 0.800 1.12 1.41 1.78

1 1.00 1.00 0.993 0.935 0.883 0.801 0.756 0.742 0.570 0.0 0.0 2 0.991 0.993 0.994 0.970 0.966 0.930 0.884 0.815 0.592 0.179 0.0 3 0.996 0.990 0.985 0.972 0.965 0.934 0.872 0.808 0.589 0.132 0.09 4 0.994 0.997 0.991 0.976 0.968 0.927 0.880 0.823 0.590 0.95 0.07

X 0.991 0.995 0.991 0.963 0.945 0.898 0.848 0.797 0.585 0.102 0.08

0” 0.002 0.004 0.004 0.016 0.036 0.056 0.053 0.032 0.009 0.066 0.04

The effects of inhomogeneous particles 291

Fig. 4. The main field of this scanning electron micrograph shows a collection of 1.6 pm radius NaCl particles produced by the evaporation of solution droplets. The enlarged inset shows a particle of similar size made by the evaporation of seawater.

Optical scattering by inhomogeneous aerosol particles

The calculation of the optics of irregular fine particles is very difficult (Kerker, 1969). Moreover, since we do not know the orientation of any particle in the optical single particle counter, we are limited to an attempt to model the scattering of irregular particles averaged over all orientation angles. This is equivalent to computing the scattering from a “representative” inhomogeneous particle with spherical symmetry, an approximation required in any event by classical Mie theory (Kerker, 1969).

The problem of calculating the scattering ampli- tudes and phases from spherically symmetrical, layered “onion shells” of differing indices of refraction has been outlined by Kerker (1969). We have modified an algorithm originally written for a three shelled onion by Higgins and Bray of the Boeing Scientific Research Laboratories. This algorithm uses an upwards re- cursion formula for computing appropriate Ricatti-Bessel functions, which is valid for size par- ameters (2nr/A) less than or equal to SO, a condition easily met by all the particles we considered. A CDC 6400 computer with 60 bit precision was em- ployed for all computations.

Guided by the photographs of Fig. 4 we have examined the theoretical optical scattering of three

classes of spherically symmetric two-shelled onions. The first attempts to model the hollow aggregate of the insert in Fig. 4 by a family of hollow shells having cores of unit index of refraction out to 4/lOths the exterior radii (type A, Fig. 4), inside mantles of NaCl with index 1.55 x 10e9i. The second two model the rough ex- teriors of irregular NaCl particles by assuming outer layers of index 1.33 x 10e9i. The outer layer thickness of the first of these two particles was 2/lOths (type B) and the second was 4/lOths (type C) of the external radii. This index corresponds to a rough edge of NaCl with 45 7; void space (or, alternatively but not to our purposes, a layer of water).

The optical scattering amplitudes and phase func- tions for each of our synthetic, layered particles were computed for 71 sizes with equal logarithmic intervals between a radius of 0.15 and 6.5pm. The phase functions were then weighted by the angular accep- tance function of the Royce mode1 220, and integrated over the acceptance angles. The product of the lamp brightness and photomultiplier sensitivity yields a rather sharply peaked response centered on 0.55pm (Sverdrup, 1977). Since the scattering is dependent on the size paramater (2ar/A), we can integrate over size in a way that is equivalent to integrating over wavelength, providing the refractive index is independent of 1. This is a good assumption for the narrow range of wave-

298 LEE HARRISON and HALSTEAD HARRIsoh

lengths being considered, and it saves much computer mission curve probably result from irregularities of

time. shape and orientation, which we do not model.

To model the polyvinyl latex aerosol used for calibrating the optical counter we performed similar computations also for spherically homogeneous par- ticles with the index of refraction of latex, 1.60. Then to obtain the optical sizes of the synthetic layered par- ticles we compared their acceptance-angle averaged scattering amplitudes with the similar amplitudes of the latex particles of known radii, by a linear interpolation.

Aerodynamic scaling

Real irregular aerosols

For each inhomogeneous particle, an equivalent aerodynamic size can be computed from the definition of the Stokes number (Pavlik and Willeke, 1978)

p VCD’

s=-?

where p = particle, density, V = jet velocity, C = Cunningham slip factor, D = particle diameter, p = fluid viscosity, IV= jet diameter.

