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

  • Eric R. Moline and Robert F. Phalen

    Department of Community and

    Environmental Medicine,

    University of California, Irvine

    Irvine, CA 92717-1825 ,

    O1.;~,+, 6EZoSiZ

  • 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

  • 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

  • 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) .

  • 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

    I

  • 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

  • "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 .

  • 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 .

  • 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

  • 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

  • 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 )

  • 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

  • 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.

  • 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