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