Abstract

The development of initial disturbances is relevant to the understanding of atomization processes in which droplets are generated by the breakup of a liquid jet. We theoretically and experimentally demonstrate that such disturbances can be characterized by rainbow sizing. More specifically, for a liquid jet with a diameter of 600 μm, disturbances in the range from 10 nm to 0.2 μm are accessible.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. Lord Rayleigh, “On the instabilities of jets,” London Math. Soc. 10, 361–371 (1879).
  3. D. D. Joseph, Stability of Fluid Motions (Springer-Verlag, Berlin, 1976), Vol. II.
  4. K. K. Kuo, ed., Spray Atomization and Drop Burning Phenomena, Vol. 1 of Recent Advances in Spray Combustion (American Institute of Aeronautics and Astronautics, Reston, Va., 1996).
  5. J. L. Z. Tarqui, A. Silveira-Neto, T. W. Mendoza-Harrell, “Short exposure photographic technique applied to visualize a free liquid jet,” J. Flow Visualization Image Process. 4, 1–8 (1997).
  6. S. Adeline, J. B. Blaisot, S. Belaid, M. Ledoux, “Determination of instability scales on a liquid jet though an image analysis method,” In 7th International Conference on Liquid Atomization Systems, ICLASS 97 (Kyunghee, Seoul, Korea, 1997), pp. 102–109.
  7. A. J. Yule, D. G. Salters, “A conductivity probe technique for investigating the breakup of diesel sprays,” Atomization Sprays 4, 41–63 (1994).
  8. G. E. Cossali, A. Coghe, “A new laser based technique for instability growth rate evaluation in liquid jets,” Exp. Fluids 14, 233–240 (1993).
    [CrossRef]
  9. H. H. Taub, “Investigation of nonlinear waves on liquid jets,” Phys. Fluids 19, 1124–1129 (1976).
    [CrossRef]
  10. P. C. Hsing, R. S. Tankin, “Measurement of droplet size, velocity, and temperature distributions in Rayleigh flow,” Exp. Fluids 22, 144–152 (1996).
    [CrossRef]
  11. J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.
  12. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  13. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, 1992).
    [CrossRef]
  14. P. L. Marston, “Rainbow phenomena and the detection of nonsphericity in drops,” Appl. Opt. 19, 680–685 (1980).
    [CrossRef] [PubMed]
  15. J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
    [CrossRef] [PubMed]
  16. N. Roth, K. Anders, A. Frohn, “Refractive-index measurements for the correction of particle sizing methods,” Appl. Opt. 30, 4960–4965 (1991).
    [CrossRef] [PubMed]
  17. J. P. A. J. van Beeck, M. L. Riethmuller, “Nonintrusive measurements of temperature and size of single falling raindrops,” Appl. Opt. 34, 1633–1639 (1995).
    [CrossRef] [PubMed]
  18. L. Lorenz, “Lysbevaegelsen i og uden for en af plane Lysbølger belyst Kulge,” Vidensk. Selk. Skr. 6, 1–62 (1890).
  19. G. Mie, “Beiträge zur Optik Trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–452 (1908).
  20. J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. (Paris) 33, 189–195 (1955).
  21. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  22. K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in GLMT—framework, formulation, and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
    [CrossRef]
  23. G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Optics (Paris) 26, 225–239 (1995).
    [CrossRef]
  24. J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinite long homogeneous circular cylinder. I. Parametrization of the incident beam and the far-zone scattered intensity,” J. Opt. Soc. Am. A 14, 640–652 (1997).
    [CrossRef]
  25. J. Domnick, H. Ertel, C. Tropea, “Processing of phase-Doppler signals using the cross-spectral density function,” presented at the 5th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, 20–23 July 1988.
  26. J. P. A. J. van Beeck, M. L. Riethmuller, “Surface integral method to quantify the droplet non-sphericity effect on rainbow thermometry,” presented at the 81st Fluid Dynamics Symposium on Advanced Aerodynamic Measurement Technology, Seattle, Wash., 22–25 September 1997.
  27. W. Möbius, “Zur Theorie des Regenbogens und ihrer experimentellen Prüfung,” Annal. Phys. IV, 1498–1558 (1911).
  28. L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. (to be published).
  29. C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers,” in The Third International conference on Fluid Dynamic measurement and Its Applications (International Academic Publisher, Beijing, 1997), pp. 39–44.

1997 (3)

1996 (3)

1995 (2)

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Optics (Paris) 26, 225–239 (1995).
[CrossRef]

J. P. A. J. van Beeck, M. L. Riethmuller, “Nonintrusive measurements of temperature and size of single falling raindrops,” Appl. Opt. 34, 1633–1639 (1995).
[CrossRef] [PubMed]

1994 (1)

A. J. Yule, D. G. Salters, “A conductivity probe technique for investigating the breakup of diesel sprays,” Atomization Sprays 4, 41–63 (1994).

