Abstract

We used a two-angle scattering technique to investigate the soot distribution in an ethylene diffusion flame in conjunction with extinction measurements. In the framework of a fractal description, we introduced a modified structure factor to interpret the scattering intensity from polydisperse aggregates. The connection between a mean value of a structural radius of gyration, R gm1, and the quantities experimentally measured was then established. Soot parameters (volume fraction, particle size, and number densities) were determined along three radial sections of a 8-cm high-diffusion flame. The stability of the results with respect to the parameters of the distribution function was studied.

© 1998 Optical Society of America

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    [CrossRef]
  3. P. S. Greenberg, J. C. Ku, “Soot volume fraction imaging,” Appl. Opt. 36, 5514–5522 (1997).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  8. R. L. Vander Wal, “Laser-induced incandescence: detection issues,” Appl. Opt. 35, 6548–6559 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
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  15. R. J. Santoro, T. T. Yeh, J. J. Horvath, H. G. Semerjian, “The transport and growth of soot particles in laminar diffusion flames,” Combust. Sci. Technol. 53, 89–115 (1987).
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  16. R. A. Dobbins, C. M. Megaridis, “Morphology of flame-generated soot as determined by thermophoretic sampling,” Langmuir 3, 254–259 (1987).
    [CrossRef]
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  19. C. M. Megaridis, R. A. Dobbins, “Comparison of soot growth and oxidation in smoking and non-smoking ethylene diffusion flames,” Combust. Sci. Technol. 66, 11–16 (1989).
  20. J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
    [CrossRef]
  21. U. O. Koylu, G. M. Faeth, “Structure of overfire soot in buoyant turbulent diffusion flames at long resident times,” Combust. Flame 89, 140–156 (1992).
    [CrossRef]
  22. J. Lahaye, F. Ehrburger-Dolle, “Mechanisms of carbon black formation. Correlation with the morphology of the aggregates,” Carbon 32, 1319–1324 (1994).
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  23. I. Colbeck, E. J. Hardman, R. M. Harrison, “Optical and dynamical properties of fractal cluster of carbonaceous smoke,” J. Aerosol. Sci. 20, 765–774 (1989).
    [CrossRef]
  24. R. A. Dobbins, R. J. Santoro, H. G. Semerajian, “Analysis of light scattering from soot using optical cross sections for aggregates,” in 23rd Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1525–1532.
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    [CrossRef]
  26. P. A. Bonczyk, R. J. Hall, “Measurements of the fractal dimension of soot using UV laser radiation,” Langmuir 8, 1666–1670 (1992).
    [CrossRef]
  27. R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
    [CrossRef] [PubMed]
  28. S. Gangopadhyay, I. Elminyawi, C. M. Sorensen, “Optical structure factor measurements of soot particles in a premixed flame,” Appl. Opt. 30, 4859–4864 (1991).
    [CrossRef] [PubMed]
  29. C. M. Sorensen, J. Cai, N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
    [CrossRef] [PubMed]
  30. T. T. Charalampopoulos, H. Chang, “Effects of soot agglomeration on radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 46, 125–134 (1991).
    [CrossRef]
  31. R. Puri, T. F. Richardson, R. J. Santoro, R. A. Dobbins, “Aerosol dynamic processes of soot aggregates in a laminar ethene diffusion flame,” Combust. Flame 92, 320–333 (1993).
    [CrossRef]
  32. U. O. Koylu, G. M. Faeth, “Radiative properties of flame-generated soot,” J. Heat Transfer 115, 409–417 (1993).
    [CrossRef]
  33. U. O. Koylu, G. M. Faeth, “Optical properties of overfire soot in buoyant turbulent diffusion flames at long residence time,” J. Heat Transfer 116, 152–159 (1994).
    [CrossRef]
  34. R. A. Dobbins, G. W. Mulholland, N. P. Bryner, “Comparison of the fractal smoke optics model with light extinction measurements,” Atmos. Environ. 28, 889–897 (1994).
    [CrossRef]
  35. C. J. Dasch, “One-dimensional tomography: a conversion of Abel, onion-peeling, and filtered back projection methods,” Appl. Opt. 31, 1146–1152 (1992).
    [CrossRef] [PubMed]
  36. R. D. Mountain, G. W. Mulholland, “Light scattering from simulated smoke agglomerates,” Langmuir 4, 1321–1326 (1988).
    [CrossRef]
  37. U. O. Koylu, C. S. McEnally, D. E. Rosner, L. D. Pfefferle, “Simultaneous measurements of soot volume fraction and particle size/microstructure in flames using a thermophoretic sampling technique,” Combust. Flame 110, 494–507 (1997).
    [CrossRef]
  38. U. O. Koylu, G. M. Faeth, T. L. Farias, M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100, 621–633 (1995).
    [CrossRef]
  39. C. M. Sorensen, J. Cai, N. Lu, “Test of static structure factors for describing light scattering from fractal soot aggregates,” Langmuir 8, 2064–2069 (1992).
    [CrossRef]
  40. J. A. Pinson, T. A. Litzinger, R. J. Santoro, “New techniques for quantitative, planar soot measurements,” presented at the fall technical meeting of the Eastern States Sections, Combustion Institute, Princeton, N.J., 25–27 October 1993.
  41. H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
    [CrossRef]
  42. R. J. Santoro, H. G. Semerjian, “Soot formation in diffusion flames: flow rate, fuels species and temperature effects,” in 20th Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1984), pp. 997–1006.
  43. C. S. McEnally, U. O. Koylu, L. D. Pfefferle, D. R. Rosner, “Soot volume fraction and temperature measurements in laminar non premixed flames using thermocouples,” Combust. Flame 109, 701–720 (1997).
    [CrossRef]
  44. M. Tappe, B. S. Haynes, J. H. Kent, “The effect of alkali metals on a laminar ethylene diffusion flame,” Combust. Flame 92, 266–273 (1993).
    [CrossRef]
  45. J. Zhang, C. M. Megaridis, “Soot suppression by Ferrocene in laminar ethylene/air nonpremixed flames,” Combust. Flame 105, 528–540 (1996).
    [CrossRef]

