Abstract

A computationally fast method to determine values and their uncertainty for particulate system volume median diameter, volume fraction, and size distribution width is presented. These properties cannot be obtained for submicrometer particulate by diffraction-based methods. The technique relies on a least-mean-squares method applied over a prespecified size range and distribution width. Prespecifying the range significantly reduces the number of calculations required to determine the particulate parameters from experimental data, allowing the practical evaluation of large data sets. The solution method that was developed has significant advantages over ratio-style calculations that are more commonly performed, the primary of which is a simple method to determine errors in the measurement parameters. We evaluated the predicted performance for a specific experimental system for various levels of noise, with monodisperse and log-normal distributions, by analyzing synthetic data with the algorithm. Results were a quantitative statement of system accuracy. In addition, synthetic log-normal data evaluated with monodisperse models revealed significant and systematic errors in the predicted volume median diameter. These errors indicate that, in general, systems with a significant size distribution width must be analyzed with a model that includes this size distribution. Finally, calibrated polystyrene spheres were measured with an experimental system that used four simultaneous scattering measurements, and all diameters were within the reported uncertainty.

© 2002 Optical Society of America

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References

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  1. C. S. Johnson, D. A. Gabriel, Laser Light Scattering (Dover, New York, 1981).
  2. M. R. Zachariah, D. Chin, H. G. Semerjian, J. L. Katz, “Dynamic light scattering and angular dissymmetry for the in situ measurements of silicon dioxide particle synthesis in flames,” Appl. Opt. 28, 530–536 (1989).
    [CrossRef] [PubMed]
  3. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  4. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  5. A. J. Rulison, P. F. Miquel, J. L. Katz, “Titania and silica powders produced in a counterflow diffusion flame,” J. Mater. Res. 11, 3083–3089 (1996).
    [CrossRef]
  6. P. F. Miquel, C. H. Hung, J. L. Katz, “Formation of V2O5-based mixed oxides in flames,” J. Mater. Res. 8, 2404–2413 (1993).
    [CrossRef]
  7. J. L. Katz, P. F. Miquel, “Synthesis and applications of oxides and mixed oxides produced by a flame process,” Nanostruct. Mater. 4, 551–557 (1994).
    [CrossRef]
  8. R. L. Axelbaum, C. R. Lottes, J. I. Huertas, L. J. Rosen, “Gas-phase combustion synthesis of aluminum nitride powder,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1891–1897.
    [CrossRef]
  9. Y. Xing, U. O. Koylu, D. E. Rosner, “Synthesis and restructing of inorganic nanoparticles in laminar counterflow diffusion flames,” Combust. Flame 107, 85–102 (1996).
    [CrossRef]
  10. K. Brezinsky, “The gas phase combustion synthesis of materials,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1805–1816.
    [CrossRef]
  11. S. E. Pratsinis, “Flame aerosol synthesis of ceramic powders,” Prog. Energy Combust. Sci. 24, 197–219 (1998).
    [CrossRef]
  12. M. S. Wooldridge, “Gas phase combustion synthesis of particles,” Prog. Energy Combust. Sci. 24, 63–87 (1998).
    [CrossRef]
  13. M. R. Zachariah, P. Dimitriou, “Controlled nucleation in aerosol reactors for suppression of agglomerate formation: a numerical study,” Aerosol Sci. Technol. 13, 413–425 (1990).
    [CrossRef]
  14. I. H. Malitson, “Interspecimen comparison of refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
    [CrossRef]
  15. A. H. Lefebvre, Atomization and Sprays (Hemisphere, Washington, D.C., 1989).
  16. M. R. Zachariah, H. G. Semerjian, “Simulation of ceramic particle formation: comparison with in-situ measurements,” AIChE J. 35, 2003–2012 (1989).
    [CrossRef]
  17. R. A. Dobbins, G. W. Mulholland, “Interpretation of optical measurements of flame generated particles,” Combust. Sci. Technol. 40, 175–191 (1984).
    [CrossRef]
  18. T. Parker, E. Jepsen, H. McCann, “Measurements and error analysis of droplet size in optically thick diesel sprays,” in the Twenty-Seventh Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1998), pp. 1881–1888.
    [CrossRef]
  19. C. Xiao-shu, W. Nai-ning, W. Jing-ming, Z. Gang, “Experimental investigation of the light extinction method for measuring aerosol size distributions,” J. Aerosol Sci. 23, 749–757 (1992).
    [CrossRef]
  20. T. Wriedt, “A review of elastic light scattering theories,” Part. Part. Syst. Charact. 15, 67–74 (1997).
    [CrossRef]
  21. R. A. Dobbins, M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
    [CrossRef] [PubMed]
  22. N. G. Glumac, Y. J. Chen, G. Skandan, “Diagnostics and modeling of nanopowders synthesis in low pressure flames,” J. Mater. Res. 13, 2572–2579 (1998).
    [CrossRef]
  23. T. Hatch, S. P. Choate, “Statistical description of the size properties of non-uniform particulate substances,” J. Franklin Inst. 207, 369–387 (1929).
    [CrossRef]
  24. W. Hinds, Aerosol Technology (Wiley, New York, 1982).
  25. P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, New York, 1992).
  26. W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  27. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, Cambridge, Mass., 1988).
  28. T. Inagaki, E. T. Arakawa, R. N. Hamm, M. W. Williams, “Optical properties of polystyrene from the near infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
    [CrossRef]