1993 (1)

G. E. Cossali, A. Coghe, “A new laser based technique for instability growth rate evaluation in liquid jets,” Exp. Fluids 14, 233–240 (1993).
[CrossRef]

1991 (1)

1988 (1)

1980 (1)

1976 (1)

H. H. Taub, “Investigation of nonlinear waves on liquid jets,” Phys. Fluids 19, 1124–1129 (1976).
[CrossRef]

1955 (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. (Paris) 33, 189–195 (1955).

1911 (1)

W. Möbius, “Zur Theorie des Regenbogens und ihrer experimentellen Prüfung,” Annal. Phys. IV, 1498–1558 (1911).

1908 (1)

G. Mie, “Beiträge zur Optik Trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–452 (1908).

1890 (1)

L. Lorenz, “Lysbevaegelsen i og uden for en af plane Lysbølger belyst Kulge,” Vidensk. Selk. Skr. 6, 1–62 (1890).

1879 (1)

Lord Rayleigh, “On the instabilities of jets,” London Math. Soc. 10, 361–371 (1879).

Adeline, S.

S. Adeline, J. B. Blaisot, S. Belaid, M. Ledoux, “Determination of instability scales on a liquid jet though an image analysis method,” In 7th International Conference on Liquid Atomization Systems, ICLASS 97 (Kyunghee, Seoul, Korea, 1997), pp. 102–109.

Anders, K.

Belaid, S.

S. Adeline, J. B. Blaisot, S. Belaid, M. Ledoux, “Determination of instability scales on a liquid jet though an image analysis method,” In 7th International Conference on Liquid Atomization Systems, ICLASS 97 (Kyunghee, Seoul, Korea, 1997), pp. 102–109.

Blaisot, J. B.

S. Adeline, J. B. Blaisot, S. Belaid, M. Ledoux, “Determination of instability scales on a liquid jet though an image analysis method,” In 7th International Conference on Liquid Atomization Systems, ICLASS 97 (Kyunghee, Seoul, Korea, 1997), pp. 102–109.

J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.

Coghe, A.

G. E. Cossali, A. Coghe, “A new laser based technique for instability growth rate evaluation in liquid jets,” Exp. Fluids 14, 233–240 (1993).
[CrossRef]

Corbin, C.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers,” in The Third International conference on Fluid Dynamic measurement and Its Applications (International Academic Publisher, Beijing, 1997), pp. 39–44.

Cossali, G. E.

G. E. Cossali, A. Coghe, “A new laser based technique for instability growth rate evaluation in liquid jets,” Exp. Fluids 14, 233–240 (1993).
[CrossRef]

Domnick, J.

J. Domnick, H. Ertel, C. Tropea, “Processing of phase-Doppler signals using the cross-spectral density function,” presented at the 5th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, 20–23 July 1988.

Dumouchel, C.

J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.

Ertel, H.

J. Domnick, H. Ertel, C. Tropea, “Processing of phase-Doppler signals using the cross-spectral density function,” presented at the 5th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, 20–23 July 1988.

Frohn, A.

Garo, A.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers,” in The Third International conference on Fluid Dynamic measurement and Its Applications (International Academic Publisher, Beijing, 1997), pp. 39–44.

Godelle, J.

J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.

Gomez, A.

Gouesbet, G.

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in GLMT—framework, formulation, and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Optics (Paris) 26, 225–239 (1995).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. (to be published).

J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers,” in The Third International conference on Fluid Dynamic measurement and Its Applications (International Academic Publisher, Beijing, 1997), pp. 39–44.

Gréhan, G.

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in GLMT—framework, formulation, and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. (to be published).

J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers,” in The Third International conference on Fluid Dynamic measurement and Its Applications (International Academic Publisher, Beijing, 1997), pp. 39–44.

Han, X.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers,” in The Third International conference on Fluid Dynamic measurement and Its Applications (International Academic Publisher, Beijing, 1997), pp. 39–44.

Hsing, P. C.

P. C. Hsing, R. S. Tankin, “Measurement of droplet size, velocity, and temperature distributions in Rayleigh flow,” Exp. Fluids 22, 144–152 (1996).
[CrossRef]

Joseph, D. D.

D. D. Joseph, Stability of Fluid Motions (Springer-Verlag, Berlin, 1976), Vol. II.

Ledoux, M.

J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.

S. Adeline, J. B. Blaisot, S. Belaid, M. Ledoux, “Determination of instability scales on a liquid jet though an image analysis method,” In 7th International Conference on Liquid Atomization Systems, ICLASS 97 (Kyunghee, Seoul, Korea, 1997), pp. 102–109.

Leroux, S.

J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.

Letellier, C.

J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.

Letoulouzan, J. N.

J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.

Lock, J. A.

Lorenz, L.