1998 (1)

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

1997 (5)

C. R. Shaddix, J. F. Harrington, K. C. Smyth, “Quantitative measurements of enhanced soot production in a flickering methane/air diffusion flame,” Combust. Flame 99, 723–732 (1997).
[CrossRef]

U. O. Koylu, C. S. McEnally, D. E. Rosner, L. D. Pfefferle, “Simultaneous measurements of soot volume fraction and particle size/microstructure in flames using a thermophoretic sampling technique,” Combust. Flame 110, 494–507 (1997).
[CrossRef]

C. S. McEnally, U. O. Koylu, L. D. Pfefferle, D. R. Rosner, “Soot volume fraction and temperature measurements in laminar non premixed flames using thermocouples,” Combust. Flame 109, 701–720 (1997).
[CrossRef]

B. Mewes, J. M. Seitzman, “Soot volume fraction and particle size measurements with laser-induced incandescence,” Appl. Opt. 36, 709–717 (1997).
[CrossRef] [PubMed]

P. S. Greenberg, J. C. Ku, “Soot volume fraction imaging,” Appl. Opt. 36, 5514–5522 (1997).
[CrossRef] [PubMed]

1996 (4)

R. L. Vander Wal, “Laser-induced incandescence: detection issues,” Appl. Opt. 35, 6548–6559 (1996).
[CrossRef] [PubMed]

J. Zhang, C. M. Megaridis, “Soot suppression by Ferrocene in laminar ethylene/air nonpremixed flames,” Combust. Flame 105, 528–540 (1996).
[CrossRef]

C. R. Shaddix, R. C. Smyth, “Laser-induced incandescence measurements of soot production in steady and flickering methane, propane, and ethylene diffusion flames,” Combust. Flame 107, 418–452 (1996).
[CrossRef]

R. L. Vander Wal, Z. Zhou, M. Y. Choi, “Laser-induced incandescence calibration via gravimetric sampling,” Combust. Flame 105, 462–470 (1996).
[CrossRef]

1995 (3)

1994 (5)

F. Cignoli, S. Benecchi, G. Zizak, “Time-delayed detection of laser-induced incandescence for the two-dimensional visualization of soot in flames,” Appl. Opt. 33, 5778–5782 (1994).
[CrossRef] [PubMed]

U. O. Koylu, G. M. Faeth, “Optical properties of overfire soot in buoyant turbulent diffusion flames at long residence time,” J. Heat Transfer 116, 152–159 (1994).
[CrossRef]

R. A. Dobbins, G. W. Mulholland, N. P. Bryner, “Comparison of the fractal smoke optics model with light extinction measurements,” Atmos. Environ. 28, 889–897 (1994).
[CrossRef]

B. Quay, T. W. Lee, T. Ni, R. J. Santoro, “Spatially resolved measurements of soot volume fraction using laser-induced incandescence,” Combust. Flame 97, 384–392 (1994).
[CrossRef]

J. Lahaye, F. Ehrburger-Dolle, “Mechanisms of carbon black formation. Correlation with the morphology of the aggregates,” Carbon 32, 1319–1324 (1994).
[CrossRef]

1993 (4)

J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
[CrossRef]

R. Puri, T. F. Richardson, R. J. Santoro, R. A. Dobbins, “Aerosol dynamic processes of soot aggregates in a laminar ethene diffusion flame,” Combust. Flame 92, 320–333 (1993).
[CrossRef]

U. O. Koylu, G. M. Faeth, “Radiative properties of flame-generated soot,” J. Heat Transfer 115, 409–417 (1993).
[CrossRef]

M. Tappe, B. S. Haynes, J. H. Kent, “The effect of alkali metals on a laminar ethylene diffusion flame,” Combust. Flame 92, 266–273 (1993).
[CrossRef]

1992 (6)

P. A. Bonczyk, R. J. Hall, “Measurements of the fractal dimension of soot using UV laser radiation,” Langmuir 8, 1666–1670 (1992).
[CrossRef]

T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering techniques,” Prog. Energy Combust. Sci. 18, 13–45 (1992).
[CrossRef]

C. M. Sorensen, J. Cai, N. Lu, “Test of static structure factors for describing light scattering from fractal soot aggregates,” Langmuir 8, 2064–2069 (1992).
[CrossRef]

U. O. Koylu, G. M. Faeth, “Structure of overfire soot in buoyant turbulent diffusion flames at long resident times,” Combust. Flame 89, 140–156 (1992).
[CrossRef]

C. J. Dasch, “One-dimensional tomography: a conversion of Abel, onion-peeling, and filtered back projection methods,” Appl. Opt. 31, 1146–1152 (1992).
[CrossRef] [PubMed]

C. M. Sorensen, J. Cai, N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
[CrossRef] [PubMed]

1991 (4)

P. A. Bonczyk, R. J. Hall, “Fractal properties of soot agglomerates,” Langmuir 7, 1274–1280 (1991).
[CrossRef]

T. T. Charalampopoulos, H. Chang, “Effects of soot agglomeration on radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 46, 125–134 (1991).
[CrossRef]

R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
[CrossRef] [PubMed]

S. Gangopadhyay, I. Elminyawi, C. M. Sorensen, “Optical structure factor measurements of soot particles in a premixed flame,” Appl. Opt. 30, 4859–4864 (1991).
[CrossRef] [PubMed]

1990 (2)

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

C. M. Megaridis, R. A. Dobbins, “Morphology description of flame-generated materials,” Combust. Sci. Technol. 71, 95–109 (1990).
[CrossRef]

1989 (3)

C. M. Megaridis, R. A. Dobbins, “Comparison of soot growth and oxidation in smoking and non-smoking ethylene diffusion flames,” Combust. Sci. Technol. 66, 11–16 (1989).