1998

S. E. Pratsinis, “Flame aerosol synthesis of ceramic powders,” Prog. Energy Combust. Sci. 24, 197–219 (1998).
[CrossRef]

M. S. Wooldridge, “Gas phase combustion synthesis of particles,” Prog. Energy Combust. Sci. 24, 63–87 (1998).
[CrossRef]

N. G. Glumac, Y. J. Chen, G. Skandan, “Diagnostics and modeling of nanopowders synthesis in low pressure flames,” J. Mater. Res. 13, 2572–2579 (1998).
[CrossRef]

1997

T. Wriedt, “A review of elastic light scattering theories,” Part. Part. Syst. Charact. 15, 67–74 (1997).
[CrossRef]

1996

Y. Xing, U. O. Koylu, D. E. Rosner, “Synthesis and restructing of inorganic nanoparticles in laminar counterflow diffusion flames,” Combust. Flame 107, 85–102 (1996).
[CrossRef]

A. J. Rulison, P. F. Miquel, J. L. Katz, “Titania and silica powders produced in a counterflow diffusion flame,” J. Mater. Res. 11, 3083–3089 (1996).
[CrossRef]

1994

J. L. Katz, P. F. Miquel, “Synthesis and applications of oxides and mixed oxides produced by a flame process,” Nanostruct. Mater. 4, 551–557 (1994).
[CrossRef]

1993

P. F. Miquel, C. H. Hung, J. L. Katz, “Formation of V2O5-based mixed oxides in flames,” J. Mater. Res. 8, 2404–2413 (1993).
[CrossRef]

1992

C. Xiao-shu, W. Nai-ning, W. Jing-ming, Z. Gang, “Experimental investigation of the light extinction method for measuring aerosol size distributions,” J. Aerosol Sci. 23, 749–757 (1992).
[CrossRef]

1991

1990

M. R. Zachariah, P. Dimitriou, “Controlled nucleation in aerosol reactors for suppression of agglomerate formation: a numerical study,” Aerosol Sci. Technol. 13, 413–425 (1990).
[CrossRef]

1989

1984

R. A. Dobbins, G. W. Mulholland, “Interpretation of optical measurements of flame generated particles,” Combust. Sci. Technol. 40, 175–191 (1984).
[CrossRef]

1977

T. Inagaki, E. T. Arakawa, R. N. Hamm, M. W. Williams, “Optical properties of polystyrene from the near infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

1965

1929

T. Hatch, S. P. Choate, “Statistical description of the size properties of non-uniform particulate substances,” J. Franklin Inst. 207, 369–387 (1929).
[CrossRef]

Arakawa, E. T.

