Abstract

The dependence of fluorescent and scattered light intensities from spherical droplets on droplet diameter was evaluated using Mie theory. The emphasis is on the evaluation of droplet sizing, based on the ratio of laser-induced fluorescence and scattered light intensities (LIF/Mie technique). A parametric study is presented, which includes the effects of scattering angle, the real part of the refractive index and the dye concentration in the liquid (determining the imaginary part of the refractive index). The assumption that the fluorescent and scattered light intensities are proportional to the volume and surface area of the droplets for accurate sizing measurements is not generally valid. More accurate sizing measurements can be performed with minimal dye concentration in the liquid and by collecting light at a scattering angle of 60° rather than the commonly used angle of 90°. Unfavorable to the sizing accuracy are oscillations of the scattered light intensity with droplet diameter that are profound at the sidescatter direction (90°) and for droplets with refractive indices around 1.4.

© 2011 Optical Society of America

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2011

E. Kristensson, E. Berrocal, R. Wellander, M. Ritcher, M. Aldén, and M. Linne, “Structured illumination for 3D Mie imaging and 2D attenuation measurements in optically dense sprays,” Proc. Combust. Inst. 33, 855–861 (2011).
[CrossRef]

2010

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49, 417–434 (2010).
[CrossRef]

B. Frackowiak and C. Tropea, “Numerical analysis of diameter influence on droplet fluorescence,” Appl. Opt. 49, 2363–2370 (2010).
[CrossRef] [PubMed]

B. Frackowiak and C. Tropea, “Fluorescence modeling of droplets intersecting a focused laser beam,” Opt. Lett. 35, 1386–1388 (2010).
[CrossRef] [PubMed]

2008

2005

2004

I. Duwel, J. Schorr, P. Peuser, P. Zeller, J. Wolfrum, and C. Schulz, “Spray diagnostics using an all-solid-state Nd:YAlO3 laser and fluorescence tracers in commercial gasoline and diesel fuels,” Appl. Phys. B 79, 249–254 (2004).
[CrossRef]

I. Duwel, J. Schorr, J. Wolfrum, and C. Schulz, “Laser-induced fluorescence of tracers dissolved in evaporating droplets,” Appl. Phys. B 78, 127–131 (2004).
[CrossRef]

2003

L. A. Melton and C. W. Lipp, “Criteria for quantitative PLIF experiments using high-power lasers,” Exp. Fluids 35, 310–316 (2003).
[CrossRef]

K. Jung, H. Koh, and Y. Yoon, “Assessment of planar liquid-laser-induced fluorescence measurements for spray mass distributions of like-doublet injectors,” Meas. Sci. Technol. 14, 1387–1395 (2003).
[CrossRef]

L. Zimmer and Y. Ikeda, “Planar droplet sizing for the characterization of droplet clusters in an industrial gun-type burner,” Part. Part. Syst. Charact. 20, 199–208 (2003).
[CrossRef]

L. Zimmer, R. Domann, Y. Hardalupas, and Y. Ikeda, “Simultaneous laser-induced fluorescence and Mie scattering for droplet cluster measurements,” AIAA J. 41, 2170–2178 (2003).
[CrossRef]

R. Domann and Y. Hardalupas, “Quantitative measurement of planar droplet sauter mean diameter in sprays using planar droplet sizing,” Part. Part. Syst. Charact. 20, 209–218 (2003).
[CrossRef]

2002

M. Maeda, Y. Akasaka, and T. Kawaguchi, “Improvements of the interferometric technique for simultaneous measurement of droplet size and velocity vector field and its application to a transient spray,” Exp. Fluids 33, 125–134 (2002).

R. Domann, Y. Hardalupas, and A. R. Jones, “A study of the influence of absorption on the spatial distribution of fluorescence intensity within large droplets using Mie theory, geometrical optics and imaging experiments,” Meas. Sci. Technol. 13, 280–291 (2002).
[CrossRef]

S. Park, H. Cho, I. Yoon, and K. Min, “Measurement of droplet size distribution of gasoline direct injection spray by droplet generator and planar image technique,” Meas. Sci. Technol. 13, 859–864 (2002).
[CrossRef]

2001

B. D. Stojkovic and V. Sick, “Evolution and impingement of an automotive fuel spray investigated with simultaneous Mie/LIF techniques,” Appl. Phys. B 73, 75–83 (2001).

R. Domann and Y. Hardalupas, “A study of parameters that influence the accuracy of the planar droplet sizing (PDS) technique,” Part. Part. Syst. Charact. 18, 3–11 (2001).
[CrossRef]

P. Lavieille, F. Lemoine, G. Lavergne, and M. Lebouche, “Evaporating and combusting droplet temperature measurements using two-color laser-induced fluorescence,” Exp. Fluids 31, 45–55 (2001).
[CrossRef]

V. Sick and B. Stojkovic, “Attenuation effects on imaging diagnostics of hollow-cone sprays,” Appl. Opt. 40, 2435–2442 (2001).
[CrossRef]

R. Domann and Y. Hardalupas, “Spatial distribution of fluorescence intensity within large droplets and its dependence on dye concentration,” Appl. Opt. 40, 3586–3597 (2001).
[CrossRef]

2000

M. Maeda, T. Kawaguchi, and K. Hishida, “Novel interferometric measurement of size and velocity distributions of spherical particles in fluid flows,” Meas. Sci. Technol. 11, L13–L18 (2000).
[CrossRef]

M. C. Jermy and D. A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710(2000).
[CrossRef]

1999

P. Le Gal, “Laser sheet dropsizing of dense sprays,” Opt. Laser Technol. 31, 75–83 (1999).
[CrossRef]

S. V. Sankar, K. E. Maher, and D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbine Power 121, 409–414 (1999).
[CrossRef]

K. Matsumoto, T. Fujii, M. Suzuki, D. Segawa, and T. Kadota, “Laser-induced fluorescence for the non-intrusive diagnostics of a fuel droplet burning under microgravity in a drop shaft,” Meas. Sci. Technol. 10, 853–858 (1999).
[CrossRef]

1995

1994

Y. Hardalupas and A. M. K. P. Taylor, “Phase validation criteria of size measurements for the phase Doppler technique,” Exp. Fluids 17, 253–258 (1994).
[CrossRef]

1992

E. Cossali and Y. Hardalupas, “Comparison between laser diffraction and phase doppler-velocimeter techniques in high turbidity, small diameter sprays,” Exp. Fluids 13, 414–422(1992).
[CrossRef]

1991

1990

1988

Y. Hardalupas and A. M. K. P. Taylor, “The identification of LDA seeding particles by the phase-Doppler technique,” Exp. Fluids 6, 137–140 (1988).