S. Kumar, C. L. Tien “Effective diameter of agglomerates for radiative extinction and scattering,” Combust. Sci. Technol. 66, 199–216 (1989).
[CrossRef]

I. Colbeck, E. J. Hardman, R. M. Harrison, “Optical and dynamical properties of fractal cluster of carbonaceous smoke,” J. Aerosol. Sci. 20, 765–774 (1989).
[CrossRef]

1988 (1)

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

1987 (2)

R. J. Santoro, T. T. Yeh, J. J. Horvath, H. G. Semerjian, “The transport and growth of soot particles in laminar diffusion flames,” Combust. Sci. Technol. 53, 89–115 (1987).
[CrossRef]

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

1983 (1)

R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot particle measurements in diffusion flames,” Combust. Flame 51, 203–218 (1983).
[CrossRef]

Barbini, M.

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

Benecchi, S.

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

F. Cignoli, S. Benecchi, G. Zizak, “Time-delayed detection of laser-induced incandescence for the two-dimensional visualization of soot in flames,” Appl. Opt. 33, 5778–5782 (1994).
[CrossRef] [PubMed]

Bonczyk, P. A.

P. A. Bonczyk, R. J. Hall, “Measurements of the fractal dimension of soot using UV laser radiation,” Langmuir 8, 1666–1670 (1992).
[CrossRef]

P. A. Bonczyk, R. J. Hall, “Fractal properties of soot agglomerates,” Langmuir 7, 1274–1280 (1991).
[CrossRef]

Bryner, N. P.

R. A. Dobbins, G. W. Mulholland, N. P. Bryner, “Comparison of the fractal smoke optics model with light extinction measurements,” Atmos. Environ. 28, 889–897 (1994).
[CrossRef]

Cai, J.

J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
[CrossRef]

C. M. Sorensen, J. Cai, N. Lu, “Test of static structure factors for describing light scattering from fractal soot aggregates,” Langmuir 8, 2064–2069 (1992).
[CrossRef]

C. M. Sorensen, J. Cai, N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
[CrossRef] [PubMed]

Carvalho, M. G.

U. O. Koylu, G. M. Faeth, T. L. Farias, M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100, 621–633 (1995).
[CrossRef]

Chang, H.

T. T. Charalampopoulos, H. Chang, “Effects of soot agglomeration on radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 46, 125–134 (1991).
[CrossRef]

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

Charalampopoulos, T. T.

T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering techniques,” Prog. Energy Combust. Sci. 18, 13–45 (1992).
[CrossRef]

T. T. Charalampopoulos, H. Chang, “Effects of soot agglomeration on radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 46, 125–134 (1991).
[CrossRef]

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

Choi, M. Y.

R. L. Vander Wal, Z. Zhou, M. Y. Choi, “Laser-induced incandescence calibration via gravimetric sampling,” Combust. Flame 105, 462–470 (1996).
[CrossRef]

Cignoli, F.

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

F. Cignoli, S. Benecchi, G. Zizak, “Time-delayed detection of laser-induced incandescence for the two-dimensional visualization of soot in flames,” Appl. Opt. 33, 5778–5782 (1994).
[CrossRef] [PubMed]

Colbeck, I.

I. Colbeck, E. J. Hardman, R. M. Harrison, “Optical and dynamical properties of fractal cluster of carbonaceous smoke,” J. Aerosol. Sci. 20, 765–774 (1989).
[CrossRef]

Dasch, C. J.

De Iuliis, S.

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

Dobbins, R. A.

R. A. Dobbins, G. W. Mulholland, N. P. Bryner, “Comparison of the fractal smoke optics model with light extinction measurements,” Atmos. Environ. 28, 889–897 (1994).
[CrossRef]

R. Puri, T. F. Richardson, R. J. Santoro, R. A. Dobbins, “Aerosol dynamic processes of soot aggregates in a laminar ethene diffusion flame,” Combust. Flame 92, 320–333 (1993).
[CrossRef]

R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
[CrossRef] [PubMed]

C. M. Megaridis, R. A. Dobbins, “Morphology description of flame-generated materials,” Combust. Sci. Technol. 71, 95–109 (1990).
[CrossRef]

C. M. Megaridis, R. A. Dobbins, “Comparison of soot growth and oxidation in smoking and non-smoking ethylene diffusion flames,” Combust. Sci. Technol. 66, 11–16 (1989).

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

R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot particle measurements in diffusion flames,” Combust. Flame 51, 203–218 (1983).
[CrossRef]

R. A. Dobbins, R. J. Santoro, H. G. Semerajian, “Analysis of light scattering from soot using optical cross sections for aggregates,” in 23rd Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1525–1532.

C. M. Megaridis, R. A. Dobbins, “Soot aerosol dynamics in a laminar ethylene diffusion flame,” in 22nd Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1988), pp. 353–362.

Ehrburger-Dolle, F.