T. Inagaki, E. T. Arakawa, R. N. Hamm, M. W. Williams, “Optical properties of polystyrene from the near infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Axelbaum, R. L.

R. L. Axelbaum, C. R. Lottes, J. I. Huertas, L. J. Rosen, “Gas-phase combustion synthesis of aluminum nitride powder,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1891–1897.
[CrossRef]

Bevington, P. R.

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, New York, 1992).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Brezinsky, K.

K. Brezinsky, “The gas phase combustion synthesis of materials,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1805–1816.
[CrossRef]

Chen, Y. J.

N. G. Glumac, Y. J. Chen, G. Skandan, “Diagnostics and modeling of nanopowders synthesis in low pressure flames,” J. Mater. Res. 13, 2572–2579 (1998).
[CrossRef]

Chin, D.

Choate, S. P.

T. Hatch, S. P. Choate, “Statistical description of the size properties of non-uniform particulate substances,” J. Franklin Inst. 207, 369–387 (1929).
[CrossRef]

Dimitriou, P.

M. R. Zachariah, P. Dimitriou, “Controlled nucleation in aerosol reactors for suppression of agglomerate formation: a numerical study,” Aerosol Sci. Technol. 13, 413–425 (1990).
[CrossRef]

Dobbins, R. A.

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

R. A. Dobbins, G. W. Mulholland, “Interpretation of optical measurements of flame generated particles,” Combust. Sci. Technol. 40, 175–191 (1984).
[CrossRef]

Eckbreth, A. C.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, Cambridge, Mass., 1988).

Flannery, B. P.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Gabriel, D. A.

C. S. Johnson, D. A. Gabriel, Laser Light Scattering (Dover, New York, 1981).

Gang, Z.

C. Xiao-shu, W. Nai-ning, W. Jing-ming, Z. Gang, “Experimental investigation of the light extinction method for measuring aerosol size distributions,” J. Aerosol Sci. 23, 749–757 (1992).
[CrossRef]

Glumac, N. G.

N. G. Glumac, Y. J. Chen, G. Skandan, “Diagnostics and modeling of nanopowders synthesis in low pressure flames,” J. Mater. Res. 13, 2572–2579 (1998).
[CrossRef]

Hamm, R. N.

T. Inagaki, E. T. Arakawa, R. N. Hamm, M. W. Williams, “Optical properties of polystyrene from the near infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Hatch, T.

T. Hatch, S. P. Choate, “Statistical description of the size properties of non-uniform particulate substances,” J. Franklin Inst. 207, 369–387 (1929).
[CrossRef]

Hinds, W.

W. Hinds, Aerosol Technology (Wiley, New York, 1982).

Huertas, J. I.

R. L. Axelbaum, C. R. Lottes, J. I. Huertas, L. J. Rosen, “Gas-phase combustion synthesis of aluminum nitride powder,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1891–1897.
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hung, C. H.

P. F. Miquel, C. H. Hung, J. L. Katz, “Formation of V2O5-based mixed oxides in flames,” J. Mater. Res. 8, 2404–2413 (1993).
[CrossRef]

Inagaki, T.

T. Inagaki, E. T. Arakawa, R. N. Hamm, M. W. Williams, “Optical properties of polystyrene from the near infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Jepsen, E.

T. Parker, E. Jepsen, H. McCann, “Measurements and error analysis of droplet size in optically thick diesel sprays,” in the Twenty-Seventh Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1998), pp. 1881–1888.
[CrossRef]

Jing-ming, W.

C. Xiao-shu, W. Nai-ning, W. Jing-ming, Z. Gang, “Experimental investigation of the light extinction method for measuring aerosol size distributions,” J. Aerosol Sci. 23, 749–757 (1992).
[CrossRef]

Johnson, C. S.

C. S. Johnson, D. A. Gabriel, Laser Light Scattering (Dover, New York, 1981).

Katz, J. L.