1986

A. A. Hamidi and J. Swithenbank, “Treatment of multiple-scattering of light in laser diffraction measurement techniques in dense sprays and particle fields,” J. Inst. Energy 59, 101–105 (1986).

1984

L. G. Dodge, “Calibration of the Malvern particle sizer,” Appl. Opt. 23, 2415–2419 (1984).
[CrossRef] [PubMed]

W. D. Bachalo and M. J. Houser, “Phase Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).

1963

R. A. Dobbins, L. Crocco, and I. Glassman, “Measurement of mean particle sizes of sprays from diffractively scattered light,” AIAA J. 1, 1882–1886 (1963).
[CrossRef]

1908

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. 330, 377–455 (1908).
[CrossRef]

1890

L. Lorenz, “Lysbevaegelsen i og uden for en af plane Lysbolger belyst Kulge,” Det Kongelige Danske Videnskabernes Selskabs Skrifter 6, 1–62 (1890).

Akasaka, Y.

M. Maeda, Y. Akasaka, and T. Kawaguchi, “Improvements of the interferometric technique for simultaneous measurement of droplet size and velocity vector field and its application to a transient spray,” Exp. Fluids 33, 125–134 (2002).

Alden, M.

Aldén, M.

E. Kristensson, E. Berrocal, R. Wellander, M. Ritcher, M. Aldén, and M. Linne, “Structured illumination for 3D Mie imaging and 2D attenuation measurements in optically dense sprays,” Proc. Combust. Inst. 33, 855–861 (2011).
[CrossRef]

Anderson, R. C.

M. M. Zaller, R. C. Anderson, Y. R. Hicks, and R. J. Locke, “Comparison of techniques for non-intrusive fuel drop size measurements in a subscale gas turbine conbustor,” NASA/TM-1999-208909 (NASA, 1999).

Araneo, L.

L. Araneo and R. Payri, “Experimental quantification of the planar droplet sizing. Technique error for micro-metric mono-dispersed spherical particles,” in 22nd Annual Conference on Liquid Atomization and Spray Systems, Lake Como, Italy, 8–10 Sept., 2008.

Bachalo, W. D.

W. D. Bachalo and M. J. Houser, “Phase Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).

Bakic, S.

Bauckhage, K.

K. Bauckhage and H. Flogel, “Simultaneous measurement of droplet size and velocity in nozzle sprays,” presented at the Second International Symposium of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2–5 July, 1984.

Berrocal, E.

Bohren, C. F.

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

Boyle, R. D.

Charalampous, G.

G. Charalampous, Y. Hardalupas, and A. M. K. P. Taylor, “Optimisation of the droplet sizing accuracy of the combined scattering (Mie)/laser induced fluorescence (LIF) technique,” in Twelfth International Symposium of Laser Techniques to Fluids Mechanics Lisbon, Portugal, 12–15 July, 2004.

Cho, H.

S. Park, H. Cho, I. Yoon, and K. Min, “Measurement of droplet size distribution of gasoline direct injection spray by droplet generator and planar image technique,” Meas. Sci. Technol. 13, 859–864 (2002).
[CrossRef]

Cossali, E.

E. Cossali and Y. Hardalupas, “Comparison between laser diffraction and phase doppler-velocimeter techniques in high turbidity, small diameter sprays,” Exp. Fluids 13, 414–422(1992).
[CrossRef]

Crocco, L.

R. A. Dobbins, L. Crocco, and I. Glassman, “Measurement of mean particle sizes of sprays from diffractively scattered light,” AIAA J. 1, 1882–1886 (1963).
[CrossRef]

Damaschke, N.

Dobbins, R. A.

R. A. Dobbins, L. Crocco, and I. Glassman, “Measurement of mean particle sizes of sprays from diffractively scattered light,” AIAA J. 1, 1882–1886 (1963).
[CrossRef]

Dodge, L. G.

Domann, R.

L. Zimmer, R. Domann, Y. Hardalupas, and Y. Ikeda, “Simultaneous laser-induced fluorescence and Mie scattering for droplet cluster measurements,” AIAA J. 41, 2170–2178 (2003).
[CrossRef]

R. Domann and Y. Hardalupas, “Quantitative measurement of planar droplet sauter mean diameter in sprays using planar droplet sizing,” Part. Part. Syst. Charact. 20, 209–218 (2003).
[CrossRef]

R. Domann, Y. Hardalupas, and A. R. Jones, “A study of the influence of absorption on the spatial distribution of fluorescence intensity within large droplets using Mie theory, geometrical optics and imaging experiments,” Meas. Sci. Technol. 13, 280–291 (2002).
[CrossRef]

R. Domann and Y. Hardalupas, “A study of parameters that influence the accuracy of the planar droplet sizing (PDS) technique,” Part. Part. Syst. Charact. 18, 3–11 (2001).
[CrossRef]

R. Domann and Y. Hardalupas, “Spatial distribution of fluorescence intensity within large droplets and its dependence on dye concentration,” Appl. Opt. 40, 3586–3597 (2001).
[CrossRef]

R. Domann and Y. Hardalupas, “Characterisation of spray unsteadiness,” in 18th Annual Conference on Liquid Atomization & Spray Systems, 9–11 Sept., 2002, pp. 287–292.

Durst, F.

F. Durst and M. Zare, “Laser Doppler measurements in two-phase flows,” in The Accuracy of Flow Measurements by Laser Doppler Methods: Proceedings of the LDA Symposium (Copenhagen, 1975), pp. 403–429.