L. Lorenz, “Lysbevaegelsen i og uden for en af plane Lysbølger belyst Kulge,” Vidensk. Selk. Skr. 6, 1–62 (1890).

Maheu, B.

Marston, P. L.

Mees, L.

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. (to be published).

Mendoza-Harrell, T. W.

J. L. Z. Tarqui, A. Silveira-Neto, T. W. Mendoza-Harrell, “Short exposure photographic technique applied to visualize a free liquid jet,” J. Flow Visualization Image Process. 4, 1–8 (1997).

Mie, G.

G. Mie, “Beiträge zur Optik Trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–452 (1908).

Min, S. L.

Möbius, W.

W. Möbius, “Zur Theorie des Regenbogens und ihrer experimentellen Prüfung,” Annal. Phys. IV, 1498–1558 (1911).

Nussenzveig, H. M.

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, 1992).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “On the instabilities of jets,” London Math. Soc. 10, 361–371 (1879).

Ren, K. F.

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in GLMT—framework, formulation, and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. (to be published).

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers,” in The Third International conference on Fluid Dynamic measurement and Its Applications (International Academic Publisher, Beijing, 1997), pp. 39–44.

Riethmuller, M. L.

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, M. L. Riethmuller, “Nonintrusive measurements of temperature and size of single falling raindrops,” Appl. Opt. 34, 1633–1639 (1995).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, M. L. Riethmuller, “Surface integral method to quantify the droplet non-sphericity effect on rainbow thermometry,” presented at the 81st Fluid Dynamics Symposium on Advanced Aerodynamic Measurement Technology, Seattle, Wash., 22–25 September 1997.

Roth, N.

Salters, D. G.

A. J. Yule, D. G. Salters, “A conductivity probe technique for investigating the breakup of diesel sprays,” Atomization Sprays 4, 41–63 (1994).

Silveira-Neto, A.

J. L. Z. Tarqui, A. Silveira-Neto, T. W. Mendoza-Harrell, “Short exposure photographic technique applied to visualize a free liquid jet,” J. Flow Visualization Image Process. 4, 1–8 (1997).

Tankin, R. S.

P. C. Hsing, R. S. Tankin, “Measurement of droplet size, velocity, and temperature distributions in Rayleigh flow,” Exp. Fluids 22, 144–152 (1996).
[CrossRef]

Tarqui, J. L. Z.

J. L. Z. Tarqui, A. Silveira-Neto, T. W. Mendoza-Harrell, “Short exposure photographic technique applied to visualize a free liquid jet,” J. Flow Visualization Image Process. 4, 1–8 (1997).

Taub, H. H.

H. H. Taub, “Investigation of nonlinear waves on liquid jets,” Phys. Fluids 19, 1124–1129 (1976).
[CrossRef]

Tropea, C.

J. Domnick, H. Ertel, C. Tropea, “Processing of phase-Doppler signals using the cross-spectral density function,” presented at the 5th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, 20–23 July 1988.

van Beeck, J. P. A. J.

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, M. L. Riethmuller, “Nonintrusive measurements of temperature and size of single falling raindrops,” Appl. Opt. 34, 1633–1639 (1995).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, M. L. Riethmuller, “Surface integral method to quantify the droplet non-sphericity effect on rainbow thermometry,” presented at the 81st Fluid Dynamics Symposium on Advanced Aerodynamic Measurement Technology, Seattle, Wash., 22–25 September 1997.

van de Hulst, H. C.

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

Wait, J. R.

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. (Paris) 33, 189–195 (1955).

Wu, Z. S.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers,” in The Third International conference on Fluid Dynamic measurement and Its Applications (International Academic Publisher, Beijing, 1997), pp. 39–44.

Yule, A. J.

A. J. Yule, D. G. Salters, “A conductivity probe technique for investigating the breakup of diesel sprays,” Atomization Sprays 4, 41–63 (1994).

Ann. Phys. (Leipzig) (1)

G. Mie, “Beiträge zur Optik Trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–452 (1908).

Annal. Phys. (1)

W. Möbius, “Zur Theorie des Regenbogens und ihrer experimentellen Prüfung,” Annal. Phys. IV, 1498–1558 (1911).

Appl. Opt. (5)

Atomization Sprays (1)

A. J. Yule, D. G. Salters, “A conductivity probe technique for investigating the breakup of diesel sprays,” Atomization Sprays 4, 41–63 (1994).

Exp. Fluids (2)

G. E. Cossali, A. Coghe, “A new laser based technique for instability growth rate evaluation in liquid jets,” Exp. Fluids 14, 233–240 (1993).
[CrossRef]

P. C. Hsing, R. S. Tankin, “Measurement of droplet size, velocity, and temperature distributions in Rayleigh flow,” Exp. Fluids 22, 144–152 (1996).
[CrossRef]

J. Flow Visualization Image Process. (1)

J. L. Z. Tarqui, A. Silveira-Neto, T. W. Mendoza-Harrell, “Short exposure photographic technique applied to visualize a free liquid jet,” J. Flow Visualization Image Process. 4, 1–8 (1997).

