Modeling the Swelling of Hydrogels with Application to Storage of Stormwater

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 D. The geometrical variables influence both the maximum possible absorbed volume and the time to reach that volume. The diffusion coefficient D 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 (Dt) 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%.

Control of Ferroelectric Domain Wall Motion using Electrodes with Limited Conductivity

This chapter addresses the experimental control of ferroelectric DW motion in thin films using electron-beam induced deposition (EBID) electrodes with limited conductivity which governs the supply of charges required for DW nucleation and propagation. The problem of a moving domain boundary, addressed in this chapter, belongs to the general class of free-boundary problems, or Stefan problems, after Josef Stefan who mathematically described ice formation and then demonstrated generality of his approach by applying the same technique to describe diffusion. In the frame of this approach the position of the boundary is determined from the transport of a physical quantity, flowing through and partially consumed at the boundary. Nowadays mathematical modelling of Stefan problems has developed into a rich field of knowledge where both analytical and numerical methods are applied to solve various important applied tasks. In this chapter, the process is described by analogy to the classical Stefan model, historically applied to the motion of phase boundaries under propagation of heat but which is here applied to precisely describe DW motion under linear electrodes and the 2D growth of a circular domain.