Duwel, I.

I. Duwel, J. Schorr, J. Wolfrum, and C. Schulz, “Laser-induced fluorescence of tracers dissolved in evaporating droplets,” Appl. Phys. B 78, 127–131 (2004).
[CrossRef]

I. Duwel, J. Schorr, P. Peuser, P. Zeller, J. Wolfrum, and C. Schulz, “Spray diagnostics using an all-solid-state Nd:YAlO3 laser and fluorescence tracers in commercial gasoline and diesel fuels,” Appl. Phys. B 79, 249–254 (2004).
[CrossRef]

Flogel, H.

K. Bauckhage and H. Flogel, “Simultaneous measurement of droplet size and velocity in nozzle sprays,” presented at the Second International Symposium of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2–5 July, 1984.

Frackowiak, B.

Fujii, T.

K. Matsumoto, T. Fujii, M. Suzuki, D. Segawa, and T. Kadota, “Laser-induced fluorescence for the non-intrusive diagnostics of a fuel droplet burning under microgravity in a drop shaft,” Meas. Sci. Technol. 10, 853–858 (1999).
[CrossRef]

Girasole, T.

D. Stepowski, O. Werquin, C. Roze, and T. Girasole, “Account for extinction and multiple scattering in planar droplet sizing of dense sprays,” in Thirteenth International Symposium of Laser Techniques to Fluids Mechanics, Lisbon, Portugal, 26–29 June, 2006.

Glassman, I.

R. A. Dobbins, L. Crocco, and I. Glassman, “Measurement of mean particle sizes of sprays from diffractively scattered light,” AIAA J. 1, 1882–1886 (1963).
[CrossRef]

Glover, A. R.

Greenhalgh, D. A.

M. C. Jermy and D. A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710(2000).
[CrossRef]

Hamidi, A. A.

A. A. Hamidi and J. Swithenbank, “Treatment of multiple-scattering of light in laser diffraction measurement techniques in dense sprays and particle fields,” J. Inst. Energy 59, 101–105 (1986).

Hardalupas, Y.

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49, 417–434 (2010).
[CrossRef]

L. Zimmer, R. Domann, Y. Hardalupas, and Y. Ikeda, “Simultaneous laser-induced fluorescence and Mie scattering for droplet cluster measurements,” AIAA J. 41, 2170–2178 (2003).
[CrossRef]

R. Domann and Y. Hardalupas, “Quantitative measurement of planar droplet sauter mean diameter in sprays using planar droplet sizing,” Part. Part. Syst. Charact. 20, 209–218 (2003).
[CrossRef]

R. Domann, Y. Hardalupas, and A. R. Jones, “A study of the influence of absorption on the spatial distribution of fluorescence intensity within large droplets using Mie theory, geometrical optics and imaging experiments,” Meas. Sci. Technol. 13, 280–291 (2002).
[CrossRef]

R. Domann and Y. Hardalupas, “A study of parameters that influence the accuracy of the planar droplet sizing (PDS) technique,” Part. Part. Syst. Charact. 18, 3–11 (2001).
[CrossRef]

R. Domann and Y. Hardalupas, “Spatial distribution of fluorescence intensity within large droplets and its dependence on dye concentration,” Appl. Opt. 40, 3586–3597 (2001).
[CrossRef]

Y. Hardalupas and A. M. K. P. Taylor, “Phase validation criteria of size measurements for the phase Doppler technique,” Exp. Fluids 17, 253–258 (1994).
[CrossRef]

E. Cossali and Y. Hardalupas, “Comparison between laser diffraction and phase doppler-velocimeter techniques in high turbidity, small diameter sprays,” Exp. Fluids 13, 414–422(1992).
[CrossRef]

Y. Hardalupas and A. M. K. P. Taylor, “The identification of LDA seeding particles by the phase-Doppler technique,” Exp. Fluids 6, 137–140 (1988).

R. Domann and Y. Hardalupas, “Characterisation of spray unsteadiness,” in 18th Annual Conference on Liquid Atomization & Spray Systems, 9–11 Sept., 2002, pp. 287–292.

G. Charalampous, Y. Hardalupas, and A. M. K. P. Taylor, “Optimisation of the droplet sizing accuracy of the combined scattering (Mie)/laser induced fluorescence (LIF) technique,” in Twelfth International Symposium of Laser Techniques to Fluids Mechanics Lisbon, Portugal, 12–15 July, 2004.

Heinisch, C.

Hicks, Y. R.

M. M. Zaller, R. C. Anderson, Y. R. Hicks, and R. J. Locke, “Comparison of techniques for non-intrusive fuel drop size measurements in a subscale gas turbine conbustor,” NASA/TM-1999-208909 (NASA, 1999).

Hishida, K.

M. Maeda, T. Kawaguchi, and K. Hishida, “Novel interferometric measurement of size and velocity distributions of spherical particles in fluid flows,” Meas. Sci. Technol. 11, L13–L18 (2000).
[CrossRef]

Houser, M. J.

W. D. Bachalo and M. J. Houser, “Phase Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).

Huffman, D. R.

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

Ikeda, Y.

L. Zimmer, R. Domann, Y. Hardalupas, and Y. Ikeda, “Simultaneous laser-induced fluorescence and Mie scattering for droplet cluster measurements,” AIAA J. 41, 2170–2178 (2003).
[CrossRef]

L. Zimmer and Y. Ikeda, “Planar droplet sizing for the characterization of droplet clusters in an industrial gun-type burner,” Part. Part. Syst. Charact. 20, 199–208 (2003).
[CrossRef]

Jermy, M.

Jermy, M. C.

M. C. Jermy and D. A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710(2000).
[CrossRef]

Jin, S. H.

S. H. Jin, “An experimental study of the spray from an air-assisted direct fuel injector,” Proc. Inst. Mech. Eng., E J. Process Mech. Eng. 222, 1883–1894 (2008).
[CrossRef]

Jones, A. R.