J. Lahaye, F. Ehrburger-Dolle, “Mechanisms of carbon black formation. Correlation with the morphology of the aggregates,” Carbon 32, 1319–1324 (1994).
[CrossRef]

Elminyawi, I.

Faeth, G. M.

U. O. Koylu, G. M. Faeth, T. L. Farias, M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100, 621–633 (1995).
[CrossRef]

U. O. Koylu, G. M. Faeth, “Optical properties of overfire soot in buoyant turbulent diffusion flames at long residence time,” J. Heat Transfer 116, 152–159 (1994).
[CrossRef]

U. O. Koylu, G. M. Faeth, “Radiative properties of flame-generated soot,” J. Heat Transfer 115, 409–417 (1993).
[CrossRef]

U. O. Koylu, G. M. Faeth, “Structure of overfire soot in buoyant turbulent diffusion flames at long resident times,” Combust. Flame 89, 140–156 (1992).
[CrossRef]

Farias, T. L.

U. O. Koylu, G. M. Faeth, T. L. Farias, M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100, 621–633 (1995).
[CrossRef]

Gangopadhyay, S.

Greenberg, P. S.

Gupta, S.

Hall, R. J.

P. A. Bonczyk, R. J. Hall, “Measurements of the fractal dimension of soot using UV laser radiation,” Langmuir 8, 1666–1670 (1992).
[CrossRef]

P. A. Bonczyk, R. J. Hall, “Fractal properties of soot agglomerates,” Langmuir 7, 1274–1280 (1991).
[CrossRef]

Hardman, E. J.

I. Colbeck, E. J. Hardman, R. M. Harrison, “Optical and dynamical properties of fractal cluster of carbonaceous smoke,” J. Aerosol. Sci. 20, 765–774 (1989).
[CrossRef]

Harrington, J. F.

C. R. Shaddix, J. F. Harrington, K. C. Smyth, “Quantitative measurements of enhanced soot production in a flickering methane/air diffusion flame,” Combust. Flame 99, 723–732 (1997).
[CrossRef]

Harrison, R. M.

I. Colbeck, E. J. Hardman, R. M. Harrison, “Optical and dynamical properties of fractal cluster of carbonaceous smoke,” J. Aerosol. Sci. 20, 765–774 (1989).
[CrossRef]

Haynes, B. S.

M. Tappe, B. S. Haynes, J. H. Kent, “The effect of alkali metals on a laminar ethylene diffusion flame,” Combust. Flame 92, 266–273 (1993).
[CrossRef]

Horvath, J. J.

R. J. Santoro, T. T. Yeh, J. J. Horvath, H. G. Semerjian, “The transport and growth of soot particles in laminar diffusion flames,” Combust. Sci. Technol. 53, 89–115 (1987).
[CrossRef]

Kent, J. H.

M. Tappe, B. S. Haynes, J. H. Kent, “The effect of alkali metals on a laminar ethylene diffusion flame,” Combust. Flame 92, 266–273 (1993).
[CrossRef]

Koylu, U. O.

C. S. McEnally, U. O. Koylu, L. D. Pfefferle, D. R. Rosner, “Soot volume fraction and temperature measurements in laminar non premixed flames using thermocouples,” Combust. Flame 109, 701–720 (1997).
[CrossRef]

U. O. Koylu, C. S. McEnally, D. E. Rosner, L. D. Pfefferle, “Simultaneous measurements of soot volume fraction and particle size/microstructure in flames using a thermophoretic sampling technique,” Combust. Flame 110, 494–507 (1997).
[CrossRef]

U. O. Koylu, G. M. Faeth, T. L. Farias, M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100, 621–633 (1995).
[CrossRef]

U. O. Koylu, G. M. Faeth, “Optical properties of overfire soot in buoyant turbulent diffusion flames at long residence time,” J. Heat Transfer 116, 152–159 (1994).
[CrossRef]

U. O. Koylu, G. M. Faeth, “Radiative properties of flame-generated soot,” J. Heat Transfer 115, 409–417 (1993).
[CrossRef]

U. O. Koylu, G. M. Faeth, “Structure of overfire soot in buoyant turbulent diffusion flames at long resident times,” Combust. Flame 89, 140–156 (1992).
[CrossRef]

Ku, J. C.

Kumar, S.

S. Kumar, C. L. Tien “Effective diameter of agglomerates for radiative extinction and scattering,” Combust. Sci. Technol. 66, 199–216 (1989).
[CrossRef]

Lahaye, J.

J. Lahaye, F. Ehrburger-Dolle, “Mechanisms of carbon black formation. Correlation with the morphology of the aggregates,” Carbon 32, 1319–1324 (1994).
[CrossRef]

Lee, T. W.

B. Quay, T. W. Lee, T. Ni, R. J. Santoro, “Spatially resolved measurements of soot volume fraction using laser-induced incandescence,” Combust. Flame 97, 384–392 (1994).
[CrossRef]

Leipertz, A.

Litzinger, T. A.

J. A. Pinson, T. A. Litzinger, R. J. Santoro, “New techniques for quantitative, planar soot measurements,” presented at the fall technical meeting of the Eastern States Sections, Combustion Institute, Princeton, N.J., 25–27 October 1993.

Lu, N.

J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
[CrossRef]

C. M. Sorensen, J. Cai, N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
[CrossRef] [PubMed]

C. M. Sorensen, J. Cai, N. Lu, “Test of static structure factors for describing light scattering from fractal soot aggregates,” Langmuir 8, 2064–2069 (1992).
[CrossRef]

McEnally, C. S.

