AEROSOL SPECTROMETER AND ITS APPLICATION 
the aerosol contains particles with larger, dis- 
crete Stokes’ diameters representing aggregates 
of (2, 3, or more) individual particles (Fig. 4a). 
Such aggregates can be eliminated by passing 
the test aerosol through a cascade of two A.S.’s 
and operating the first under conditions of N, O 
so that the smallest (doublet) aggregates are 
eliminated just before the channel end. The aero- 
sol leaving is thus truly monodisperse as it enters 
the second A.S. which is operated under standard 
conditions of N, O. A deposit is produced herein 
which has the same La as that without passing 
the first A.S., but devoid of any deposit discon- 
tinuity for L < Ly. Such strictly monodisperse 
spectra, when analyzed by count or photometry, 
result in the distributions Z(L) and S(Z) in Fig- 
ure 7. The distribution is not identical because of 
different orifices in the channels (thus different 
values of Lg corresponding to d = 0.56 uw). The 
invariance of Zz with L is strikingly evident, 
while S,, the photometer indication, shows fluc- 
tuations, probably because a few dust particles 
or local surface impurities which are disregarded 
by the counting process. 
Since Zz, Sg can be assumed to be constant 
for L < La, the concentration Cz, that is, the 
relative frequency of occurrence of particles of 
size d, results as Cy = (ZL)ab’, where b’, the 
average width of the deposit (b’ = 1) represents 
a scale factor. For S,’ as the specific scattering 
power of the same particle size d follows: Ca = 
(SL/S')a - 
For polydisperse deposits these relations yield 
4 C(d) 
Z(d) = i -d 
» L(d) 
2 C(d) - S’(d) 
S(d) = SS, (3) 
(d) I Lid) d+S8 3 
where So is the level of background scattering. 
The derivative of (3) results in the size-distri- 
bution function 
C(d) = L(d)dZ(d) /od 
= L(d)S’(d)“0S(d)/dd_ (4) 
A convenient procedure is first to plot the 
Z(L) or S(L) record as Z(d) or S(d) by means of 
the pertinent L(d) characteristic (Fig. 3) and to 
determine from these plots the differences as 
AZ, or ASqg over equidistant intervals Ad, so 
that AZ, ~ AZ,/Ad ~ 0Z(d) /dd, or, other things 
being equal, for AS, . AZ is then multiplied with 
t 
i 
N=12000 d*56yp 
9,760 
5 10 15 
a L(cm) = 
the 
monodisperse aerosol deposit obtained by count- 
ing Ay = 3 X 10°-* em? as Z(L) and by micropho- 
tometer A; = 6 X 1073 em? as S(L) 
Fic. 7—Micro-analyzer records of same 
the corresponding La , and ASq with La/Sa’; the 
resulting Cy values are then plotted versus d. 
The relative mass-size distribution J/(d) re- 
sults from C(d) because of Wa Ca X d for 
aerosols of fairly uniform specific gravity of their 
components. Hence the A scale on the ordinate 
results from multiplying each C value with the 
cube of the corresponding d value. 
This procedure is demonstrated graphically for 
the same multidisperse latex aerosol as used pre- 
viously in monodisperse form in Figure 8. The 
resulting size distribution—typical for the multi- 
disperse aerosol—indicates the predominance of 
single particles to be expected for a suitable 
method of aerosol generation [Silverman, 1956], 
but also particles corresponding to the Stokes’ 
diameters of aggregates 2, 3, and more particles 
at d = 0.64 u, 0.73 p, 0.81 pu, etc. at gradually 
lesser defined sizes. This is also to be expected 
because the Stokes’ diameters of higher aggre- 
gates should for statistical reasons become in- 
creasingly indefinite with larger component num- 
bers. The frequency of single particles results as 
62% of the total number, 22% for double, 9% 
for triple, 5% for quadruple, and 2% for still 
larger agglomerates. 
Definition of particle size—In the foregoing it 
has not been necessary to distinguish between the 
geometrical d and the Stokes’ diameters 6 of 
spherical particles because the specific gravity p 
is close to unity for the latex particles used to 
calibrate and define d. The difference between d, 
and 6 becomes significant when an aerosol con- 
tains components of different densities. This case 
warrants brief discussion: The Stokes-Cunning- 
ham law predicts the time 7, required for the fall 