R. Domann, Y. Hardalupas, and A. R. Jones, “A study of the influence of absorption on the spatial distribution of fluorescence intensity within large droplets using Mie theory, geometrical optics and imaging experiments,” Meas. Sci. Technol. 13, 280–291 (2002).
[CrossRef]

Jung, K.

K. Jung, H. Koh, and Y. Yoon, “Assessment of planar liquid-laser-induced fluorescence measurements for spray mass distributions of like-doublet injectors,” Meas. Sci. Technol. 14, 1387–1395 (2003).
[CrossRef]

Kadota, T.

K. Matsumoto, T. Fujii, M. Suzuki, D. Segawa, and T. Kadota, “Laser-induced fluorescence for the non-intrusive diagnostics of a fuel droplet burning under microgravity in a drop shaft,” Meas. Sci. Technol. 10, 853–858 (1999).
[CrossRef]

Kamimoto, T.

C. N. Yeh, H. Kosaka, and T. Kamimoto, “A fluorescence/scattering imaging technique for instantaneous 2-D measurements of particle size distribution in a transient spray,” in Proceedings of the 3rd Congress on Optical Particle Sizing (1993), pp. 355–361.

T. Kamimoto, “Diagnostics of transient sprays by means of laser sheet techniques,” in COMODIA 1994, Yokohama, Japan, 11–14 July, 1994, pp. 33–41.

Kawaguchi, T.

M. Maeda, Y. Akasaka, and T. Kawaguchi, “Improvements of the interferometric technique for simultaneous measurement of droplet size and velocity vector field and its application to a transient spray,” Exp. Fluids 33, 125–134 (2002).

M. Maeda, T. Kawaguchi, and K. Hishida, “Novel interferometric measurement of size and velocity distributions of spherical particles in fluid flows,” Meas. Sci. Technol. 11, L13–L18 (2000).
[CrossRef]

Koh, H.

K. Jung, H. Koh, and Y. Yoon, “Assessment of planar liquid-laser-induced fluorescence measurements for spray mass distributions of like-doublet injectors,” Meas. Sci. Technol. 14, 1387–1395 (2003).
[CrossRef]

Kosaka, H.

C. N. Yeh, H. Kosaka, and T. Kamimoto, “A fluorescence/scattering imaging technique for instantaneous 2-D measurements of particle size distribution in a transient spray,” in Proceedings of the 3rd Congress on Optical Particle Sizing (1993), pp. 355–361.

Kristensson, E.

E. Kristensson, E. Berrocal, R. Wellander, M. Ritcher, M. Aldén, and M. Linne, “Structured illumination for 3D Mie imaging and 2D attenuation measurements in optically dense sprays,” Proc. Combust. Inst. 33, 855–861 (2011).
[CrossRef]

E. Berrocal, E. Kristensson, M. Richter, M. Linne, and M. Alden, “Application of structured illumination for multiple scattering suppression in planar laser imaging of dense sprays,” Opt. Express 16, 17870–17881 (2008).
[CrossRef] [PubMed]

Lavergne, G.

P. Lavieille, F. Lemoine, G. Lavergne, and M. Lebouche, “Evaporating and combusting droplet temperature measurements using two-color laser-induced fluorescence,” Exp. Fluids 31, 45–55 (2001).
[CrossRef]

Lavieille, P.

P. Lavieille, F. Lemoine, G. Lavergne, and M. Lebouche, “Evaporating and combusting droplet temperature measurements using two-color laser-induced fluorescence,” Exp. Fluids 31, 45–55 (2001).
[CrossRef]

Le Gal, P.

P. Le Gal, “Laser sheet dropsizing of dense sprays,” Opt. Laser Technol. 31, 75–83 (1999).
[CrossRef]

Lebouche, M.

P. Lavieille, F. Lemoine, G. Lavergne, and M. Lebouche, “Evaporating and combusting droplet temperature measurements using two-color laser-induced fluorescence,” Exp. Fluids 31, 45–55 (2001).
[CrossRef]

Lemoine, F.

P. Lavieille, F. Lemoine, G. Lavergne, and M. Lebouche, “Evaporating and combusting droplet temperature measurements using two-color laser-induced fluorescence,” Exp. Fluids 31, 45–55 (2001).
[CrossRef]

Linne, M.

E. Kristensson, E. Berrocal, R. Wellander, M. Ritcher, M. Aldén, and M. Linne, “Structured illumination for 3D Mie imaging and 2D attenuation measurements in optically dense sprays,” Proc. Combust. Inst. 33, 855–861 (2011).
[CrossRef]

E. Berrocal, E. Kristensson, M. Richter, M. Linne, and M. Alden, “Application of structured illumination for multiple scattering suppression in planar laser imaging of dense sprays,” Opt. Express 16, 17870–17881 (2008).
[CrossRef] [PubMed]

Lipp, C. W.

L. A. Melton and C. W. Lipp, “Criteria for quantitative PLIF experiments using high-power lasers,” Exp. Fluids 35, 310–316 (2003).
[CrossRef]

Locke, R. J.

M. M. Zaller, R. C. Anderson, Y. R. Hicks, and R. J. Locke, “Comparison of techniques for non-intrusive fuel drop size measurements in a subscale gas turbine conbustor,” NASA/TM-1999-208909 (NASA, 1999).

Lorenz, L.

L. Lorenz, “Lysbevaegelsen i og uden for en af plane Lysbolger belyst Kulge,” Det Kongelige Danske Videnskabernes Selskabs Skrifter 6, 1–62 (1890).

L. Lorenz, “Sur la lumiere reflechie et refractee par une sphere transparente,” in Oeuvres Scientifiques de L. Lorenz, Revues et Annotees par H. Valentiner (Librairie Lehmann et Stage, 1898).

Maeda, M.

M. Maeda, Y. Akasaka, and T. Kawaguchi, “Improvements of the interferometric technique for simultaneous measurement of droplet size and velocity vector field and its application to a transient spray,” Exp. Fluids 33, 125–134 (2002).

M. Maeda, T. Kawaguchi, and K. Hishida, “Novel interferometric measurement of size and velocity distributions of spherical particles in fluid flows,” Meas. Sci. Technol. 11, L13–L18 (2000).
[CrossRef]

Maher, K. E.