A. J. Rulison, P. F. Miquel, J. L. Katz, “Titania and silica powders produced in a counterflow diffusion flame,” J. Mater. Res. 11, 3083–3089 (1996).
[CrossRef]

J. L. Katz, P. F. Miquel, “Synthesis and applications of oxides and mixed oxides produced by a flame process,” Nanostruct. Mater. 4, 551–557 (1994).
[CrossRef]

P. F. Miquel, C. H. Hung, J. L. Katz, “Formation of V2O5-based mixed oxides in flames,” J. Mater. Res. 8, 2404–2413 (1993).
[CrossRef]

M. R. Zachariah, D. Chin, H. G. Semerjian, J. L. Katz, “Dynamic light scattering and angular dissymmetry for the in situ measurements of silicon dioxide particle synthesis in flames,” Appl. Opt. 28, 530–536 (1989).
[CrossRef] [PubMed]

Koylu, U. O.

Y. Xing, U. O. Koylu, D. E. Rosner, “Synthesis and restructing of inorganic nanoparticles in laminar counterflow diffusion flames,” Combust. Flame 107, 85–102 (1996).
[CrossRef]

Lefebvre, A. H.

A. H. Lefebvre, Atomization and Sprays (Hemisphere, Washington, D.C., 1989).

Lottes, C. R.

R. L. Axelbaum, C. R. Lottes, J. I. Huertas, L. J. Rosen, “Gas-phase combustion synthesis of aluminum nitride powder,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1891–1897.
[CrossRef]

Malitson, I. H.

McCann, H.

T. Parker, E. Jepsen, H. McCann, “Measurements and error analysis of droplet size in optically thick diesel sprays,” in the Twenty-Seventh Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1998), pp. 1881–1888.
[CrossRef]

Megaridis, M.

Miquel, P. F.

A. J. Rulison, P. F. Miquel, J. L. Katz, “Titania and silica powders produced in a counterflow diffusion flame,” J. Mater. Res. 11, 3083–3089 (1996).
[CrossRef]

J. L. Katz, P. F. Miquel, “Synthesis and applications of oxides and mixed oxides produced by a flame process,” Nanostruct. Mater. 4, 551–557 (1994).
[CrossRef]

P. F. Miquel, C. H. Hung, J. L. Katz, “Formation of V2O5-based mixed oxides in flames,” J. Mater. Res. 8, 2404–2413 (1993).
[CrossRef]

Mulholland, G. W.

R. A. Dobbins, G. W. Mulholland, “Interpretation of optical measurements of flame generated particles,” Combust. Sci. Technol. 40, 175–191 (1984).
[CrossRef]

Nai-ning, W.

C. Xiao-shu, W. Nai-ning, W. Jing-ming, Z. Gang, “Experimental investigation of the light extinction method for measuring aerosol size distributions,” J. Aerosol Sci. 23, 749–757 (1992).
[CrossRef]

Parker, T.

T. Parker, E. Jepsen, H. McCann, “Measurements and error analysis of droplet size in optically thick diesel sprays,” in the Twenty-Seventh Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1998), pp. 1881–1888.
[CrossRef]

Pratsinis, S. E.

S. E. Pratsinis, “Flame aerosol synthesis of ceramic powders,” Prog. Energy Combust. Sci. 24, 197–219 (1998).
[CrossRef]

Press, W. H.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Robinson, D. K.

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, New York, 1992).

Rosen, L. J.

R. L. Axelbaum, C. R. Lottes, J. I. Huertas, L. J. Rosen, “Gas-phase combustion synthesis of aluminum nitride powder,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1891–1897.
[CrossRef]

Rosner, D. E.

Y. Xing, U. O. Koylu, D. E. Rosner, “Synthesis and restructing of inorganic nanoparticles in laminar counterflow diffusion flames,” Combust. Flame 107, 85–102 (1996).
[CrossRef]

Rulison, A. J.

A. J. Rulison, P. F. Miquel, J. L. Katz, “Titania and silica powders produced in a counterflow diffusion flame,” J. Mater. Res. 11, 3083–3089 (1996).
[CrossRef]

Semerjian, H. G.