C. S. McEnally, U. O. Koylu, L. D. Pfefferle, D. R. Rosner, “Soot volume fraction and temperature measurements in laminar non premixed flames using thermocouples,” Combust. Flame 109, 701–720 (1997).
[CrossRef]

U. O. Koylu, C. S. McEnally, D. E. Rosner, L. D. Pfefferle, “Simultaneous measurements of soot volume fraction and particle size/microstructure in flames using a thermophoretic sampling technique,” Combust. Flame 110, 494–507 (1997).
[CrossRef]

Megaridis, C. M.

J. Zhang, C. M. Megaridis, “Soot suppression by Ferrocene in laminar ethylene/air nonpremixed flames,” Combust. Flame 105, 528–540 (1996).
[CrossRef]

R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
[CrossRef] [PubMed]

C. M. Megaridis, R. A. Dobbins, “Morphology description of flame-generated materials,” Combust. Sci. Technol. 71, 95–109 (1990).
[CrossRef]

C. M. Megaridis, R. A. Dobbins, “Comparison of soot growth and oxidation in smoking and non-smoking ethylene diffusion flames,” Combust. Sci. Technol. 66, 11–16 (1989).

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

C. M. Megaridis, R. A. Dobbins, “Soot aerosol dynamics in a laminar ethylene diffusion flame,” in 22nd Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1988), pp. 353–362.

Mewes, B.

Mountain, R. D.

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

Mulholland, G. W.

R. A. Dobbins, G. W. Mulholland, N. P. Bryner, “Comparison of the fractal smoke optics model with light extinction measurements,” Atmos. Environ. 28, 889–897 (1994).
[CrossRef]

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

Ni, T.

T. Ni, J. A. Pinson, S. Gupta, R. J. Santoro, “Two-dimensional imaging of soot volume fraction by the use of laser-induced incandescence,” Appl. Opt. 34, 7083–7091 (1995).
[CrossRef] [PubMed]

B. Quay, T. W. Lee, T. Ni, R. J. Santoro, “Spatially resolved measurements of soot volume fraction using laser-induced incandescence,” Combust. Flame 97, 384–392 (1994).
[CrossRef]

Pfefferle, L. D.

C. S. McEnally, U. O. Koylu, L. D. Pfefferle, D. R. Rosner, “Soot volume fraction and temperature measurements in laminar non premixed flames using thermocouples,” Combust. Flame 109, 701–720 (1997).
[CrossRef]

U. O. Koylu, C. S. McEnally, D. E. Rosner, L. D. Pfefferle, “Simultaneous measurements of soot volume fraction and particle size/microstructure in flames using a thermophoretic sampling technique,” Combust. Flame 110, 494–507 (1997).
[CrossRef]

Pinson, J. A.

T. Ni, J. A. Pinson, S. Gupta, R. J. Santoro, “Two-dimensional imaging of soot volume fraction by the use of laser-induced incandescence,” Appl. Opt. 34, 7083–7091 (1995).
[CrossRef] [PubMed]

J. A. Pinson, T. A. Litzinger, R. J. Santoro, “New techniques for quantitative, planar soot measurements,” presented at the fall technical meeting of the Eastern States Sections, Combustion Institute, Princeton, N.J., 25–27 October 1993.

Puri, R.

R. Puri, T. F. Richardson, R. J. Santoro, R. A. Dobbins, “Aerosol dynamic processes of soot aggregates in a laminar ethene diffusion flame,” Combust. Flame 92, 320–333 (1993).
[CrossRef]

Quay, B.

B. Quay, T. W. Lee, T. Ni, R. J. Santoro, “Spatially resolved measurements of soot volume fraction using laser-induced incandescence,” Combust. Flame 97, 384–392 (1994).
[CrossRef]

Richardson, T. F.

R. Puri, T. F. Richardson, R. J. Santoro, R. A. Dobbins, “Aerosol dynamic processes of soot aggregates in a laminar ethene diffusion flame,” Combust. Flame 92, 320–333 (1993).
[CrossRef]

Rosner, D. E.

U. O. Koylu, C. S. McEnally, D. E. Rosner, L. D. Pfefferle, “Simultaneous measurements of soot volume fraction and particle size/microstructure in flames using a thermophoretic sampling technique,” Combust. Flame 110, 494–507 (1997).
[CrossRef]

Rosner, D. R.

C. S. McEnally, U. O. Koylu, L. D. Pfefferle, D. R. Rosner, “Soot volume fraction and temperature measurements in laminar non premixed flames using thermocouples,” Combust. Flame 109, 701–720 (1997).
[CrossRef]

Santoro, R. J.

T. Ni, J. A. Pinson, S. Gupta, R. J. Santoro, “Two-dimensional imaging of soot volume fraction by the use of laser-induced incandescence,” Appl. Opt. 34, 7083–7091 (1995).
[CrossRef] [PubMed]

B. Quay, T. W. Lee, T. Ni, R. J. Santoro, “Spatially resolved measurements of soot volume fraction using laser-induced incandescence,” Combust. Flame 97, 384–392 (1994).
[CrossRef]

R. Puri, T. F. Richardson, R. J. Santoro, R. A. Dobbins, “Aerosol dynamic processes of soot aggregates in a laminar ethene diffusion flame,” Combust. Flame 92, 320–333 (1993).
[CrossRef]

R. J. Santoro, T. T. Yeh, J. J. Horvath, H. G. Semerjian, “The transport and growth of soot particles in laminar diffusion flames,” Combust. Sci. Technol. 53, 89–115 (1987).
[CrossRef]

R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot particle measurements in diffusion flames,” Combust. Flame 51, 203–218 (1983).
[CrossRef]

R. A. Dobbins, R. J. Santoro, H. G. Semerajian, “Analysis of light scattering from soot using optical cross sections for aggregates,” in 23rd Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1525–1532.