S. V. Sankar, K. E. Maher, and D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbine Power 121, 409–414 (1999).
[CrossRef]

Matsumoto, K.

K. Matsumoto, T. Fujii, M. Suzuki, D. Segawa, and T. Kadota, “Laser-induced fluorescence for the non-intrusive diagnostics of a fuel droplet burning under microgravity in a drop shaft,” Meas. Sci. Technol. 10, 853–858 (1999).
[CrossRef]

Meglinski, I.

Melton, L. A.

L. A. Melton and C. W. Lipp, “Criteria for quantitative PLIF experiments using high-power lasers,” Exp. Fluids 35, 310–316 (2003).
[CrossRef]

M. Winter and L. A. Melton, “Measurement of internal circulation in droplets using laser-induced fluorescence,” Appl. Opt. 29, 4574–4577 (1990).
[CrossRef] [PubMed]

Mie, G.

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. 330, 377–455 (1908).
[CrossRef]

Min, K.

S. Park, H. Cho, I. Yoon, and K. Min, “Measurement of droplet size distribution of gasoline direct injection spray by droplet generator and planar image technique,” Meas. Sci. Technol. 13, 859–864 (2002).
[CrossRef]

Park, S.

S. Park, H. Cho, I. Yoon, and K. Min, “Measurement of droplet size distribution of gasoline direct injection spray by droplet generator and planar image technique,” Meas. Sci. Technol. 13, 859–864 (2002).
[CrossRef]

Payri, R.

L. Araneo and R. Payri, “Experimental quantification of the planar droplet sizing. Technique error for micro-metric mono-dispersed spherical particles,” in 22nd Annual Conference on Liquid Atomization and Spray Systems, Lake Como, Italy, 8–10 Sept., 2008.

Peuser, P.

I. Duwel, J. Schorr, P. Peuser, P. Zeller, J. Wolfrum, and C. Schulz, “Spray diagnostics using an all-solid-state Nd:YAlO3 laser and fluorescence tracers in commercial gasoline and diesel fuels,” Appl. Phys. B 79, 249–254 (2004).
[CrossRef]

Richter, M.

Ritcher, M.

E. Kristensson, E. Berrocal, R. Wellander, M. Ritcher, M. Aldén, and M. Linne, “Structured illumination for 3D Mie imaging and 2D attenuation measurements in optically dense sprays,” Proc. Combust. Inst. 33, 855–861 (2011).
[CrossRef]

Robart, D. M.

S. V. Sankar, K. E. Maher, and D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbine Power 121, 409–414 (1999).
[CrossRef]

Roze, C.

D. Stepowski, O. Werquin, C. Roze, and T. Girasole, “Account for extinction and multiple scattering in planar droplet sizing of dense sprays,” in Thirteenth International Symposium of Laser Techniques to Fluids Mechanics, Lisbon, Portugal, 26–29 June, 2006.

Sahu, S.

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49, 417–434 (2010).
[CrossRef]

Sankar, S. V.

S. V. Sankar, K. E. Maher, and D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbine Power 121, 409–414 (1999).
[CrossRef]

Scheimpflug, T.

T. Scheimpflug, “Improved method and apparatus for the systematic alteration or distortion of plane pictures and images by means of lenses and mirrors for photography and for other purposes,” GB patent 1196 (1904).

Schorr, J.

I. Duwel, J. Schorr, P. Peuser, P. Zeller, J. Wolfrum, and C. Schulz, “Spray diagnostics using an all-solid-state Nd:YAlO3 laser and fluorescence tracers in commercial gasoline and diesel fuels,” Appl. Phys. B 79, 249–254 (2004).
[CrossRef]

I. Duwel, J. Schorr, J. Wolfrum, and C. Schulz, “Laser-induced fluorescence of tracers dissolved in evaporating droplets,” Appl. Phys. B 78, 127–131 (2004).
[CrossRef]

Schulz, C.

I. Duwel, J. Schorr, J. Wolfrum, and C. Schulz, “Laser-induced fluorescence of tracers dissolved in evaporating droplets,” Appl. Phys. B 78, 127–131 (2004).
[CrossRef]

I. Duwel, J. Schorr, P. Peuser, P. Zeller, J. Wolfrum, and C. Schulz, “Spray diagnostics using an all-solid-state Nd:YAlO3 laser and fluorescence tracers in commercial gasoline and diesel fuels,” Appl. Phys. B 79, 249–254 (2004).
[CrossRef]

Segawa, D.

K. Matsumoto, T. Fujii, M. Suzuki, D. Segawa, and T. Kadota, “Laser-induced fluorescence for the non-intrusive diagnostics of a fuel droplet burning under microgravity in a drop shaft,” Meas. Sci. Technol. 10, 853–858 (1999).
[CrossRef]

Sick, V.

V. Sick and B. Stojkovic, “Attenuation effects on imaging diagnostics of hollow-cone sprays,” Appl. Opt. 40, 2435–2442 (2001).
[CrossRef]

B. D. Stojkovic and V. Sick, “Evolution and impingement of an automotive fuel spray investigated with simultaneous Mie/LIF techniques,” Appl. Phys. B 73, 75–83 (2001).

Skippon, S. M.

Stepowski, D.

D. Stepowski, O. Werquin, C. Roze, and T. Girasole, “Account for extinction and multiple scattering in planar droplet sizing of dense sprays,” in Thirteenth International Symposium of Laser Techniques to Fluids Mechanics, Lisbon, Portugal, 26–29 June, 2006.

Stojkovic, B.

Stojkovic, B. D.

B. D. Stojkovic and V. Sick, “Evolution and impingement of an automotive fuel spray investigated with simultaneous Mie/LIF techniques,” Appl. Phys. B 73, 75–83 (2001).

Suzuki, M.

K. Matsumoto, T. Fujii, M. Suzuki, D. Segawa, and T. Kadota, “Laser-induced fluorescence for the non-intrusive diagnostics of a fuel droplet burning under microgravity in a drop shaft,” Meas. Sci. Technol. 10, 853–858 (1999).
[CrossRef]

Swithenbank, J.