Skandan, G.

N. G. Glumac, Y. J. Chen, G. Skandan, “Diagnostics and modeling of nanopowders synthesis in low pressure flames,” J. Mater. Res. 13, 2572–2579 (1998).
[CrossRef]

Teukolsky, S. A.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

Vetterling, W. T.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Williams, M. W.

T. Inagaki, E. T. Arakawa, R. N. Hamm, M. W. Williams, “Optical properties of polystyrene from the near infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Wooldridge, M. S.

M. S. Wooldridge, “Gas phase combustion synthesis of particles,” Prog. Energy Combust. Sci. 24, 63–87 (1998).
[CrossRef]

Wriedt, T.

T. Wriedt, “A review of elastic light scattering theories,” Part. Part. Syst. Charact. 15, 67–74 (1997).
[CrossRef]

Xiao-shu, C.

C. Xiao-shu, W. Nai-ning, W. Jing-ming, Z. Gang, “Experimental investigation of the light extinction method for measuring aerosol size distributions,” J. Aerosol Sci. 23, 749–757 (1992).
[CrossRef]

Xing, Y.

Y. Xing, U. O. Koylu, D. E. Rosner, “Synthesis and restructing of inorganic nanoparticles in laminar counterflow diffusion flames,” Combust. Flame 107, 85–102 (1996).
[CrossRef]

Zachariah, M. R.

M. R. Zachariah, P. Dimitriou, “Controlled nucleation in aerosol reactors for suppression of agglomerate formation: a numerical study,” Aerosol Sci. Technol. 13, 413–425 (1990).
[CrossRef]

M. R. Zachariah, H. G. Semerjian, “Simulation of ceramic particle formation: comparison with in-situ measurements,” AIChE J. 35, 2003–2012 (1989).
[CrossRef]

M. R. Zachariah, D. Chin, H. G. Semerjian, J. L. Katz, “Dynamic light scattering and angular dissymmetry for the in situ measurements of silicon dioxide particle synthesis in flames,” Appl. Opt. 28, 530–536 (1989).
[CrossRef] [PubMed]

Aerosol Sci. Technol.

M. R. Zachariah, P. Dimitriou, “Controlled nucleation in aerosol reactors for suppression of agglomerate formation: a numerical study,” Aerosol Sci. Technol. 13, 413–425 (1990).
[CrossRef]

AIChE J.

M. R. Zachariah, H. G. Semerjian, “Simulation of ceramic particle formation: comparison with in-situ measurements,” AIChE J. 35, 2003–2012 (1989).
[CrossRef]

Appl. Opt.

Combust. Flame

Y. Xing, U. O. Koylu, D. E. Rosner, “Synthesis and restructing of inorganic nanoparticles in laminar counterflow diffusion flames,” Combust. Flame 107, 85–102 (1996).
[CrossRef]

Combust. Sci. Technol.

R. A. Dobbins, G. W. Mulholland, “Interpretation of optical measurements of flame generated particles,” Combust. Sci. Technol. 40, 175–191 (1984).
[CrossRef]

J. Aerosol Sci.

C. Xiao-shu, W. Nai-ning, W. Jing-ming, Z. Gang, “Experimental investigation of the light extinction method for measuring aerosol size distributions,” J. Aerosol Sci. 23, 749–757 (1992).
[CrossRef]

J. Franklin Inst.

T. Hatch, S. P. Choate, “Statistical description of the size properties of non-uniform particulate substances,” J. Franklin Inst. 207, 369–387 (1929).
[CrossRef]

J. Mater. Res.

N. G. Glumac, Y. J. Chen, G. Skandan, “Diagnostics and modeling of nanopowders synthesis in low pressure flames,” J. Mater. Res. 13, 2572–2579 (1998).
[CrossRef]

A. J. Rulison, P. F. Miquel, J. L. Katz, “Titania and silica powders produced in a counterflow diffusion flame,” J. Mater. Res. 11, 3083–3089 (1996).
[CrossRef]

P. F. Miquel, C. H. Hung, J. L. Katz, “Formation of V2O5-based mixed oxides in flames,” J. Mater. Res. 8, 2404–2413 (1993).
[CrossRef]

J. Opt. Soc. Am.

Nanostruct. Mater.