R. J. Santoro, H. G. Semerjian, “Soot formation in diffusion flames: flow rate, fuels species and temperature effects,” in 20th Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1984), pp. 997–1006.

J. A. Pinson, T. A. Litzinger, R. J. Santoro, “New techniques for quantitative, planar soot measurements,” presented at the fall technical meeting of the Eastern States Sections, Combustion Institute, Princeton, N.J., 25–27 October 1993.

Schraml, S.

Seitzman, J. M.

Semerajian, H. G.

R. A. Dobbins, R. J. Santoro, H. G. Semerajian, “Analysis of light scattering from soot using optical cross sections for aggregates,” in 23rd Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1525–1532.

Semerjian, H. G.

R. J. Santoro, T. T. Yeh, J. J. Horvath, H. G. Semerjian, “The transport and growth of soot particles in laminar diffusion flames,” Combust. Sci. Technol. 53, 89–115 (1987).
[CrossRef]

R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot particle measurements in diffusion flames,” Combust. Flame 51, 203–218 (1983).
[CrossRef]

R. J. Santoro, H. G. Semerjian, “Soot formation in diffusion flames: flow rate, fuels species and temperature effects,” in 20th Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1984), pp. 997–1006.

Shaddix, C. R.

C. R. Shaddix, J. F. Harrington, K. C. Smyth, “Quantitative measurements of enhanced soot production in a flickering methane/air diffusion flame,” Combust. Flame 99, 723–732 (1997).
[CrossRef]

C. R. Shaddix, R. C. Smyth, “Laser-induced incandescence measurements of soot production in steady and flickering methane, propane, and ethylene diffusion flames,” Combust. Flame 107, 418–452 (1996).
[CrossRef]

Smyth, K. C.

C. R. Shaddix, J. F. Harrington, K. C. Smyth, “Quantitative measurements of enhanced soot production in a flickering methane/air diffusion flame,” Combust. Flame 99, 723–732 (1997).
[CrossRef]

Smyth, R. C.

C. R. Shaddix, R. C. Smyth, “Laser-induced incandescence measurements of soot production in steady and flickering methane, propane, and ethylene diffusion flames,” Combust. Flame 107, 418–452 (1996).
[CrossRef]

Sorensen, C. M.

J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
[CrossRef]

C. M. Sorensen, J. Cai, N. Lu, “Test of static structure factors for describing light scattering from fractal soot aggregates,” Langmuir 8, 2064–2069 (1992).
[CrossRef]

C. M. Sorensen, J. Cai, N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
[CrossRef] [PubMed]

S. Gangopadhyay, I. Elminyawi, C. M. Sorensen, “Optical structure factor measurements of soot particles in a premixed flame,” Appl. Opt. 30, 4859–4864 (1991).
[CrossRef] [PubMed]

Tappe, M.

M. Tappe, B. S. Haynes, J. H. Kent, “The effect of alkali metals on a laminar ethylene diffusion flame,” Combust. Flame 92, 266–273 (1993).
[CrossRef]

Tien, C. L.

S. Kumar, C. L. Tien “Effective diameter of agglomerates for radiative extinction and scattering,” Combust. Sci. Technol. 66, 199–216 (1989).
[CrossRef]

Vander Wal, R. L.

R. L. Vander Wal, Z. Zhou, M. Y. Choi, “Laser-induced incandescence calibration via gravimetric sampling,” Combust. Flame 105, 462–470 (1996).
[CrossRef]

R. L. Vander Wal, “Laser-induced incandescence: detection issues,” Appl. Opt. 35, 6548–6559 (1996).
[CrossRef] [PubMed]

Will, S.

Yeh, T. T.

R. J. Santoro, T. T. Yeh, J. J. Horvath, H. G. Semerjian, “The transport and growth of soot particles in laminar diffusion flames,” Combust. Sci. Technol. 53, 89–115 (1987).
[CrossRef]

Zhang, J.

J. Zhang, C. M. Megaridis, “Soot suppression by Ferrocene in laminar ethylene/air nonpremixed flames,” Combust. Flame 105, 528–540 (1996).
[CrossRef]

Zhou, Z.

R. L. Vander Wal, Z. Zhou, M. Y. Choi, “Laser-induced incandescence calibration via gravimetric sampling,” Combust. Flame 105, 462–470 (1996).
[CrossRef]

Zizak, G.

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

F. Cignoli, S. Benecchi, G. Zizak, “Time-delayed detection of laser-induced incandescence for the two-dimensional visualization of soot in flames,” Appl. Opt. 33, 5778–5782 (1994).
[CrossRef] [PubMed]

Appl. Opt. (9)

R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
[CrossRef] [PubMed]

S. Gangopadhyay, I. Elminyawi, C. M. Sorensen, “Optical structure factor measurements of soot particles in a premixed flame,” Appl. Opt. 30, 4859–4864 (1991).
[CrossRef] [PubMed]

C. J. Dasch, “One-dimensional tomography: a conversion of Abel, onion-peeling, and filtered back projection methods,” Appl. Opt. 31, 1146–1152 (1992).
[CrossRef] [PubMed]

F. Cignoli, S. Benecchi, G. Zizak, “Time-delayed detection of laser-induced incandescence for the two-dimensional visualization of soot in flames,” Appl. Opt. 33, 5778–5782 (1994).
[CrossRef] [PubMed]

B. Mewes, J. M. Seitzman, “Soot volume fraction and particle size measurements with laser-induced incandescence,” Appl. Opt. 36, 709–717 (1997).
[CrossRef] [PubMed]