A. A. Hamidi and J. Swithenbank, “Treatment of multiple-scattering of light in laser diffraction measurement techniques in dense sprays and particle fields,” J. Inst. Energy 59, 101–105 (1986).

Taylor, A. M. K. P.

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49, 417–434 (2010).
[CrossRef]

Y. Hardalupas and A. M. K. P. Taylor, “Phase validation criteria of size measurements for the phase Doppler technique,” Exp. Fluids 17, 253–258 (1994).
[CrossRef]

Y. Hardalupas and A. M. K. P. Taylor, “The identification of LDA seeding particles by the phase-Doppler technique,” Exp. Fluids 6, 137–140 (1988).

G. Charalampous, Y. Hardalupas, and A. M. K. P. Taylor, “Optimisation of the droplet sizing accuracy of the combined scattering (Mie)/laser induced fluorescence (LIF) technique,” in Twelfth International Symposium of Laser Techniques to Fluids Mechanics Lisbon, Portugal, 12–15 July, 2004.

Tropea, C.

Tschudi, T.

van de Hulst, H. C.

Wang, R. T.

Wellander, R.

E. Kristensson, E. Berrocal, R. Wellander, M. Ritcher, M. Aldén, and M. Linne, “Structured illumination for 3D Mie imaging and 2D attenuation measurements in optically dense sprays,” Proc. Combust. Inst. 33, 855–861 (2011).
[CrossRef]

Werquin, O.

D. Stepowski, O. Werquin, C. Roze, and T. Girasole, “Account for extinction and multiple scattering in planar droplet sizing of dense sprays,” in Thirteenth International Symposium of Laser Techniques to Fluids Mechanics, Lisbon, Portugal, 26–29 June, 2006.

Winter, M.

Wolfrum, J.

I. Duwel, J. Schorr, J. Wolfrum, and C. Schulz, “Laser-induced fluorescence of tracers dissolved in evaporating droplets,” Appl. Phys. B 78, 127–131 (2004).
[CrossRef]

I. Duwel, J. Schorr, P. Peuser, P. Zeller, J. Wolfrum, and C. Schulz, “Spray diagnostics using an all-solid-state Nd:YAlO3 laser and fluorescence tracers in commercial gasoline and diesel fuels,” Appl. Phys. B 79, 249–254 (2004).
[CrossRef]

Yeh, C. N.

C. N. Yeh, H. Kosaka, and T. Kamimoto, “A fluorescence/scattering imaging technique for instantaneous 2-D measurements of particle size distribution in a transient spray,” in Proceedings of the 3rd Congress on Optical Particle Sizing (1993), pp. 355–361.

Yoon, I.

S. Park, H. Cho, I. Yoon, and K. Min, “Measurement of droplet size distribution of gasoline direct injection spray by droplet generator and planar image technique,” Meas. Sci. Technol. 13, 859–864 (2002).
[CrossRef]

Yoon, Y.

K. Jung, H. Koh, and Y. Yoon, “Assessment of planar liquid-laser-induced fluorescence measurements for spray mass distributions of like-doublet injectors,” Meas. Sci. Technol. 14, 1387–1395 (2003).
[CrossRef]

Zaller, M. M.

M. M. Zaller, R. C. Anderson, Y. R. Hicks, and R. J. Locke, “Comparison of techniques for non-intrusive fuel drop size measurements in a subscale gas turbine conbustor,” NASA/TM-1999-208909 (NASA, 1999).

Zare, M.

F. Durst and M. Zare, “Laser Doppler measurements in two-phase flows,” in The Accuracy of Flow Measurements by Laser Doppler Methods: Proceedings of the LDA Symposium (Copenhagen, 1975), pp. 403–429.

Zarogoulidis, K.

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49, 417–434 (2010).
[CrossRef]

Zeller, P.

I. Duwel, J. Schorr, P. Peuser, P. Zeller, J. Wolfrum, and C. Schulz, “Spray diagnostics using an all-solid-state Nd:YAlO3 laser and fluorescence tracers in commercial gasoline and diesel fuels,” Appl. Phys. B 79, 249–254 (2004).
[CrossRef]

Zimmer, L.

L. Zimmer and Y. Ikeda, “Planar droplet sizing for the characterization of droplet clusters in an industrial gun-type burner,” Part. Part. Syst. Charact. 20, 199–208 (2003).
[CrossRef]

L. Zimmer, R. Domann, Y. Hardalupas, and Y. Ikeda, “Simultaneous laser-induced fluorescence and Mie scattering for droplet cluster measurements,” AIAA J. 41, 2170–2178 (2003).
[CrossRef]

AIAA J.

R. A. Dobbins, L. Crocco, and I. Glassman, “Measurement of mean particle sizes of sprays from diffractively scattered light,” AIAA J. 1, 1882–1886 (1963).
[CrossRef]

L. Zimmer, R. Domann, Y. Hardalupas, and Y. Ikeda, “Simultaneous laser-induced fluorescence and Mie scattering for droplet cluster measurements,” AIAA J. 41, 2170–2178 (2003).
[CrossRef]

Ann. Phys.

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. 330, 377–455 (1908).
[CrossRef]

Appl. Opt.

Appl. Phys. B

I. Duwel, J. Schorr, P. Peuser, P. Zeller, J. Wolfrum, and C. Schulz, “Spray diagnostics using an all-solid-state Nd:YAlO3 laser and fluorescence tracers in commercial gasoline and diesel fuels,” Appl. Phys. B 79, 249–254 (2004).
[CrossRef]

B. D. Stojkovic and V. Sick, “Evolution and impingement of an automotive fuel spray investigated with simultaneous Mie/LIF techniques,” Appl. Phys. B 73, 75–83 (2001).

