Sidestream Tobacco Smoke Pipe Deposition and Fractal Properties
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Transcript of Sidestream Tobacco Smoke Pipe Deposition and Fractal Properties
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Sidestream Tobacco Smoke (STS) :
Pipe Deposition and Fractal Properties .
ICT-VII POSTER DISCUSSION: JULY 3,1995
Eric R. Moline and Robert F. Phalen
Dept. of Community and Environmental Medicine, UC Irvine, CA 92717-1825
Rationale
Current models which predict deposition efficiency of particles
assume that each particle behaves independently .
It is possible that concentrated aerosols can exhibit cloud
behavior, whereby a group of particles behaves as a single entity .
A study to test whether STS shares with cumulus clouds a
constant fractal dimension can help test whether the orpnization
of STS particles in space is similar to their atmospheric kin .
Feder (1988) states, "A fractal looks the same whatever the
scale ."
6gW.f:Zerx4 4L
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Eric R. Moline and Robert F. Phalen
Department of Community and
Environmental Medicine,
University of California, Irvine
Irvine, CA 92717-1825 ,
O1.;~,+, 6EZoSiZ
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I. Abstract
The deposition efficiencies of sidestream tobacco smoke (STS)
particles in a cylindrical aluminum pipe were compared with
theoretical predictions. IR3 research cigarettes were burned in a
0.45 m3 chamber. The smoke was sampled through the pipe and
onto a high-efficiency filter, and simultaneously sampled with a 7-
stage cascade impactor. Smoke deposits in the pipe Ad on the
filter and impactor stages were analyzed to determine deposition
efficiency in the pipe and size distribution of the STS . The
predictions were made using the size-distribution information as
applied to an accepted computational model, modified to
j incorporate the polydispersity of STS . The particle concentration
-tange was -90 to -1400 mg/m3 The corresponding mass median
f-a- .nd the geometric standard deviations (GSD) ranged from L9 to
~ aerodynamic diameters (hEVIAD) went from 0 .6 m to 1 .1 l.tm,
T:5, respectively. Inputting the MMADs and GSDs into the
deposition calculations, predictions tended to underestimate
experimental data by up to 20% for the densest aerosols (Figure
1). The fractality of these dense clouds were investigated .
Photographs of planar, laser-illuminated sections of STS displayed
a constant fractal dimension, Dsectian~ of 1 .35 0.14 over a scale of
fesolution froms--0.l mm2 to -2,000 mm2. Assuming STS is
isotropic, this Dsectfon
is equivalent to a cloud-surface fractal
dimension DsTS = 2 .35 0 .14 . Although it is not yet known how
DsTS scales with concentration, cloud fractal dimension may be a
useful parameter in improving particle deposition efficiency
calculations for dense aerosols. Supported by the National
Institutes of Health (Grant # NIEHS T32 E507157 and ROl HL
39682-05), the University of California Tobacco-Related Disease
Research Program (Grant # 1RT 324), and by additional support
from UC Irvine's Dept of Community & Environmental Medicine .
i
i
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II. Introduction and Objective
Accepted models which predict the deposition efficiency of
aerosol particles in airways account for neither concentration-
dependent effects nor the polydispersity of most aerosols (Yeh a4
Schum, 1980). Cloud behavior, present when a group of particles
behaves aerodynamically like an entity, is one effect which may
occur in concentrated aerosols . To help determine whether cloud
effects affect the deposition behavior of STS, fractal analysis of a
dense aerosol was performed . Space restrictions prevent an
explanation of the basic concept of the fractal dimension, other
than to say that the fractal dimension of an object is not necessarily
a whole number. A brief treatment of some basics appears in an
appendix to this poster (Section IX) . A fractal analysis of the
photographs revealed how the distribution of STS particles in
space scales with resolution (Figure 2), and results can then be
compared to the known fractal properties of atmospheric clouds .
Although other studies have been performed on the fractal
properties of combustion products, these are limited thus far to
cluster analysis of solid particles fixed on a slide (Xie et al., 1994) .
This is possibly the first attempt at deducing the fractal properties
of whole smoke in situ . i
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III. I`'Iethods
Four 1R3 Research Cigarettes (Univ. of Kentucky, Lexington,
KY, 1974) were exhaustively and simultaneously burned in a 0 .45
m3 chamber. During pipe and impactor sampling, HeNe laser light
at T. = 632 .8 nm (10 mW, continuous wave, Melles-Griot, Inc., San
Marcos, CA) was scattered into sheet illumination by a glass ~
stirring rod. Photographs of the red laser cross-sections were ta4n
to record inhomogeneities in the distribution of the dense smoke .
Experiments consistently show dark voids of relatively particle-
free air in the clouds which persist for up to three hours . After a
method of Beech, slides of four images were proj ected onto a wall
-(at 3_4 times magnification) and traced by hand onto paper
1eech, 1992). Figure 3 shows a sample photo, and a tracing of
one;r.egion.
e fractal analysis, which yielded expected results (< 2%
iior) _when performed on a Triadic Koch Curve prefractal and a
e
Gantor Dust prefractal (Mandelbrot, 1982), was performed in the
'follbwing manner:
1) Using 1 mm2 grid paper, basis sets of squares ranging from
; the equivalent of S-0 .3 mm on a side to S-45 mm on a side were
used to cover the boundaries of the set .
