Rayleigh Debye

The particles and the fluid are effectively transparent to x-rays and neutrons i.e., their effective refractive indices are nearly the same. Therefore, the criterion we specified in Equation (61) is easily satisfied, and we can avoid the need for the more complicated Mie theory (see Section 5.7b) and use the Rayleigh-Debye theories. 

Rayleigh-Debye theory operates under two assumptions [9] that allow the problem to be simplified, while still permitting the analysis of large particles. The first assumption is that np/ns - 1 1, which minimizes the effects of anomalous diffraction. The... 

Figure 3. The scattering intensity, Cj, per particle as a function of particle diameter according to the exact Mie theory (solid line) and the Rayleigh Debye approximation (dotted line).

Rayleigh-Debye-Gans Theory Theory of Mie Interacting Particles... 

FIGURE 5.71 The Rayleigh-Debye-Gans theory is based on the assumptions that (1) the incident beam propagates without being affected by the particles, and (2) the scattered hght, received by the detector, is a superposition of the beams emitted from the induced dipoles in the different parts of the particle. 

A rather general approach for determination of the function P(9) was proposed by Rayleigh and further developed by Debye and Gans. The main assumption in the Rayleigh-Debye-Gans (RDG) theory is that the incident beam that excites the electrical dipoles in the particle is not influenced (in either magnitude or phase) by the presence of the particle. This requirement is better satisfied by smaller particles wifh a refractive index close fo fhat of the disperse medium. The respective quantitative criterion reads... 

The conditions for Rayleigh-Debye-Gans scattering are as follows ... 

The Rayleigh-Debye-Gans differential scattering cross section in the scattering plane for vertically polarized light (Eigure 14.1) is... 

In Equation 14.22 the subscripts RDG and R denote Rayleigh-Debye-Gans and Rayleigh. In Equation 14.23b q is the scattering wave vector to be discussed below. 

The Rayleigh-Debye-Gans absorption cross section is equal to the Rayleigh absorption cross section. 

Farias, T.L., Koylu, U.O., and Carvalho, M.G., Range of validity of the Rayleigh-Debye-Gans theory for optics of fractal aggregates, Appl. Opt, 35, 6560, 1996. 

T. L. Farias, M. G. Carvalho, U. 0. Koylii, and G. M. Faeth, Computational Evaluation of Approximate Rayleigh-Debye-Gans/Fractal Aggregate Theory for the Absorption and Scattering Properties of Soot, ASME Journal of Heat Transfer, 117, pp. 152-159,1995. 

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