J. L. Katz, P. F. Miquel, “Synthesis and applications of oxides and mixed oxides produced by a flame process,” Nanostruct. Mater. 4, 551–557 (1994).
[CrossRef]

Part. Part. Syst. Charact.

T. Wriedt, “A review of elastic light scattering theories,” Part. Part. Syst. Charact. 15, 67–74 (1997).
[CrossRef]

Phys. Rev. B

T. Inagaki, E. T. Arakawa, R. N. Hamm, M. W. Williams, “Optical properties of polystyrene from the near infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Prog. Energy Combust. Sci.

S. E. Pratsinis, “Flame aerosol synthesis of ceramic powders,” Prog. Energy Combust. Sci. 24, 197–219 (1998).
[CrossRef]

M. S. Wooldridge, “Gas phase combustion synthesis of particles,” Prog. Energy Combust. Sci. 24, 63–87 (1998).
[CrossRef]

Other

A. H. Lefebvre, Atomization and Sprays (Hemisphere, Washington, D.C., 1989).

T. Parker, E. Jepsen, H. McCann, “Measurements and error analysis of droplet size in optically thick diesel sprays,” in the Twenty-Seventh Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1998), pp. 1881–1888.
[CrossRef]

R. L. Axelbaum, C. R. Lottes, J. I. Huertas, L. J. Rosen, “Gas-phase combustion synthesis of aluminum nitride powder,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1891–1897.
[CrossRef]

K. Brezinsky, “The gas phase combustion synthesis of materials,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1805–1816.
[CrossRef]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

C. S. Johnson, D. A. Gabriel, Laser Light Scattering (Dover, New York, 1981).

W. Hinds, Aerosol Technology (Wiley, New York, 1982).

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, New York, 1992).

W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, Cambridge, Mass., 1988).

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Figures (8)

Fig. 1
Fig. 1

Experimental layout of the FS measurement system. This system utilizes four photomultiplier tubes (PMTs) to detect scattering laser light.

Fig. 2
Fig. 2

Fractional error in the diameter produced for synthetic scattering signals perturbed by a known error.

Fig. 3
Fig. 3

Fractional error in the volume fraction produced for synthetic scattering signals perturbed by a known error.

Fig. 4
Fig. 4

Error-free synthetic log-normal data analyzed with a monodisperse model showing stair-step behavior. All results plotted in (a) show the solution failure. Points with χ2/ν > 2.00 are not plotted in (b) to show the solution gaps.

Fig. 5
Fig. 5

Fractional error in diameter obtained by (a) the monodisperse model and (b) the log-normal model. Note that the synthetic data are noise free so that errors stem from the size distribution effects on the signals.

Fig. 6
Fig. 6

Fractional error in the diameter for synthetic scattering signal data with a 10% error. Reduced χ2 values greater than 2 were excluded.

Fig. 7
Fig. 7

Fractional error in the volume fraction obtained with (a) the monodisperse model and (b) the log-normal model. Note that the synthetic data are noise free so that errors stem from the size distribution effects on the signals.

Fig. 8
Fig. 8

Experimentally determined volume mean diameter (vmd) compared with National Institute of Standards and Technology-traceable polystyrene spheres submerged in filtered water.

Equations (8)

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

S=RλτnetG Ebtgateδsin θ ΩN D=0 nDdσDdΩdD,
Spolarization,θλ=N D=0 nDdσDdΩdD,
Spolarization,θλ=N dσDdΩ.
VF=N D=0 nDπ6 D3dD.
nD=N2π D ln σgexp-ln D-ln DVMD22 ln2 σg,
ln Dvmd=ln Dg+3σg2,
χ2=i=14Si-NdσD,i/dΩ2σi2,
N=i=14SidσdΩσi2i=14dσ2dΩσi2.

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