P. S. Greenberg, J. C. Ku, “Soot volume fraction imaging,” Appl. Opt. 36, 5514–5522 (1997).
[CrossRef] [PubMed]

T. Ni, J. A. Pinson, S. Gupta, R. J. Santoro, “Two-dimensional imaging of soot volume fraction by the use of laser-induced incandescence,” Appl. Opt. 34, 7083–7091 (1995).
[CrossRef] [PubMed]

R. L. Vander Wal, “Laser-induced incandescence: detection issues,” Appl. Opt. 35, 6548–6559 (1996).
[CrossRef] [PubMed]

C. M. Sorensen, J. Cai, N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
[CrossRef] [PubMed]

Atmos. Environ. (1)

R. A. Dobbins, G. W. Mulholland, N. P. Bryner, “Comparison of the fractal smoke optics model with light extinction measurements,” Atmos. Environ. 28, 889–897 (1994).
[CrossRef]

Carbon (1)

J. Lahaye, F. Ehrburger-Dolle, “Mechanisms of carbon black formation. Correlation with the morphology of the aggregates,” Carbon 32, 1319–1324 (1994).
[CrossRef]

Combust. Flame (13)

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

C. R. Shaddix, R. C. Smyth, “Laser-induced incandescence measurements of soot production in steady and flickering methane, propane, and ethylene diffusion flames,” Combust. Flame 107, 418–452 (1996).
[CrossRef]

R. L. Vander Wal, Z. Zhou, M. Y. Choi, “Laser-induced incandescence calibration via gravimetric sampling,” Combust. Flame 105, 462–470 (1996).
[CrossRef]

B. Quay, T. W. Lee, T. Ni, R. J. Santoro, “Spatially resolved measurements of soot volume fraction using laser-induced incandescence,” Combust. Flame 97, 384–392 (1994).
[CrossRef]

C. R. Shaddix, J. F. Harrington, K. C. Smyth, “Quantitative measurements of enhanced soot production in a flickering methane/air diffusion flame,” Combust. Flame 99, 723–732 (1997).
[CrossRef]

R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot particle measurements in diffusion flames,” Combust. Flame 51, 203–218 (1983).
[CrossRef]

U. O. Koylu, G. M. Faeth, “Structure of overfire soot in buoyant turbulent diffusion flames at long resident times,” Combust. Flame 89, 140–156 (1992).
[CrossRef]

U. O. Koylu, C. S. McEnally, D. E. Rosner, L. D. Pfefferle, “Simultaneous measurements of soot volume fraction and particle size/microstructure in flames using a thermophoretic sampling technique,” Combust. Flame 110, 494–507 (1997).
[CrossRef]

U. O. Koylu, G. M. Faeth, T. L. Farias, M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100, 621–633 (1995).
[CrossRef]

C. S. McEnally, U. O. Koylu, L. D. Pfefferle, D. R. Rosner, “Soot volume fraction and temperature measurements in laminar non premixed flames using thermocouples,” Combust. Flame 109, 701–720 (1997).
[CrossRef]

M. Tappe, B. S. Haynes, J. H. Kent, “The effect of alkali metals on a laminar ethylene diffusion flame,” Combust. Flame 92, 266–273 (1993).
[CrossRef]

J. Zhang, C. M. Megaridis, “Soot suppression by Ferrocene in laminar ethylene/air nonpremixed flames,” Combust. Flame 105, 528–540 (1996).
[CrossRef]

R. Puri, T. F. Richardson, R. J. Santoro, R. A. Dobbins, “Aerosol dynamic processes of soot aggregates in a laminar ethene diffusion flame,” Combust. Flame 92, 320–333 (1993).
[CrossRef]

Combust. Sci. Technol. (4)

S. Kumar, C. L. Tien “Effective diameter of agglomerates for radiative extinction and scattering,” Combust. Sci. Technol. 66, 199–216 (1989).
[CrossRef]

C. M. Megaridis, R. A. Dobbins, “Morphology description of flame-generated materials,” Combust. Sci. Technol. 71, 95–109 (1990).
[CrossRef]

C. M. Megaridis, R. A. Dobbins, “Comparison of soot growth and oxidation in smoking and non-smoking ethylene diffusion flames,” Combust. Sci. Technol. 66, 11–16 (1989).

R. J. Santoro, T. T. Yeh, J. J. Horvath, H. G. Semerjian, “The transport and growth of soot particles in laminar diffusion flames,” Combust. Sci. Technol. 53, 89–115 (1987).
[CrossRef]

J. Aerosol. Sci. (1)

I. Colbeck, E. J. Hardman, R. M. Harrison, “Optical and dynamical properties of fractal cluster of carbonaceous smoke,” J. Aerosol. Sci. 20, 765–774 (1989).
[CrossRef]

J. Heat Transfer (2)

U. O. Koylu, G. M. Faeth, “Radiative properties of flame-generated soot,” J. Heat Transfer 115, 409–417 (1993).
[CrossRef]

U. O. Koylu, G. M. Faeth, “Optical properties of overfire soot in buoyant turbulent diffusion flames at long residence time,” J. Heat Transfer 116, 152–159 (1994).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

T. T. Charalampopoulos, H. Chang, “Effects of soot agglomeration on radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 46, 125–134 (1991).
[CrossRef]

Langmuir (6)

C. M. Sorensen, J. Cai, N. Lu, “Test of static structure factors for describing light scattering from fractal soot aggregates,” Langmuir 8, 2064–2069 (1992).
[CrossRef]

