Mathematical model of porous solid impregnation based on multichannel representation of the pore system

Abstract

In this work, based on the development of previously constructed concepts of modeling the process of impregnation of porous media with an unknown pore structure, a mathematical model was developed for calculation the change in water absorption of a body immersed in a liquid. The model is based on considering a porous structure in the form of a system of unconnected channels of three different radii. Using a theoretical model and experimental data approximations, the corresponding curves characterizing the truncated radial distribution of porous channels were obtained. Satisfactory agreement with experimental data was obtained for various porous materials. The presented calculations showed that, despite the roughness of the assumptions in the theory of fluid motion through pore channels and the pore system itself, the idea of multichannel is quite justified. It is possible that the variety of channels and their sizes determine mainly the fractal properties of the impregnated samples. The accepted scheme of pore channels shows somewhat underestimated values of the diameters of the middle channels. This indicates the need to include in the structure at least one more parameter, for example, tortuosity, in order to approximate the real characteristics of porous materials.