Abstract

We have measured the scattered-light intensity as a function of the scattering angle for light scattered from soot particles in a premixed methane/oxygen flame. This yields the optical structure factor for the soot particles. We find that the structure factor shows the soot particles to have a morphology consistent with a fractal interpretation with a fractal dimension in the 1.6 ≲ D ≲ 1.8 range and a radius of gyration that increases with the height above the burner. The structure factor may also show the effect of the finite monomer size of the soot clusters.

© 1991 Optical Society of America

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References

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  1. A. D'Alessio, A. DiLorenzo, A. F. Sarafim, F. Berretta, S. Masi, C. Venitozzi, “Soot formation in methane-oxygen flames,” in Fifteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1975), p. 1427.
    [CrossRef]
  2. A. D'Alessio, “Laser light scattering and fluorescence diagnostics of rich flames,” in Particulate Carbon, D. C. Siegla, G. W. Smith, eds. (Plenum, New York, 1981), p. 207.
  3. W. Hinds, P. C. Reist, “Aerosol measurement by laser Doppler spectroscopy,” Aerosol Sci. 3, 501–527 (1982).
    [CrossRef]
  4. G. B. King, C. M. Sorensen, T. W. Lester, J. F. Merklin, “Photon correlation spectroscopy used as a particle size diagnostic in sooting flames,” Appl. Opt. 21, 976–978 (1982).
    [CrossRef] [PubMed]
  5. S. M. Scrivner, T. W. Taylor, C. M. Sorensen, J. F. Merklin, “Soot particle size distribution measurements in a premixed flame using photon correlation spectroscopy,” Appl. Opt. 25, 291–297 (1986).
    [CrossRef] [PubMed]
  6. W. L. Flower, “Optical measurements of soot formation in flames,” Combust. Sci. Technol. 33, 17–33 (1983).
    [CrossRef]
  7. M. E. Weill, P. Flament, G. Gouesbet, “Diameters and number densities of soot particles in premixed flat flames, propane/oxygen,” Appl. Opt. 22, 2407–2409 (1983).
    [CrossRef] [PubMed]
  8. M. E. Weill, N. Lhuissier, G. Gouesbet, “Mean diameters and number densities of soot particles in premixed flat flames CH4–02 by diffusion broadening spectroscopy,” Appl. Opt. 25, 1676–1683 (1986).
    [CrossRef] [PubMed]
  9. S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A 12, L109–L117 (1979).
    [CrossRef]
  10. F. Family, D. P. Landau, eds., Kinetics of Aggregation and Gelation (North-Holland, Amsterdam, 1984).
  11. H. E. Stanley, N. Ostrowsky, eds., On Growth and Form (Nijhoff, Boston, 1986).
  12. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1983).
  13. T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–275 (1986).
    [CrossRef]
  14. R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
    [CrossRef]
  15. D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
    [CrossRef]
  16. A. J. Hurd, W. L. Flower, “In situ growth and structure of fractal silica aggregates in a flame,” J. Colloid Interface Sci. 122, 178–192 (1988).
    [CrossRef]
  17. H. X. Zhang, C. M. Sorensen, E. R. Ramer, B. J. Olivier, J. F. Merklin, “In-situ optical structure factor measurements of an aggregating soot aerosol,” Langmuir 4, 867–871 (1988).
    [CrossRef]
  18. M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
    [CrossRef]
  19. G. Dietler, C. Aubert, D. S. Cannell, P. Wiltzius, “Gelatin of colloidal silica,” Phys. Rev. Lett. 57, 3117–3120 (1986).
    [CrossRef] [PubMed]
  20. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  21. J. Lahaye, G. Prado, “Morphology and internal structure of carbon blacks and soot,” in Particulate Carbon, D. C. Siegla, G. W. Smith, eds. (Plenum, New York, 1981), p. 33.
  22. R. J. Samson, G. W. Mulholland, J. W. Gentry, “Structural analysis of soot agglomerates,” Langmuir 3, 272–281 (1987).
    [CrossRef]
  23. R. D. Mountain, G. W. Mulholland, H. J. Baum, “Simulation of aerosol agglomeration in the free molecular and continuum regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
    [CrossRef]
  24. R. A. Dobbins, C. M. Megaridis, “Morphology of flame generated soot as determined by thermophoretic sampling,” Langmuir 3, 254–259 (1987).
    [CrossRef]

1988 (3)

R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

A. J. Hurd, W. L. Flower, “In situ growth and structure of fractal silica aggregates in a flame,” J. Colloid Interface Sci. 122, 178–192 (1988).
[CrossRef]

