TPDSci VSF at small angles and power law slopes

VSF at the small angles for natural dispersions and power-laws

Scattering of light at small angles down to about ~0.1° by natural dispersions in water and air is mostly due to particles larger than the wavelength of light. Note that turbulence-driven variations in the refractive index of the dispersion medium may dominate light scattering at angles smaller than ~0.1° in seawater (see VSF at the small angles for natural dispersions).

Fournier and Forand (1994) developed an analytical representation of the volume scattering function (VSF) of dispersions in seawater by assuming a power-law particle size distribution for these dispersions and by using a simplified version of the ADA model of light scattering (for example, van de Hulst 1981). They showed that the slope of the power-law size distribution, s_D, and the slope, s_β, of the VSF at a small scattering angle (approaching 0°) are related as follows:

s_β = 5 - s_D

(1)

with s_D typically falling between 3 and 4 (see also Power-law PSD for natural dispersions). It follows from Eq. 1 that the slope, s_β, of the VSF decreases as the slope, s_D, of the PSD increases. The slope s_D indicates the relative concentration of the small vs. large particles. Hence, Eq. 1 indicates that with a relatively higher concentration of the large particles (s_D is small), the VSF becomes more peaked at the small angles (s_β is large).

Eq. 1 can, with the caveats discussed in Power law in spectral scattering by natural dispersions, be used to determine the slope, γ, of the power-law spectrum of the scattering coefficient and, in certain cases, attenuation coefficient for a dispersion with a power-law PSD.

CITATION:
Twardowski M., Jonasz M. 2006. VSF at the small angles for natural dispersions and power-laws (www.tpdsci.com/Tpc/VsfSmlAngNatDspSlp.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY:
Published: 07-Sep-2006
Modified: 31-Aug-2006
Peer-reviewed: 13-Nov-2006

Topics in Particle and Dispersion Science