Rayleigh-Debye theory

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... 

Lichtenbelt et al. (19) made a detailed comparison of extinction cross sections for real doublets and for hypothetical doublets coalesced into spheres. Using the Rayleigh-Debye theory for a up to three, Lichtenbelt et al. determined that the coalescence assumption leads to 10% larger values of the scattering cross section than would be found for real doublets created in coagulation. This is because a real doublet is less compact than a coalesced doublet of the same volume therefore, the interference between light waves, scattered by different parts of the real... 

Section 5.5 moves on to an extension of the Rayleigh theory essential for colloid science, namely, the Debye theory for particles of the order of the wavelength of the radiation source. The important concept of interference effects, the form factor, the Zimm plot, and... 

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... 

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. 

There is extensive literature on / /(q) for particles for which the Rayleigh-Debye criterion breaks down. Complete solutions of the problem are available for spherical particles (Mie theory) of arbitrary size and refractive index and some solutions are available for cylindrical particles. The works by van de Hulst (1957) and Kerker (1969) discuss these cases in detail. 

Figure 7.6 Intensity of light scattered from an unpolarised beam by a large spherical particle at the origin, as a function of scattering angle 6 (Rayleigh-Gahs-Debye theory). The intensity of light scattered at 135° is less than that at 45°.

Light scattered from coagulating systems can be evaluated by one of three theories Rayleigh, Rayleigh-Debye, or Mie, depending on the size... 

Mie Scattering. For systems more complex than very small particles (Rayleigh) or small particles with low refractive indices (Rayleigh-Debye), the scattering from widely separated spherical particles requires solving Maxwells equations. The solution of these boundary-value problems for a plane wave incident upon a particle of arbitrary size, shape, orientation, and index of refraction has not been achieved mathematically, except for spheres via the Mie theory (12,13). Mie obtained a series expression in terms of spherical harmonics for the intensity of scattered light emergent from a sphere of arbitrary size and index of fraction. The coeflBcients of this series are functions of the relative refractive index m and the dimensionless size parameter a = ird/k. 

Throughout this discussion, we have implicitly assumed that the rod is optically homogenous with a single index of refraction and that the Rayleigh-Debye-Gans theory is valid, which basically restricts the theory to thin rods, unless the refractive index of the cylinder is close to that of the solvent used [73]. 

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