H. X. Zhang, C. M. Sorensen, E. R. Ramer, B. J. Olivier, J. F. Merklin, “In-situ optical structure factor measurements of an aggregating soot aerosol,” Langmuir 4, 867–871 (1988).
[CrossRef]

1987 (2)

R. J. Samson, G. W. Mulholland, J. W. Gentry, “Structural analysis of soot agglomerates,” Langmuir 3, 272–281 (1987).
[CrossRef]

R. A. Dobbins, C. M. Megaridis, “Morphology of flame generated soot as determined by thermophoretic sampling,” Langmuir 3, 254–259 (1987).
[CrossRef]

1986 (6)

R. D. Mountain, G. W. Mulholland, H. J. Baum, “Simulation of aerosol agglomeration in the free molecular and continuum regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
[CrossRef]

S. M. Scrivner, T. W. Taylor, C. M. Sorensen, J. F. Merklin, “Soot particle size distribution measurements in a premixed flame using photon correlation spectroscopy,” Appl. Opt. 25, 291–297 (1986).
[CrossRef] [PubMed]

M. E. Weill, N. Lhuissier, G. Gouesbet, “Mean diameters and number densities of soot particles in premixed flat flames CH4–02 by diffusion broadening spectroscopy,” Appl. Opt. 25, 1676–1683 (1986).
[CrossRef] [PubMed]

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

G. Dietler, C. Aubert, D. S. Cannell, P. Wiltzius, “Gelatin of colloidal silica,” Phys. Rev. Lett. 57, 3117–3120 (1986).
[CrossRef] [PubMed]

T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–275 (1986).
[CrossRef]

1984 (1)

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

1983 (2)

1982 (2)

1979 (1)

S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A 12, L109–L117 (1979).
[CrossRef]

Aubert, C.

G. Dietler, C. Aubert, D. S. Cannell, P. Wiltzius, “Gelatin of colloidal silica,” Phys. Rev. Lett. 57, 3117–3120 (1986).
[CrossRef] [PubMed]

Baum, H. J.

R. D. Mountain, G. W. Mulholland, H. J. Baum, “Simulation of aerosol agglomeration in the free molecular and continuum regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
[CrossRef]

Berretta, F.

A. D'Alessio, A. DiLorenzo, A. F. Sarafim, F. Berretta, S. Masi, C. Venitozzi, “Soot formation in methane-oxygen flames,” in Fifteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1975), p. 1427.
[CrossRef]

Berry, M. V.

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

Cannell, D. S.

G. Dietler, C. Aubert, D. S. Cannell, P. Wiltzius, “Gelatin of colloidal silica,” Phys. Rev. Lett. 57, 3117–3120 (1986).
[CrossRef] [PubMed]

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

D'Alessio, A.

A. D'Alessio, “Laser light scattering and fluorescence diagnostics of rich flames,” in Particulate Carbon, D. C. Siegla, G. W. Smith, eds. (Plenum, New York, 1981), p. 207.

A. D'Alessio, A. DiLorenzo, A. F. Sarafim, F. Berretta, S. Masi, C. Venitozzi, “Soot formation in methane-oxygen flames,” in Fifteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1975), p. 1427.
[CrossRef]

Dietler, G.

G. Dietler, C. Aubert, D. S. Cannell, P. Wiltzius, “Gelatin of colloidal silica,” Phys. Rev. Lett. 57, 3117–3120 (1986).
[CrossRef] [PubMed]

DiLorenzo, A.

A. D'Alessio, A. DiLorenzo, A. F. Sarafim, F. Berretta, S. Masi, C. Venitozzi, “Soot formation in methane-oxygen flames,” in Fifteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1975), p. 1427.
[CrossRef]

Dobbins, R. A.

R. A. Dobbins, C. M. Megaridis, “Morphology of flame generated soot as determined by thermophoretic sampling,” Langmuir 3, 254–259 (1987).
[CrossRef]

Flament, P.

Flower, W. L.

A. J. Hurd, W. L. Flower, “In situ growth and structure of fractal silica aggregates in a flame,” J. Colloid Interface Sci. 122, 178–192 (1988).
[CrossRef]

W. L. Flower, “Optical measurements of soot formation in flames,” Combust. Sci. Technol. 33, 17–33 (1983).
[CrossRef]

Forrest, S. R.

S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A 12, L109–L117 (1979).
[CrossRef]

Freltoft, T.

T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–275 (1986).
[CrossRef]

Gentry, J. W.

R. J. Samson, G. W. Mulholland, J. W. Gentry, “Structural analysis of soot agglomerates,” Langmuir 3, 272–281 (1987).
[CrossRef]

Gouesbet, G.