M. C. Jermy and D. A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710(2000).
[CrossRef]

I. Duwel, J. Schorr, J. Wolfrum, and C. Schulz, “Laser-induced fluorescence of tracers dissolved in evaporating droplets,” Appl. Phys. B 78, 127–131 (2004).
[CrossRef]

Det Kongelige Danske Videnskabernes Selskabs Skrifter

L. Lorenz, “Lysbevaegelsen i og uden for en af plane Lysbolger belyst Kulge,” Det Kongelige Danske Videnskabernes Selskabs Skrifter 6, 1–62 (1890).

Exp. Fluids

L. A. Melton and C. W. Lipp, “Criteria for quantitative PLIF experiments using high-power lasers,” Exp. Fluids 35, 310–316 (2003).
[CrossRef]

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49, 417–434 (2010).
[CrossRef]

Y. Hardalupas and A. M. K. P. Taylor, “Phase validation criteria of size measurements for the phase Doppler technique,” Exp. Fluids 17, 253–258 (1994).
[CrossRef]

Y. Hardalupas and A. M. K. P. Taylor, “The identification of LDA seeding particles by the phase-Doppler technique,” Exp. Fluids 6, 137–140 (1988).

P. Lavieille, F. Lemoine, G. Lavergne, and M. Lebouche, “Evaporating and combusting droplet temperature measurements using two-color laser-induced fluorescence,” Exp. Fluids 31, 45–55 (2001).
[CrossRef]

E. Cossali and Y. Hardalupas, “Comparison between laser diffraction and phase doppler-velocimeter techniques in high turbidity, small diameter sprays,” Exp. Fluids 13, 414–422(1992).
[CrossRef]

M. Maeda, Y. Akasaka, and T. Kawaguchi, “Improvements of the interferometric technique for simultaneous measurement of droplet size and velocity vector field and its application to a transient spray,” Exp. Fluids 33, 125–134 (2002).

J. Eng. Gas Turbine Power

S. V. Sankar, K. E. Maher, and D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbine Power 121, 409–414 (1999).
[CrossRef]

J. Inst. Energy

A. A. Hamidi and J. Swithenbank, “Treatment of multiple-scattering of light in laser diffraction measurement techniques in dense sprays and particle fields,” J. Inst. Energy 59, 101–105 (1986).

Meas. Sci. Technol.

M. Maeda, T. Kawaguchi, and K. Hishida, “Novel interferometric measurement of size and velocity distributions of spherical particles in fluid flows,” Meas. Sci. Technol. 11, L13–L18 (2000).
[CrossRef]

K. Jung, H. Koh, and Y. Yoon, “Assessment of planar liquid-laser-induced fluorescence measurements for spray mass distributions of like-doublet injectors,” Meas. Sci. Technol. 14, 1387–1395 (2003).
[CrossRef]

K. Matsumoto, T. Fujii, M. Suzuki, D. Segawa, and T. Kadota, “Laser-induced fluorescence for the non-intrusive diagnostics of a fuel droplet burning under microgravity in a drop shaft,” Meas. Sci. Technol. 10, 853–858 (1999).
[CrossRef]

R. Domann, Y. Hardalupas, and A. R. Jones, “A study of the influence of absorption on the spatial distribution of fluorescence intensity within large droplets using Mie theory, geometrical optics and imaging experiments,” Meas. Sci. Technol. 13, 280–291 (2002).
[CrossRef]

S. Park, H. Cho, I. Yoon, and K. Min, “Measurement of droplet size distribution of gasoline direct injection spray by droplet generator and planar image technique,” Meas. Sci. Technol. 13, 859–864 (2002).
[CrossRef]

Opt. Eng.

W. D. Bachalo and M. J. Houser, “Phase Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).

Opt. Express

Opt. Laser Technol.

P. Le Gal, “Laser sheet dropsizing of dense sprays,” Opt. Laser Technol. 31, 75–83 (1999).
[CrossRef]

Opt. Lett.

Part. Part. Syst. Charact.

R. Domann and Y. Hardalupas, “A study of parameters that influence the accuracy of the planar droplet sizing (PDS) technique,” Part. Part. Syst. Charact. 18, 3–11 (2001).
[CrossRef]

L. Zimmer and Y. Ikeda, “Planar droplet sizing for the characterization of droplet clusters in an industrial gun-type burner,” Part. Part. Syst. Charact. 20, 199–208 (2003).
[CrossRef]

R. Domann and Y. Hardalupas, “Quantitative measurement of planar droplet sauter mean diameter in sprays using planar droplet sizing,” Part. Part. Syst. Charact. 20, 209–218 (2003).
[CrossRef]

Proc. Combust. Inst.

E. Kristensson, E. Berrocal, R. Wellander, M. Ritcher, M. Aldén, and M. Linne, “Structured illumination for 3D Mie imaging and 2D attenuation measurements in optically dense sprays,” Proc. Combust. Inst. 33, 855–861 (2011).
[CrossRef]

Proc. Inst. Mech. Eng., E J. Process Mech. Eng.

S. H. Jin, “An experimental study of the spray from an air-assisted direct fuel injector,” Proc. Inst. Mech. Eng., E J. Process Mech. Eng. 222, 1883–1894 (2008).
[CrossRef]

Other

R. Domann and Y. Hardalupas, “Characterisation of spray unsteadiness,” in 18th Annual Conference on Liquid Atomization & Spray Systems, 9–11 Sept., 2002, pp. 287–292.

M. M. Zaller, R. C. Anderson, Y. R. Hicks, and R. J. Locke, “Comparison of techniques for non-intrusive fuel drop size measurements in a subscale gas turbine conbustor,” NASA/TM-1999-208909 (NASA, 1999).

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

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

G. Charalampous, Y. Hardalupas, and A. M. K. P. Taylor, “Optimisation of the droplet sizing accuracy of the combined scattering (Mie)/laser induced fluorescence (LIF) technique,” in Twelfth International Symposium of Laser Techniques to Fluids Mechanics Lisbon, Portugal, 12–15 July, 2004.

D. Stepowski, O. Werquin, C. Roze, and T. Girasole, “Account for extinction and multiple scattering in planar droplet sizing of dense sprays,” in Thirteenth International Symposium of Laser Techniques to Fluids Mechanics, Lisbon, Portugal, 26–29 June, 2006.