For differing particles passing through an aerody- namic separator, with constant flow conditions, trajec- tories are similar for equal Stokes numbers. Since all the variables remain constant except p and D, we can define the equivalent aerodynamic radii very simply by

where

R, = R, J’pciis. *

R, is the defined aerodynamic radius,

R, is the geometric radius, pr is the density of the calibration aerosols, and

p, is the average density of the inhomogeneous

To estimate the total variance of contributions of shape and size irregularities to the flattening of the experimental transmission curve for NaCl in Fig. 3, we have explored various non-linear regression models to produce this curve from the calibration for uniform

particles, smeared by a Gaussian filter. This is equiv- alent to assuming that each optical size class is com- posed of a Gaussian distribution of aerodynamic sizes. These exercises produced multiple correlations as high as 0.97 but must be interpreted cautiously, owing to the very few genuinely independent degrees of freedom contained in the bland transmission curves. A serial correlation analysis revealed that between three and four degrees are justified, which supports the regression’s determination of a best estimate for the width of a Gaussian filter as 2.8 + 1.1 channels, with zero offset of the filter from its mean. Since each channel along the logarithmic abscissa of Fig. 3 differs from its adjacent channel by a size ratio of 1.26, in linear terms the Gaussian width corresponds to a factor of 1.26 r-s*t.I or 1.5 -+ 2.5, or approx. 2. That is. inferences of aerodynamic sizes from optical scattering measurements involve uncertainties of factors of two, for irregular particles. The inverse inference of optical sizes from aerodynamic measurements is also un- certain by factors of two, providing optical and aerodynamic radii are linearly proportional to one another. This is true for the synthetic onions we modeled. but the present experiment is unable to resolve this point for the real NaCl aerosols.

aerosols. By these precedures and scaling assumptions, and

for the three classes of synthetic aerosols we show in Fig. 5(a) the ratios of aerodynamic to optical radii plotted against exterior geometric radii, and in Fig. 5(b) we show the same ratios plotted against optical radii. Clearly, much “color” is apparent in the rapidly varying ratios, especially at radii below 3pm. It is interesting also to note that the curves of Fig. 5(b) are not single valued at the larger radii, an artifact resulting from resonances in the computed optical scattering angular cross sections, which are sensitive in these fairly regular synthetic aerosols to small increments in size. For aerosols of greater structural irregularity with finite absorptivities the resonances would be muted (Harrison er al., 1972).

Conclusion

In Fig. 6 we show the theoretical transmission curves

which these synthetic aerosols would be expected to display in the dichotomous separator under our test conditions, together for comparison with the mea- sured transmission for uniform Carbowax aerosols. This figure illustrates the smearing of the 50 “/, trans- mission point and the flattening of the transmission curve expected for mixtures of irregular particles, as perceived by optical counting. Additional variance in the scattering and further flattening of the trans-

Our Carbowax test results are an independent verification of the transmission properties of the Sierra Model 240 impactor, when it is used to separate spherical homogeneous particles. However, we have demonstrated a severe degradation of the impactor’s performance, as perceived by a Royce 220 Single Particle Counter, when measuring irregular particles. We have attributed this loss of performance to the physical variability of both the aerodynamic and optical properties of Irregular particles, properties which are not functions of the geometries or flows of particular aerodynamic devices. Therefore it seems likely to us that similar behavior will occur with all aerodynamic separators, although optical particle counters which accept a larger fraction of the total scattering function may reduce the discrepancy.

Salt aerosol particles produced by evaporation at radii smaller than 0.5pm are predominantly single crystals (Hobbs et al., 1975). These will probably show less variability in optical and aerodynamic properties than agglomerated larger particles such as those shown in Fig. 5. Thus the accuracy to which optical properties can be inferred from aerodynamic measurements (or rice uvsu) may be dependent on the particle size, and

