Modeling and simulation of the chemically induced swelling behavior of anionic polyelectrolyte gels by applying the theory of porous media

Ionic hydrogels belong to the class of polyelectrolyte gels, also known as ionic gels. Their ability to swell or shrink under different environmental conditions such as change of pH, ion concentration or temperature make them promising materials for new sensoric or actuatoric devices. Numerical simulations play a crucial role for further developing hydrogel based devices. In the present contribution, a thermodynamically consistent continuum model based on the theory of porous media is derived. The governing field equations are solved on a one-dimensional domain by applying the finite element method. For the time discretization an Euler backward algorithm is implemented. The hydrogel swelling behavior is triggered by a chemical stimulus and is analyzed in space and time. Two mechanical configurations are considered: the hydrogel free swelling behavior and a mechanically clamped configuration, where the hydrogel swelling is hindered, are evaluated in detail. The presented results lead to a precise understanding of the chemo-electro-mechanical behavior and the driving pressure contributions.