Hinds, W.

W. Hinds, P. C. Reist, “Aerosol measurement by laser Doppler spectroscopy,” Aerosol Sci. 3, 501–527 (1982).
[CrossRef]

Hurd, A. J.

A. J. Hurd, W. L. Flower, “In situ growth and structure of fractal silica aggregates in a flame,” J. Colloid Interface Sci. 122, 178–192 (1988).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

King, G. B.

Kjems, J. K.

T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–275 (1986).
[CrossRef]

Lahaye, J.

J. Lahaye, G. Prado, “Morphology and internal structure of carbon blacks and soot,” in Particulate Carbon, D. C. Siegla, G. W. Smith, eds. (Plenum, New York, 1981), p. 33.

Lester, T. W.

Lhuissier, N.

Mandelbrot, B.

B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1983).

Martin, J. E.

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Masi, S.

A. D'Alessio, A. DiLorenzo, A. F. Sarafim, F. Berretta, S. Masi, C. Venitozzi, “Soot formation in methane-oxygen flames,” in Fifteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1975), p. 1427.
[CrossRef]

Megaridis, C. M.

R. A. Dobbins, C. M. Megaridis, “Morphology of flame generated soot as determined by thermophoretic sampling,” Langmuir 3, 254–259 (1987).
[CrossRef]

Merklin, J. F.

Mountain, R. D.

R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

R. D. Mountain, G. W. Mulholland, H. J. Baum, “Simulation of aerosol agglomeration in the free molecular and continuum regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
[CrossRef]

Mulholland, G. W.

R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

R. J. Samson, G. W. Mulholland, J. W. Gentry, “Structural analysis of soot agglomerates,” Langmuir 3, 272–281 (1987).
[CrossRef]

R. D. Mountain, G. W. Mulholland, H. J. Baum, “Simulation of aerosol agglomeration in the free molecular and continuum regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
[CrossRef]

Olivier, B. J.

H. X. Zhang, C. M. Sorensen, E. R. Ramer, B. J. Olivier, J. F. Merklin, “In-situ optical structure factor measurements of an aggregating soot aerosol,” Langmuir 4, 867–871 (1988).
[CrossRef]

Percival, I. C.

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

Prado, G.

J. Lahaye, G. Prado, “Morphology and internal structure of carbon blacks and soot,” in Particulate Carbon, D. C. Siegla, G. W. Smith, eds. (Plenum, New York, 1981), p. 33.

Ramer, E. R.

H. X. Zhang, C. M. Sorensen, E. R. Ramer, B. J. Olivier, J. F. Merklin, “In-situ optical structure factor measurements of an aggregating soot aerosol,” Langmuir 4, 867–871 (1988).
[CrossRef]

Reist, P. C.

W. Hinds, P. C. Reist, “Aerosol measurement by laser Doppler spectroscopy,” Aerosol Sci. 3, 501–527 (1982).
[CrossRef]

Samson, R. J.

R. J. Samson, G. W. Mulholland, J. W. Gentry, “Structural analysis of soot agglomerates,” Langmuir 3, 272–281 (1987).
[CrossRef]

Sarafim, A. F.

A. D'Alessio, A. DiLorenzo, A. F. Sarafim, F. Berretta, S. Masi, C. Venitozzi, “Soot formation in methane-oxygen flames,” in Fifteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1975), p. 1427.
[CrossRef]

Schaefer, D. W.

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Scrivner, S. M.

Sinha, S. K.

T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–275 (1986).
[CrossRef]

Sorensen, C. M.

Taylor, T. W.

Venitozzi, C.

A. D'Alessio, A. DiLorenzo, A. F. Sarafim, F. Berretta, S. Masi, C. Venitozzi, “Soot formation in methane-oxygen flames,” in Fifteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1975), p. 1427.
[CrossRef]

Weill, M. E.

Wiltzius, P.

G. Dietler, C. Aubert, D. S. Cannell, P. Wiltzius, “Gelatin of colloidal silica,” Phys. Rev. Lett. 57, 3117–3120 (1986).
[CrossRef] [PubMed]

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Witten, T. A.

S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A 12, L109–L117 (1979).
[CrossRef]

Zhang, H. X.

