The paper presents a discussion of the use of both transport approximation for scattering phase function and diffusion-based models for radiative transfer in absorbing and anisotropically scattering media like many disperse systems in nature and engineering. The main attention is paid to heat transfer problems and traditional methods of identification of spectral radiative properties of dispersed materials when the details of angular distribution of the radiation intensity are not so important. The latter makes reasonable use of the above-mentioned approximations. In more complex applied problems, the diffusion approximation appears to be a good approach as the first step of a combined two-step solution. Some example problems solved recently by the author and his colleagues are used to illustrate the approach considered in the paper.

A modified two-flux approximation is suggested for calculating the hemispherical transmittance and reflectance of a refracting, absorbing, and scattering medium in the case of collimated irradiation of the sample along the normal to the interface. The Fresnel reflection is taken into account in this approach. It is shown that the new approximation is rather accurate for the model transport scattering function. For an arbitrary scattering medium, the error of the modified two-flux approximation is estimated by comparison with the exact numerical calculations for the Henyey–Greenstein scattering function in a wide range of albedos and optical thicknesses. Possible applications of the derived analytical solution to identification problems are discussed.

The Voronoi entropy is a mathematical tool for quantitative characterization of the orderliness of points distributed on a surface. The tool is useful to study various surface self-assembly processes. We provide the historical background, from Kepler and Descartes to our days, and discuss topological properties of the Voronoi tessellation, upon which the entropy concept is based, and its scaling properties, known as the Lewis and Aboav–Weaire laws. The Voronoi entropy has been successfully applied to recently discovered self-assembled structures, such as patterned microporous polymer surfaces obtained by the breath figure method and levitating ordered water microdroplet clusters.