2) The logarithm of the measure of the boundary length for
each S, equal to the number of basis squares N(S) needed to
completely enclose the set times the basis square length, 6, was
plotted against the logarithm of the length of the side of the basis
square. Thus, log{N(S)(b)} was plotted vs . log(b) (Feder, 1988) .
3) As S approaches the total set (smoke image) size, the
length of the set approaches b . Points at and beyond these regions
were thus omitted from the regressions (Figure 4) .
4) The fractal dimension of the remaining set equals one
minus the slope 'of the line so generated (Feder, 1988, Figure 5) .
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IV. Results
A. Pipe Deposition
Particle deposition efficiency data to date may suggest a
systematic underestimation of efficiency with increasing STS ~
concentration (Figure 1) . More data are needed to test for a
significant correlation .
B. Fractal Analysis
The average slope of the four regression lines generated equals
-0.35 -h 0.14 (mean =L 2 SD). Thus 1- Dse~tion -0.35, where
Dsection
is the fractal dimension of a two-dimensional cross-section
of the cloud. It follows that Dse ,tjon = 1
.35 +_ 0.14 (mean 4-,2 SD) .
After Mandelbrot (1982), Malinowski and Zawadzki (1993) state
that the following procedure may often be used (in isotropic cases)
for transforming a cross-sectional fractal dimension into the fractal
dimension of the whole set : If Ds,tion is the fractal dimension of
the N-dimensional cross-section ot the tractal set which exists in
M-dimensional space (M> N), add the quantity M- N to Dse~tlon to
obtain DS,, . . Thus, for three-dimensional sidestream tobacco
smoke clouds at a particulate mass concentration of---1 .4 g/m3, the
fractal dimension DsTS of the whole cloud in the photograph is :
DsTS=
Dsection +(3 - 2) = Dsectton + 1- 2 .35 (Figure 6) .
N
Cn
O
N
W
-1
V
N
V
A
I
ir
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V. Discussion
Malinowski and Zawadzki (1993) found that the fractal
dimension of the surface of cumulus clouds to be 2 .55 0 .08
(mean 2 SD). Sidestream tobacco smoke clouds art wispier in ~
appearance than the popcorn-like surfaces of cumulus clouds, thus,
a lower fractal dimension is expected. Further work could
examine how these fractal properties of sidestream smoke scale
with concentration, using a 5 W Argon-ion laser to illuminate less
concentrated aerosols, and/or employing an analytical method
adapted from Beech (1992) . A plot of log(total smoke mass) vs.
log(boundary length of smoke) may provide a valuable key to help
improve current particle deposition models . It would scale with
concentration of particles by modeling STS cloud surfaces as
crumpled "sheets" of various masses (in a fixed volume) . Such
fractal plots of smoke concentration vs . smoke surface area could
thus account for the severity of any cloud effects .
It is important to note that the wisp-like structure of cigarette
smoke clouds seems to depend upon some mechanism by which
+Clean air can ba,"folded" into the cloud's structure . In the
experiments, sampling of the smoke (through the pipe and the
impactor) causes a slight negative pressure to exist within the
chamber, which allows clean air from inward-flowing leaks to be
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"M
V. Discussion (cont.)
introduced into the cloud . In a way perhaps similar to how two
different colors of dough might be kneaded together by a baker's
hands, fluid mechanics appear to drive the mixing of*clean air into a
the clouds. Surprising, however, is the fact that the clean-air voids
in the cloud persisf -for well over an hour . The photographs were
taken opportunistically, on two separate days, to show the fine
structure which can appear in the smoke. In the absence of inward
air chamber leaks and with thermal agitation minimized, it is
observed with the naked eye that STS clouds become much more
homogeneous in structure .
Sheet-illuminated STS clouds in a tightly stoppered 2 liter
Erlemneyer flask, however, show that another source of clean air
exists. There is a relatively smoke-free space left in the top of the
chamber after the cloud has partially settled . Photographs taken of
clouds within such a system showed similarly spectacular
structures as seen in the chamber, but the fractal properties were
not quantitated .
0 An automated method for counting squares of various sizes,
especially those of one square millimeter or less, needs to be
found. This would serve to objectify the analytic process, as well
as greatly increase its speed and facility .
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VI. Conclusions
STS has a constant cloud-surface fractal dimension, Dsrs -
2 .35 ~_L 0 .14, at a mass concentration of - 1 .4 g/m3 . Therefore,
photographs of STS at this concentration will look the same at
the studied resolutions .
If treating STS as fractals succeeds, cloud-surf&ce fractal 0
dimension may be a useful parameter for improving the
accuracy of current deposition models at high aerosol
concentrations .
~
VII. References ~
W IL
-4
~
Beech, M. (1992). "The Projection of Fractal Objects ."-4
I
Astrophysics and Space Science 192 : 103-111 . ;
Feder, J. (1988). Fractals. Plenum Publishing Corp .: London.
