Dependent radiation scattering for which the independent scattering theory fails to predict the scattering properties is important in analyzing radiative transfer in packed and fluidized beds. In this paper the dependent scattering properties have been derived assuming the Rayleigh–Debye scattering approximation for two cases: two identical spheres and a cloud of spherical particles. The two-sphere calculated results compare well with the exact solutions in the literature, giving confidence in the present analytical approach. The gas model and packed-sphere model have been employed to calculate dependent scattering properties for a cloud of particles of small and large particle volume fraction, respectively. The calculated dependent scattering efficiencies for a cloud of particles are smaller than the independent scattering efficiencies and decrease with increasing particle volume fraction. A regime map for independent and dependent scattering has been constructed and compared with existing empirical criteria.

Dependent radiative scattering by particles is experimentally investigated using plane-parallel cells containing latex spheres of 11, 2, and 0.08 μm diameter dispersed in an air or water matrix. The dependent scattering efficiencies and the bidirectional transmittance and reflectance were measured and compared with analytical results. The close-packed 2-μm spheres, which were expected to show dependent scattering from the previous criterion, gave results identical to independent scattering. Measured dependent scattering efficiencies of the small particles tested decrease with increasing particle volume fraction and were compared with those predicted by the theoretical investigation. The bidirectional transmittance and reflectance of dependent scattering were compared with those of independent scattering with the same number of spheres within the test cells. Several different patterns of dependent transmittance and reflectance appeared depending on the optical thickness. Finally, a newly proposed regime map bounding independent and dependent scattering is compared with the present and previous experimental data.

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The far-infrared spectra of A-type zeolite samples show broad bands sensitive to cationic exchange. We present the far-infrared spectra of five A zeolites with Li+, Na+, K+, or Ca2+ cations. The vibrational frequencies of the exchangeable cations with respect to the anionic framework have been calculated, taking in account the ions of eight sodalite units. In the potential interaction between cation and framework (electrostatic, polarization, dispersion, and repulsion), the repulsion constants are determined by a combination method, and the effective ionic charges by the orbital electronegativity method.