Rigorous derivation of a new macroscopic model for modeling partially-saturated flow of a liquid in multilayered thin swelling porous media

Abstract

In this study we use an averaging approach for modeling a system consisting of multiple layers of thin, absorbing swelling porous media as the layer-wise 2D interacting continua, to rigorously derive a quasi- 2D averaged macroscopic mass-balance model for each layer for a system of thin porous layers made of one liquid (water) and two deformable solid phases (fiber and hydrogel). The developed model consists of a set of partial differential equations that keep track the time dependent behavior of variables such as saturation, piezometric head, porosity, and layer thickness, as the liquid moves throughout the multi-layered porous medium. Hence, this model can be used to describe the absorbency process, to predict and understand the flow and storage of a liquid in conjunction with the deformation of layers in multilayered thin porous media that is absorbing the liquid and swelling during deformation. This model will enormously improve the computational speeds, allowing one to develop a fast and reasonably accurate simulation of the unsaturated flow.