Modeling the Swelling of Hydrogels with Application to Storage of Stormwater

• Main Authors: Hans O. Åkerstedt, T. Staffan Lundström, I.A. Sofia Larsson, Jiri Marsalek, Maria Viklander
• Format: Article
• Language: English
• Published: MDPI AG 2021-12-01
• Series: Water
• Subjects: stormwater; storage; sponge-like porous media; swelling; hydrogel; modeling
• Online Access: https://www.mdpi.com/2073-4441/13/1/34

The swelling effect in hydrogel bodies or sponge-like porous bodies (SPB) used in a specific stormwater storage concept of the down-flow type is considered. A macroscopic swelling model is proposed, in which water is assumed to penetrate into the hydrogel by diffusion described by diffusion equations together with a free-moving boundary separating the interface between the water and hydrogel. Such a type of problem belongs to the certain class of problems called Stefan-problems. The main objective of this contribution is to compare how the theoretical total amount of absorbed water is modified by the inclusion of swelling, when compared to the previously studied SPB devices analyzed only for the effect of diffusion. The results can be summarized in terms of the geometrical dimensions of the storage device and the magnitude of the diffusion coefficient <i>D</i>. The geometrical variables influence both the maximum possible absorbed volume and the time to reach that volume. The diffusion coefficient <inline-formula><math display="inline"><semantics><mi>D</mi></semantics></math></inline-formula> only influences the rate of volume growth and the time to reach the maximum volume of stored water. The initial swelling of the hydrogel SPB grows with time (<inline-formula><math display="inline"><semantics><mrow><msqrt><mrow><mi>D</mi><mi>t</mi></mrow></msqrt></mrow></semantics></math></inline-formula>) until the steady state is reached and the swelling rate approaches zero. In all the cases considered, the swelling in general increases the maximum possible absorbed water volume by an amount of 14%.