H. X. Zhang, C. M. Sorensen, E. R. Ramer, B. J. Olivier, J. F. Merklin, “In-situ optical structure factor measurements of an aggregating soot aerosol,” Langmuir 4, 867–871 (1988).
[CrossRef]

Aerosol Sci. (1)

W. Hinds, P. C. Reist, “Aerosol measurement by laser Doppler spectroscopy,” Aerosol Sci. 3, 501–527 (1982).
[CrossRef]

Appl. Opt. (4)

Combust. Sci. Technol. (1)

W. L. Flower, “Optical measurements of soot formation in flames,” Combust. Sci. Technol. 33, 17–33 (1983).
[CrossRef]

J. Colloid Interface Sci. (2)

A. J. Hurd, W. L. Flower, “In situ growth and structure of fractal silica aggregates in a flame,” J. Colloid Interface Sci. 122, 178–192 (1988).
[CrossRef]

R. D. Mountain, G. W. Mulholland, H. J. Baum, “Simulation of aerosol agglomeration in the free molecular and continuum regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
[CrossRef]

J. Phys. A (1)

S. R. Forrest, T. A. Witten, “Long-range correlations in smoke-particle aggregates,” J. Phys. A 12, L109–L117 (1979).
[CrossRef]

Langmuir (4)

H. X. Zhang, C. M. Sorensen, E. R. Ramer, B. J. Olivier, J. F. Merklin, “In-situ optical structure factor measurements of an aggregating soot aerosol,” Langmuir 4, 867–871 (1988).
[CrossRef]

R. A. Dobbins, C. M. Megaridis, “Morphology of flame generated soot as determined by thermophoretic sampling,” Langmuir 3, 254–259 (1987).
[CrossRef]

R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

R. J. Samson, G. W. Mulholland, J. W. Gentry, “Structural analysis of soot agglomerates,” Langmuir 3, 272–281 (1987).
[CrossRef]

Opt. Acta (1)

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

Phys. Rev. B (1)

T. Freltoft, J. K. Kjems, S. K. Sinha, “Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering,” Phys. Rev. B 33, 269–275 (1986).
[CrossRef]

Phys. Rev. Lett. (2)

D. W. Schaefer, J. E. Martin, P. Wiltzius, D. S. Cannell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

G. Dietler, C. Aubert, D. S. Cannell, P. Wiltzius, “Gelatin of colloidal silica,” Phys. Rev. Lett. 57, 3117–3120 (1986).
[CrossRef] [PubMed]

Other (7)

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

J. Lahaye, G. Prado, “Morphology and internal structure of carbon blacks and soot,” in Particulate Carbon, D. C. Siegla, G. W. Smith, eds. (Plenum, New York, 1981), p. 33.

F. Family, D. P. Landau, eds., Kinetics of Aggregation and Gelation (North-Holland, Amsterdam, 1984).

H. E. Stanley, N. Ostrowsky, eds., On Growth and Form (Nijhoff, Boston, 1986).

B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1983).

A. D'Alessio, A. DiLorenzo, A. F. Sarafim, F. Berretta, S. Masi, C. Venitozzi, “Soot formation in methane-oxygen flames,” in Fifteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1975), p. 1427.
[CrossRef]

A. D'Alessio, “Laser light scattering and fluorescence diagnostics of rich flames,” in Particulate Carbon, D. C. Siegla, G. W. Smith, eds. (Plenum, New York, 1981), p. 207.

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Figures (6)

Fig. 1
Fig. 1

Intensity scattered at θ = 90° as a function of the distance from the center of the burner to the scattering volume x. The incident beam is along the x axis. Intensities at the height above burner h = 8 and 10 mm have been multiplied by 2 and 3, respectively.

Fig. 2
Fig. 2

Scattered light intensity I (q) as a function of the scattering wave vector q for five different heights above burner h for the C/O = 0.69 flame.

Fig. 3
Fig. 3

Scattered light intensity I (q) as a function of the scattering wave vector q for five different heights above burner h for the C/O = 0.75 flame.

Fig. 4
Fig. 4

Graph of the inverse normalized scattering intensity I (0)/I (q) versus wave vector squared q2 for the C/O = 0.69 flame. Linearity is in accord with Eq. (6), and the slopes yield the Rg values as labeled in the diagram.

Fig. 5
Fig. 5

Soot particle radius of gyration Rg as a function of height above burner h for both flames.

Fig. 6
Fig. 6

Graph of the normalized scattering intensity plotted so that the slope is equal to –D/2, D = 1.6.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

N R g D ,
S ( q ) q D ,
S ( q ) = S ( o ) ( 1 + 2 q 2 R g 2 / 3 D ) D / 2 ,
q = 4 π λ 1 sin θ / 2 ,
S ( q ) S ( 0 ) ( 1 1 / 3 q 2 R g 2 ) .
I ( q ) = I ( 0 ) ( 1 1 / 3 q 2 R g 2 ) ,
S ( q ) tot = S ( q ) F ( a q ) ,

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