J. Opt. Soc. Am. A (3)

J. Optics (Paris) (1)

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Optics (Paris) 26, 225–239 (1995).
[CrossRef]

J. Phys. (Paris) (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. (Paris) 33, 189–195 (1955).

London Math. Soc. (1)

Lord Rayleigh, “On the instabilities of jets,” London Math. Soc. 10, 361–371 (1879).

Phys. Fluids (1)

H. H. Taub, “Investigation of nonlinear waves on liquid jets,” Phys. Fluids 19, 1124–1129 (1976).
[CrossRef]

Vidensk. Selk. Skr. (1)

L. Lorenz, “Lysbevaegelsen i og uden for en af plane Lysbølger belyst Kulge,” Vidensk. Selk. Skr. 6, 1–62 (1890).

Other (10)

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. (to be published).

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers,” in The Third International conference on Fluid Dynamic measurement and Its Applications (International Academic Publisher, Beijing, 1997), pp. 39–44.

J. Domnick, H. Ertel, C. Tropea, “Processing of phase-Doppler signals using the cross-spectral density function,” presented at the 5th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, 20–23 July 1988.

J. P. A. J. van Beeck, M. L. Riethmuller, “Surface integral method to quantify the droplet non-sphericity effect on rainbow thermometry,” presented at the 81st Fluid Dynamics Symposium on Advanced Aerodynamic Measurement Technology, Seattle, Wash., 22–25 September 1997.

D. D. Joseph, Stability of Fluid Motions (Springer-Verlag, Berlin, 1976), Vol. II.

K. K. Kuo, ed., Spray Atomization and Drop Burning Phenomena, Vol. 1 of Recent Advances in Spray Combustion (American Institute of Aeronautics and Astronautics, Reston, Va., 1996).

S. Adeline, J. B. Blaisot, S. Belaid, M. Ledoux, “Determination of instability scales on a liquid jet though an image analysis method,” In 7th International Conference on Liquid Atomization Systems, ICLASS 97 (Kyunghee, Seoul, Korea, 1997), pp. 102–109.

J. Godelle, C. Letellier, J. N. Letoulouzan, G. Gréhan, G. Gouesbet, C. Dumouchel, S. Leroux, J. B. Blaisot, M. Ledoux, “Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,” in 7th International Conference on Liquid Atomization and Spray Systems, ICLASS-97, (Kyunghee, Seoul, Korea, 1997), pp. 117–124.

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

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, 1992).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Schematic of the optics of the rainbow. x is the distance of a ray from the axis; ρ = x/ d is the impact parameter. The three rays (labeled a, b, A) undergo one internal reflection (p = 2) and are at the origin of the rainbow. Ray A, which corresponds to the Descartes ray, is scattered at the rainbow angle θ R . Rays a and b interfere, creating the Airy structure. Furthermore, externaly reflected rays (p = 0) also interfere, creating the ripple structure of the rainbow.

Fig. 2
Fig. 2

Typical rainbow computed in the framework of the Lorenz–Mie theory.

Fig. 3
Fig. 3

Rainbows for two particles of nearly the same size (α1 = 2978.75 and α2 = 2978.99).

Fig. 4
Fig. 4

(a) Magnitude of the CSD versus frequency, (b) phase of the CSD versus frequency.

Fig. 5
Fig. 5

Phase difference versus the cylinder diameter. The reference has been arbitrarily fixed at 600.00 μm.

Fig. 6
Fig. 6

Typical recorded rainbow (continuous curve) compared with a computed rainbow (dashed curve with circles) for d = 600.000 μm, m = 1.3334, and λ = 0.6328 μm (α = 2978.75).

Fig. 7
Fig. 7

Evolution of the liquid jet diameter versus the distance from the origin, obtained from the ripple frequency.

Fig. 8
Fig. 8

Phase difference behavior at 3 mm below the orifice.

Fig. 9
Fig. 9

Rainbow corresponding to spurious discontinuities.

Fig. 10
Fig. 10

FFT spectrum of the curves of Fig. 8: PSD, power spectral density.

Fig. 11
Fig. 11

Logarithm of the mean amplitude of the dominant FFT peak versus location of the measurement point.

Fig. 12
Fig. 12

Amplitude of the dominant FFT peak for 10 consecutive records of 512 rainbows, with the location of the measurement point as a parameter.

Fig. 13
Fig. 13

Behavior of the recorded phase difference at 18 mm from the orifice for two different recordings.

Fig. 14
Fig. 14

FFT spectrum for measurements at 18 mm from the orifice for two different recordings: PSD, power spectral density.

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