Mathematical Modeling of the Process of Humid Absorption in a Porous Medium on the Example of Moisture of Lime Composites

Abstract

A mathematical description of the dependence of the equilibrium moisture content of the porous material of the lime composite on the relative humidity of the air - curves of moisture adsorption in the material under study is considered. Mathematical modeling of the moisture absorption process was performed on the basis of the representation of a certain elementary volume of a lime composite in the form of a volume-porous medium with averaged physicochemical parameters. Mathematical modeling is used for theoretical study of the laws of the process of wetting dry construction mixes. Comparison of calculated and experimental data is carried out, their good consistency is shown. The moistened material is a material with a developed surface throughout the volume and can be considered as a porous medium with effective characteristics distributed throughout the volume, such as porosity, thermal conductivity, mass diffusivity, adsorption characteristics, etc. In the process of moistening the material of the medium at each point of the porous space, an adsorption reaction occurs moisture, which has its macro and microkinetic patterns. Moist air is supplied to the internal, hard-to-reach areas of the porous material due to diffusion and air flow caused by various reasons. The speed of the microscopic reaction of wetting the surface of the composite granules should be taken into account in accordance with the theory of the dependence of the moisture content of the material on the relative humidity of the air. Analysis of the type of sorption curves makes it possible to notice that for a mathematical description of experimental dependence, it is advisable to distinguish two sections on each curve: a section with a bulge up and a segment with a bulge down. The basic equation of moisture transfer in a porous medium is a three-dimensional parabolic differential equation. Under certain conditions, the process of moistening a porous material has the same regularities on any straight line perpendicular to the air-medium interface, which makes it possible to reduce the equation to one-dimensional in spatial variables. The presented calculation results show that the value of the diffusion coefficient significantly affects the process of moistening a porous material and can be used as a measure of the possible moisture content of the composite.