Approximation of the light scattering cross-section for aggregated spherical non-absorbent particles

Abstract

Powders of metallic oxides (ZrO2, TiO2, Al2O3, SiO2 …) are used as precursors in ceramic industry or as pigments in paints. Aggregation occurs in the suspension of such particles in water. The most often, the formed aggregates contain few primary particles. The on-line characterization of the suspension is made by spectral turbidimetry, i.e attenuation of a light beam by particles scattering and absorption. In order to analyse the corresponding signal, i.e turbidity, the scattering cross section and anisotropy factor of aggregates are needed. It exists an important literature about the calculation of the light scattering of aggregates. For instance, Xu [1] proposed an exact calculation based on a generalization of the Mie theory. In a previous work [2] we compare the exact value of scattering cross section (Csca) got from Xu's theory to the corresponding one from the following approximations: Effective Refractive Index (ERI) method, Percival-Berry-Khlebtsov (PBK) method, Anomalous Diffraction (AD) approximation for different aggregates morphology. We conclude that ERI method is the most conclusive over all the size parameter range α∈[0.01; 10] and for the 3 materials. Tested materials are the ones with low (SiO2, m=1.08), intermediate (Al2O3, m=1.32) and high (TiO2, m=1.94) optical contrast in water. In turbidimetry, another relevant parameter is the radiation pressure cross section (Cpr).The topic of this paper is, to extend this work by comparing the Cpr obtained with the exact theory and the one calculated with ERI method.

Light Scattering Reviews 5

“…The proportionality factors, denoted respectively p1 and p2, can be expressed as a function of a single parameter: 1 / N da   . Corresponding expressions can be found in (Jacquier and Gruy, 2007b). Table 3 presents the performances of ERI/G, Pp1 and Pp2.…”

“…In the same way that we showed the effectiveness of the ERI approximate method, for calculation of Csca, we evaluated (Jacquier and Gruy, 2007b) its performances for the calculation of Cpr. The ratio of the radiation pressure cross sections obtained on the one hand with the exact (GMM) method and on the other hand with the ERI method is denoted Lm: The deviation of Lm from 1 (Fig.…”

“…23) leads to the search of a corrective factor in order to reduce it. Jacquier and Gruy (2007b) proposed a corrective factor as a multi-parameter function   1 , , / G x N d a for the radiation pressure cross section ,, pr ERI N…”

“…Fig.7: KXu as a function of the size parameter for the linear configuration with N primary particles(2, 4, 8, 16) and for SiO2(Jacquier and Gruy, 2007a): (a) for the range…”

Relationship between the morphology and the light scattering cross section of optically soft aggregates

“…Thus simple and accurate expressions for the optical properties of aggregates are needed. Simplified methods were developed for predicting the scattering and absorption cross sections of aggregates for several practical situations [12][13][14][15].…”