P. A. Bonczyk, R. J. Hall, “Fractal properties of soot agglomerates,” Langmuir 7, 1274–1280 (1991).
[CrossRef]

P. A. Bonczyk, R. J. Hall, “Measurements of the fractal dimension of soot using UV laser radiation,” Langmuir 8, 1666–1670 (1992).
[CrossRef]

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

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

J. Cai, N. Lu, C. M. Sorensen, “Comparison of size and morphology of soot aggregates as determined by light scattering and electron microscope analysis,” Langmuir 9, 2861–2867 (1993).
[CrossRef]

Opt. Lett. (1)

Proc. R. Soc. London Ser. A (1)

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

Prog. Energy Combust. Sci. (1)

T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering techniques,” Prog. Energy Combust. Sci. 18, 13–45 (1992).
[CrossRef]

Other (4)

R. A. Dobbins, R. J. Santoro, H. G. Semerajian, “Analysis of light scattering from soot using optical cross sections for aggregates,” in 23rd Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1525–1532.

C. M. Megaridis, R. A. Dobbins, “Soot aerosol dynamics in a laminar ethylene diffusion flame,” in 22nd Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1988), pp. 353–362.

J. A. Pinson, T. A. Litzinger, R. J. Santoro, “New techniques for quantitative, planar soot measurements,” presented at the fall technical meeting of the Eastern States Sections, Combustion Institute, Princeton, N.J., 25–27 October 1993.

R. J. Santoro, H. G. Semerjian, “Soot formation in diffusion flames: flow rate, fuels species and temperature effects,” in 20th Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1984), pp. 997–1006.

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Figures (11)

Fig. 1
Fig. 1

Dependence of the moment ratio f n on the distribution standard deviation σ for two values of N m .

Fig. 2
Fig. 2

Integral function S qR g ¯ (symbols) and its fitting function S* in the form of Eq. (21). The two values of R gm1 and their related distribution parameters are shown.

Fig. 3
Fig. 3

Dependence of R gm1 on the intensity ratio I 1/I 2for σ = 2.1, σ = 1.7, and σ = 2.5.

Fig. 4
Fig. 4

Experimental setup: PMT, photomultiplier tube.

Fig. 5
Fig. 5

Soot volume fraction profiles at the three levels investigated.

Fig. 6
Fig. 6

Radial profiles of R gm1 at the three levels.

Fig. 7
Fig. 7

Volume-mean diameter profiles.

Fig. 8
Fig. 8

Primary particle diameter profiles.

Fig. 9
Fig. 9

Radial profiles of (a) the number of the primary particles per aggregate , (b) the number of aggregates per unit volume N a , (c) the number of particles per unit volume N p .

Fig. 10
Fig. 10

Dependence of S* on the scattering wave vector and shift of this quantity with the standard deviation σ for (a) large and (b) small aggregates.

Fig. 11
Fig. 11

Modification of the profiles of (a) R gm1 , (b) D 30, and (c) dp with the standard deviation at the second level investigated (0.60 of the total flame height).

Equations (30)

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

τ λ = ln I L / I 0 = - K ext L ,
K abs = 36 π E m f v λ .
E m = 1 6 Im m 2 - 1 m 2 + 2 = nk n 2 + k 2 + 2 2 + 4 n 2 k 2 ,
f v = π 8   dp 3 N p = π 8   D 30 3 N a ,
N = K f R g / dp D f ,
R g 2 = i r i 2 N ,
C vv p = x p 6 F m / k 2 ,
F m = m 2 - 1 m 2 + 2 2 .
C vv a ϑ = C vv p N 2 S qR g ,
q = 4 π λ sin ϑ 2 .
I scatt m ϑ = η I 0 N a C vv a = η I 0 C vv p N a N 2 S qR g ,
S qR g = 1 + s = 1 4   C s qR g 2 s - D f / 8 ,
m q ¯ = 0   N q p N d N .
I scatt p ϑ = N a     I scatt ϑ ,   N p N d N = η I 0 C vv p N a     N 2 S qR g p N d N ,
I scatt p ϑ = η I 0 C vv p N a m 2 ¯ S qR g ¯ = η I 0 Q vv ϑ ,
S qR g ¯ = S * qR gs
D 30 = λ π 4 π E m Q vv ϑ F m f n S qR g ¯ K abs 1 / 3 .
D 30 3 = dp 3 N p N a = dp 3 N ¯ .
R g ¯ =   R g p N d N ;
R g 2 ¯ =   R g 2 N 2 p N d N   N 2 p N d N ;
R gKF 2 ¯ =   R g 2 D f p N d N   R g D f p N d N 2 / D f ;
R gm 1 = dp N ¯ / K f 1 / D f .
R g 2 ¯ 1 / 2 R g ¯ = m 2 + 2 / D f ¯ 1 / 2 m 1 / D f ¯ m 2 ¯ 1 / 2 ,
R gKF ¯ R g ¯ = m 2 ¯ 1 / D f m 1 / D f m 1 ¯ 1 / D f ,
R gm 1 R g ¯ = m 1 ¯ 1 / D f m 1 / D f ¯ .
p N = exp - 1 2 ln   N / N m ln   σ 2 2 π   N   ln   σ ,
S * qR gm 1 = 1 1 + P 1 qR gm 1   +   P 2 qR gm 1 2 + P 3 qR gm 1 3 + P 4 qR gm 1 4 ,
I 1 I 2 =   S q 1 R g N 2 p N d N   S q 2 R g N 2 p N d N = S * q 1 R gm 1 S * q 2 R gm 1 .
R gm 1 = n = 0 9   C n I 1 / I 2 n ,
dp 3 - D f = D 30 3 K f R gm 1 D f .

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