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Radiative properties of water droplets in near infrared

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Radiative Properties of Water Droplets in the Near-Infrared Spectral Range

Leonid A. Dombrovsky

Following from: The Mie solution for spherical particles, Radiative properties of semi-transparent spherical particles

It goes without saying that absorption and scattering of visible and infrared radiation by water droplets are important in numerous applications. One can remember the known problems of atmospheric optics and the thermal regime of the Earth atmosphere (Liou, 2002; Kondratyev et al., 2006). Analysis of radiation heat transfer in the presence of water droplets is also important for the calculation of fire suppression by water sprays and protection of industrial installations or other facilities from fire radiation by water curtains (Berour et al., 2004; Yang et al., 2004; Buchlin, 2005; Sacadura, 2005).

The spectral optical constants of pure water in a wide spectral range are well known (Hale and Querry, 1973; Zolotarev and Dyomin, 1977). In Fig. 1, the spectral dependences of water optical constants are given in the spectral range, which is more interesting for radiation heat transfer problems. One can see that water is semi-transparent not only in the visible (which is well known) but also in the short-wave part of the near-infrared spectral range. Two strong peaks of absorption are placed at wavelengths λ = 3 µm and 6 µm.

Figure 1.  Spectral optical constants of water.

The results of Mie theory calculations for water droplets of different sizes are presented in Fig. 2. One can see the complex resonance behavior of both absorption and transport extinction. The Rayleigh conditions are realized for very small droplets in the long-wave range. Contrary, the geometrical optics limit is observed only for large particles in the range of semi-transparency; i.e., at λ < 2.5 µm. A comparison of spectral dependences Qa(λ) and κ(λ) shows that absorption of radiation by small water droplets with a 1 µm radius follows the index of absorption. The spectral behavior of efficiency factors Qa and Qstr changes considerably with the droplet size. It is important that the approximation suggested for large semi-transparent particles gives fairly good results for water droplets of radius a ≥ 10 µm. Additional data on the radiative properties of water droplets can be found in the recent work by Dombrovsky and Baillis (2010).

Figure 2.  Spectral radiative properties of water droplets: solid curves, Mie solution; dashed curves approximation (3) from the article Radiative properties of semi-transparent spherical particles.

REFERENCES

Berour, N., Lacroix, D., Boulet, P., and Jeandel, G., Radiative and conductive heat transfer in a nongrey semitransparent medium: Application to fire protection curtains, J. Quant. Spectrosc. Radiat. Transf., vol. 86, no. 1, pp. 9–30, 2004.

Buchlin, J.-M., Thermal shielding by water spray curtain, J. Loss Prev. Process. Ind., vol. 18, no. 4-6, pp. 423–432, 2005.

Dombrovsky, L. A. and Baillis, D., Thermal Radiation in Disperse Systems: An Engineering Approach, Redding, CT: Begell House, 2010.

Hale, G. M. and Querry, M. P., Optical constants of water in the 200 nm to 200 mm wavelength region, Appl. Optics, vol. 12, no. 3, pp. 555–563, 1973.

Kondratyev, K. Ya., Ivlev, L. S., Krapivin, V. F., and Varostos, C. A., Atmospheric Aerosol Properties: Formation, Processes and Impacts, Chichester, UK: Praxis, 2006.

Liou, K. N., An Introduction to Atmospheric Radiation, 2nd ed., vol. 84, San Diego: Academic, 2002.

Sacadura, J.-F., Radiative heat transfer in fire safety science, J. Quant. Spectrosc. Radiat. Transf., vol. 93, no. 1-3, pp. 5–24, 2005.

Yang, W., Parker, T., Ladouceur, H. D., and Kee, R. J., The interaction of thermal radiation and water mist in fire suppression, Fire Saf. J., vol. 39, no. 1, pp. 41–66, 2004.

Zolotarev, V. M. and Dyomin, A. V., Optical constants in wide wavelength range 0.1 Å–1 m, Opt. Spectrosc., vol. 43, no. 2, pp. 271–279, 1977.

References

  1. Berour, N., Lacroix, D., Boulet, P., and Jeandel, G., Radiative and conductive heat transfer in a nongrey semitransparent medium: Application to fire protection curtains, J. Quant. Spectrosc. Radiat. Transf., vol. 86, no. 1, pp. 9–30, 2004.
  2. Buchlin, J.-M., Thermal shielding by water spray curtain, J. Loss Prev. Process. Ind., vol. 18, no. 4-6, pp. 423–432, 2005.
  3. Dombrovsky, L. A. and Baillis, D., Thermal Radiation in Disperse Systems: An Engineering Approach, Redding, CT: Begell House, 2010.
  4. Hale, G. M. and Querry, M. P., Optical constants of water in the 200 nm to 200 mm wavelength region, Appl. Optics, vol. 12, no. 3, pp. 555–563, 1973.
  5. Kondratyev, K. Ya., Ivlev, L. S., Krapivin, V. F., and Varostos, C. A., Atmospheric Aerosol Properties: Formation, Processes and Impacts, Chichester, UK: Praxis, 2006.
  6. Liou, K. N., An Introduction to Atmospheric Radiation, 2nd ed., vol. 84, San Diego: Academic, 2002.
  7. Sacadura, J.-F., Radiative heat transfer in fire safety science, J. Quant. Spectrosc. Radiat. Transf., vol. 93, no. 1-3, pp. 5–24, 2005.
  8. Yang, W., Parker, T., Ladouceur, H. D., and Kee, R. J., The interaction of thermal radiation and water mist in fire suppression, Fire Saf. J., vol. 39, no. 1, pp. 41–66, 2004.
  9. Zolotarev, V. M. and Dyomin, A. V., Optical constants in wide wavelength range 0.1 Å–1 m, Opt. Spectrosc., vol. 43, no. 2, pp. 271–279, 1977.

Following from:

Mie solution for spherical particles
Radiative properties of semi-transparent particles

This article belongs to the following areas:

Cooling, Refrigeration and Air-Conditioning in Applications
Thermal Processing in Applications
Energy and Buildings in Applications
Renewable Energy in Applications
Environmental Systems in Applications
Geophysical Applications in Applications
Industrial Thermal Engineering in Applications
Nuclear Engineering in Applications
Spherical particles in Fundamentals
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