L. Araneo and R. Payri, “Experimental quantification of the planar droplet sizing. Technique error for micro-metric mono-dispersed spherical particles,” in 22nd Annual Conference on Liquid Atomization and Spray Systems, Lake Como, Italy, 8–10 Sept., 2008.

C. N. Yeh, H. Kosaka, and T. Kamimoto, “A fluorescence/scattering imaging technique for instantaneous 2-D measurements of particle size distribution in a transient spray,” in Proceedings of the 3rd Congress on Optical Particle Sizing (1993), pp. 355–361.

T. Kamimoto, “Diagnostics of transient sprays by means of laser sheet techniques,” in COMODIA 1994, Yokohama, Japan, 11–14 July, 1994, pp. 33–41.

F. Durst and M. Zare, “Laser Doppler measurements in two-phase flows,” in The Accuracy of Flow Measurements by Laser Doppler Methods: Proceedings of the LDA Symposium (Copenhagen, 1975), pp. 403–429.

K. Bauckhage and H. Flogel, “Simultaneous measurement of droplet size and velocity in nozzle sprays,” presented at the Second International Symposium of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2–5 July, 1984.

L. Lorenz, “Sur la lumiere reflechie et refractee par une sphere transparente,” in Oeuvres Scientifiques de L. Lorenz, Revues et Annotees par H. Valentiner (Librairie Lehmann et Stage, 1898).

T. Scheimpflug, “Improved method and apparatus for the systematic alteration or distortion of plane pictures and images by means of lenses and mirrors for photography and for other purposes,” GB patent 1196 (1904).

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Figures (14)

Fig. 1
Fig. 1

Example of the experimental arrangement of the LIF/Mie technique.

Fig. 2
Fig. 2

Scattering of a light ray at the interface of a droplet.

Fig. 3
Fig. 3

Scattered light intensity collected by (a) an infinitely small solid angle, (b) a solid angle of 3.8 ° . The significant oscillations of the scattered light intensity around the main trend that exist when light is collected by an infinitely small aperture are dampened when the light is collected. Calculations for m = 1.33 , c = 0.001 g / l , and θ = 90 ° .

Fig. 4
Fig. 4

Absorption cross section of droplets as a function of droplet diameter from low, c = 0.001 g / l , to high, c = 0.100 g / l , dye concentrations for m = 1.30 .

Fig. 5
Fig. 5

Exponent b f of Eq. (3) as a function of dye concentration in the liquid for different values of the real refractive index. Lowest dye concentrations result in closest matching of b f to the ideal value of 3.

Fig. 6
Fig. 6

Region of influence of scattered light components (diffraction and external reflection p = 0 , refraction p = 1 , first internal reflection p = 2 , second internal reflection p = 3 ). Folding of lines indicates multiple contribution of the scattered light component.

Fig. 7
Fig. 7

Real refractive index and scattering angle ( m - θ ) domain divided into 6 regions depending on the contributions of the components of scattered light (diffraction and external reflection p = 0 , refraction p = 1 , first internal reflection p = 2 , second internal reflection p = 3 ).

Fig. 8
Fig. 8

Contours of (a) exponent b s and (b) coefficient of determination R 2 of the power law fit of scattered light intensity, I s ( D ) , as a function of droplet diameter of Eq. (7), in the m - θ domain for dye concentration in the liquid c = 0.001 g / l .

Fig. 9
Fig. 9

Dependence of scattered light intensity, I s ( D ) , on droplet diameter at (a)  θ = 60 ° and (b)  θ = 90 ° for dye concentration in liquid c = 0.001 g / l and m = 1.41 . The oscillations of I s ( D ) at θ = 90 ° are attenuated when light is collected at θ = 60 ° .

Fig. 10
Fig. 10

Contours of (a) exponent b s and (b) coefficient of determination R 2 of the power law fit of scattered light intensity, I s ( D ) , as a function of droplet diameter of Eq. (7), in the m - θ domain for dye concentration in the liquid c = 0.010 g / l .

Fig. 11
Fig. 11

Dependence of scattered light intensity, I s ( D ) , on droplet diameter at θ = 90 ° , for dye concentration in the liquid c = 0.010 g / l and m = 1.41 . Oscillations of I s ( D ) persist at this dye concentration.

Fig. 12
Fig. 12

Contours of (a) exponent b s and (b) coefficient of determination R 2 of the power law fit of scattered light intensity, I s ( D ) , as a function of droplet diameter of Eq. (7), in the m - θ domain for dye concentration in the liquid c = 0.100 g / l .

Fig. 13
Fig. 13

Profile of I s ( D ) at θ = 90 ° for dye concentration in the liquid c = 0.100 g / l and m = 1.41 . Oscillations of I s ( D ) are severely attenuated at this dye concentration.

Fig. 14
Fig. 14

Profile of the I f ( D ) / I s ( D ) ratio for dye concentration in the liquid c = 0.001 g / l and m = 1.40 . In (a), θ = 60 ° , there is a linear dependence of I f ( D ) / I s ( D ) to droplet diameter with minimal oscillations of I f ( D ) / I s ( D ) . In (b), θ = 90 ° , there is a nonlinear and non monotonic dependence of I f ( D ) / I s ( D ) ratio on droplet diameter with large oscillations of I f ( D ) / I s ( D ) .

Tables (2)

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Table 1 Ranges of Parameters Considered

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Table 2 Absorption Coefficient for Various Dyes

Equations (8)

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SMD = D = 0 D 3 d N ( D ) D = 0 D 2 d N ( D )
I s ( D ) = a s D 2 ,
I f ( D ) = a f D 3 .
SMD = D = 0 D 3 d N ( D ) D = 0 D 2 d N ( D ) = D = 0 1 a f · I f ( D ) · d N ( D ) D = 0 1 a s · I s ( D ) · d N ( D ) = 1 K · D = 0 I f ( D ) · d N ( D ) D = 0 I s ( D ) · d N ( D ) ,
C abs = Q abs · A
I f = a f D b f ,
I s ( D ) = a s D b s
R 2 = 1 SS err SS tot ,

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