AEROSOL SPECTROMETER AND ITS APPLICATION 171 
a conical helix of constant pitch a, on a plane 
results in a sequence of v sectors of an Archi- 
median spiral, if y designates the number of com- 
plete turns of the helix. The width 6’ = 6 sec a 
of the channel is thus the width of a spiral band 
on the foil; a double helix of the same width b’ 
develops two identical spiral bands with corre- 
sponding points shifted by w/2. 
Geometrically the channel deposits are defined 
with relation to the foil boundaries in polar co- 
ordinates (r, g) as follows (Fig. 5). 
The radius vector r originates at the intersec- 
tion of the straight edges of the foil, while r = ro 
for the cirele which coincides with the start of 
the channels, and g = 0 is (arbitrarily) defined by 
the intersection with the upper border of the 
left spiral channel I. The value of ¢ increases in 
the flow direction, that is, anticlockwise. Hence 
the upper border of channel I is defined by 
rm =r +q-¢ for m<nu <n; 
the lower border by 
Tr = to t+ ay + 89) =m + 9p + OW’, 
since 6g = b’/q 
for 
tm <1, <M; (—-b¢) < eo < Ww — by) (1b) 
Channel IT is defined by (la) and (1b), if ¢ 
is replaced by g’ = g + w/2. The pitch of the 
spirals q is related to that of the helices on the 
rotor q, by 
q = qr/w = g,/(360°-sin a) 
Numerically these dimensions are ro = 7.4 
em, 71 = 14.5 cm, dg = 39.4°, w = 93.5°, gq = 
2.92 x 10% cm/deg, org = 1.67 cm/radian, 
bi = 1:15 em: 
The distance L from the channel entry r = ro ; 
—de = 9 =o of any pointr <n jorge < vw 
along the channel wall results from the rectifica- 
tion of the spiral which passes through this point 
in terms of r as 
L= [7 + qin +7] 
ro 
for [R= Ve +r] (2) 
Due to the velocity distribution within the 
laminar flow the actual borders of the deposit de- 
viates from this pattern, because of the effect of 
the boundary layer on the horizontal channel 
walls. This causes b’ to decrease slightly with L 
(Fig. 4); hence g¢ becomes somewhat larger for the 
upper, and smaller for the lower deposit border 
than the value derived from q, . (This evidence of 
the existence of a gas layer at rest with the chan- 
nel walls—and thereby above the foil surface— 
appears to be of prime significance because it in- 
dicates absence of any disturbance of the particles 
after deposit.) 
The loci of all points of equal Z values on the 
spiral bands are concentric circles, the radii r of 
which vary with Z according to (2). This results 
in a simple method for determining approximate 
L values on a foil deposit as follows. A trans- 
parent sheet 1s used upon which a family of con- 
centric circles, with radii corresponding to equal 
intervals of L and the outline of the foil itself, are 
imprinted; thus, the sheet can be superimposed 
upon the deposit (Fig. 6). The end of the particle 
spectrum in each channel will then coincide with 
a section of the circle, which represents Lg , that 
is, the smallest particle size noticeably present in 
the deposit. 
For the same reason, a foil, cut along several 
of these circles into concentric annular sectors, 
yields its deposit divided into equivalent size 
classes available for separate analysis. 
Determination of the distribution function—The 
particle size (and mass) distribution C(d) and 
M (qd) of the foil deposit is derived from the varia- 
tion of the local deposit density Z along the chan- 
nels, that is, Z(L). Hence the indicating device 
for Z for any L value must be able to scan the 
entire length of the deposit along the spiral pat- 
tern, and the reference area A, over which the 
individual Z values are determined has to be 
small. 
The direct determination of Z requires micro- 
scopic counting and thus optical systems resolv- 
ing each individual particle. Micro-opties involv- 
ing low-angle reflected dark-field illumination 
(such as the Ultropak system of Leitz with mir- 
ror condensor and 20 to 50x objective magni- 
fication) permit the identification (though not 
necessarily the true resolution) of scattering ob- 
jects down to less than 0.1 diameter, provided 
that the foil surface does not scatter appreciably. 
(This latter condition has been fulfilled by the 
use of thin, 0.1 mm, bronze foils, chromium 
plated and highly polished so that all polish 
marks were parallel, while the azimuth fraction 
of the illuminating beam which the marks would 
scatter was eliminated.) 