Malinowski, S. P., and Zawadzki, I. (1993) . "On the Surface of
Clouds." J. Atmospheric Sci. 50(1): 5-14, 1 January 1993 .
Mandelbrot, B. B. (1982). The Fractal Geometry ofNature .
W. H. Freeman: New York .
Schum, G. M., and Yeh, H. C. (1980). "Theoretical Evaluation
of Aerosol Deposition in Anatomical Models of Mammalian Lung
Airways." Bull. Math. Biol. 42 : 1-15 .
Xie, Y., Hopke, P. K., Casuccio, G. and Henderson, B. (1994).
"Use of Multiple Fractal Dimensions to Quantify Airborne Particle
Shape." Aerosol Sci. Technol. 20: 161-168 .
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VIII. Acknowledgments
This research was supported by the National Institutes of
Health (Grant Nos. NIEHS T32 E507157 and RO1 HL 39682-05),
the University of California Tobacco-Related Disease Research
Program (Grant No . 1RT 324), and by supplemental support frorPl
UCI's Department of Community and Environmental Medicine . I
aiso thank Dr. Robert Phalen and the other members of my
dissertation committee . Special thanks go to my wife, Beth, and
my daughter, Heather for helping me keep things in perspective .
a
IX. Appendix
Measuring the "Size" of a Surface (Feder, 1988)
Let Ao = the normal measure of a smooth surface .
The surface area is ~ the number of squares, N(S), each of area 52, times the area of a
square. The approximation of the area, A, converges to Ao as
Sa0:
A = N(s) s2 = {N(s) 6,4 }s - -~ Ao 6 = Ao
Thus DT = 2 is where the measure of the set passes from infmity to zero .
ro
Note that a smooth surface cannot be covered by a finite length of ~o
]in_ segrnents, nor does it can it have a volume (see the equations below) : ~
V
~CO
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Measuring the "Size" of a Surface (concl .)
With a smooth surface, the dimensions are restricted to whole numbers, and D= 2 is
the point through which the set measure passes from zero to infinity .
A fractal object has this value D as a positive real number . For example, the
dimension of a semicircle is one : its length can be found to arbitrary precision. The @
coastline of Britain has D - 1 .3, and Feder (1988) found that the coast of Norway has
D - 1 .52 . These non-integer dimensions lead to the property that the boundary length
depends upon the fineness of resolution used to measure the set .
Measuring the "Size" of a Surface (cont .)
A=N(S)S2 ={N(S)Sz}S-) AS=A
S-> 0
N
V= N(S) 8 3={N(S) S' } S' -3 A S 1= 0 0
S-> 0
N
w
i
V
L= N(S) 6' ={N(8) 8' }S 1> A l 81 -~ eo ~
I
I
I
6 --> 0
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Figure 1 : Ratio of Observed Deposition
Efficiency/Predicted Efficiency vs . STS Concentration
00.~,..,~
cz
04
0.5 1 1.5 2 2.5 3 3.5
STS Concentration
-~
(# of 1R3 cigarettes burned/0 .45 m3)
Ratio = 0.14(STS Concentration) + 0 .94 ;
(R2 = 0.15 )
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Figure 2: An Example of Fractality
(Self-Similarity Over Scale)
Hypothetical images of aerosol particles :
s
-0.1-mm -c' ~a--- -1 mm
Conclusion: Complexity remains fairly ~
constant. The set may fit a fractal model.
~
V
N
W
i
Q
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Figure 3 : An STS Cross-Sectional
Photograph with a Hand Tracing
zss4iszoSZ 1 `
0
-
Figure 4: Plot of All Data (Photos A-D)
/-
r:l
10000
~i~
1000
10
m
Since b > or = (set size) '
near here, points from here
on were excluded from
0
regressions.
.0
0
10 100 1000
Resolution = 3 .4(S) (mm)
-
Figure 5: Fractal Analysis of Photo "D"
with Regression
3 .5
~
-
3.0
, ~
CIO
~ 2.5
~
;
~
2.0
0 1 5
~
.
+ 1 .0
M
~
0 0.5
0.04--
0.0
0
3
. . . ..-- . . -- I
0.5 1 .0 1.5 2.0
0.53 + 1og(S) (mm)
2.5
Linear regression equation :
log{length(S)} = (-0 .25)log(S) + 3 .06. (R2 = 0 .94)
Thus Dpro;e
,tio D= 1
.25, and DsTS, photo D-
2.25.
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Figure 6: Fractal Analysis of Photos A-D
3 .5
3
~
~
~ '~.5
,-~-,
~
DO
2
~
u0
L
~ 1.5
r~.+
~
0 1
+
~ 0.5
0
0
~
0 0
0
0 0.5 1 1.5
0.53 + log(S) (mm)
2.5
Linear Regression on all data :
log{length(S)} = (-0 .35)log(5) + 2.73. (R2 = 0.88) .
Alternatively: Length(S) = 540(S)-0
.35 ~
~
W
Thus D = 1-(-0 .35) = 1 .35, and DsTS = 2 .35. y
rojection mp
ch