The effects of inhomogeneous particles 299

,I.40 -

k.30 - -1 2 1.20 -

8 1.10 - \ # 1.00 - -

,” .90 - S “z 00-

& 0 .70 - I% a .60 -

0 b

n=l55

m n=l.33

I n = 1.00

.50 ’ I 1 I I I , 1 I

0 .?5 1.50 2.25 3.00 3.75 4.50 5.25 6.00 675 7.50

0 TRUE RADIUS (Am)

1.50 -

1.40 -

z I.30 - v, ; 1.20 -

?I IO - 8 2 1.00 - 8 z .90 -

5 a .60-

5 8 .fO - IY 2 .60 -

.500 75 1 I I 1 I 50 2.25 I 3.00 I 3.75 1 4.50 I 5.25 I 6.00 6.75 7.50

b OPTICAL SIZE (radius inpm)

Fig. 5. Plots showing the results of Mie calculations for three classes of synthetic, spherically symmetric radially inhomogeneous aerosols.

may be very sensitive to the mechanisms of particle production. When measurements are made on irre- gular or inhomogeneous aerosols, our data indicate that it will be difficult to infer optical radii from aerodynamic sizing to accuracies of better than a factor of two.

This conclusion has strong implications for the interpretation of experiments which relate the fine particle mass concentration to the scattering extinction coefficient. An experiment done by Waggoner and Weiss (1980) found correlations between the two of approx. 0.95 at a variety of sites. These high cor-

relations clearly depend on the absence of irregular particles. Our results suggest that the ratio of fine particle mass concentration to the optical scattering extinction will be more variable when a significant contribution is made by irregular particles: an event which is likely to occur when the mean mass diameter exceeds 1 pm (for example, well aged Los Angeles aerosol). Thus the relationship between fine particle mass and the scattering extinction appears to be most reliable in relatively clean environments.

Our results also imply that the lung deposition of inhaled irregular aerosols will be poorly estimated by

LEE HARRISON and HALSTEAD HARRISON

OPTICAL SIZE (radius in gn)

Fig. 6. Calculated transmission functions for the three synthetic aerosols dlustrated in Fig. 5. The measured Carbowax transmission curve is shown also for comparison.

electron micrography or optical scattering measure- ments made on the dry particles. In this regard we point out that the Kiihler rates (Fletcher, 1962) for the growth of solution droplets are fast enough that initially dry salt aerosols will become droplets during inhalation. (Numerical integration of the growth rate equation for a 0.4 pm radius salt nucleus yields a 1 pm radius droplet in approx. 0.1 s at 95 %.) Therefore it seems sensible to us that size segregation studies to be used for the assessment of health effects should be done at high relative humidity. Solution droplets are clearly spherical and homogeneous, and this will make the interpretation of either dichotomous separator or optical scattering experiments less ambiguous when working with hydrophilic aerosols.

REFERENCES

Fletcher N. H. (1962) The Physics ofRain Clouds. Cambridge University Press, London.

Harrison H., Herbert .I. and Waggoner A. P. (1972) Mie theory computations of Lidar and nephelometric par-

ameters for power law aerosols. Appl. Optics 11, 288& 2885.

Hobbs, P. V., Radke L. F. and West H. W. (1976) Second Progress Report on the Development of an Instrument for Measuring Sodium Chloride Particles in the Air. Naval Research Laboratory Contract NOOO14-76-C-0140.’

Kerker M. (1969) Scattering of Light and Other Elec- tromagnetic Radiation. Academic Press, New York.

Loo B. w., Adachi R. S., Cork C. P., Goulding F. J., Jaklevic J. M.. Landis D. A. and Sea&s W. L. (1979) A Second Geneiation Dichotomous Sampler for Large Scale Moni- toring of Airborne Particulate Matter. Lawrence Berkeley Laboratory Report LBL-8725.*

Pavlik R. E. and Willeke K. (1978) Variable-cut particle-size classification by opposing jets. Am. Ind. Hyg. Assoc. J. 39, 952-957.

Sverdrup G. (1977) Parametric Measurement of Submicron Atmospheric Aerosol Size Distributions, Progress Report 803851-02 Formation of Atmospheric Aerosols. Particle Technology Laboratory Publication No. 320, EPA Grant R803851-02.C

Willeke K. and Liu Y. H. (1976) Single particle optical counter: principle and application. Fine Particles: Aerosol Sampling, Generation, and Analysis, pp. 698-729. Ac- ademic Press, New York.

l These reports may be obtained by requesting them from the authors of this paper.