Swelling Phenomena in Electro-Chemically Active Hydrated Porous Media

Abstract

Charged hydrated materials exhibit internal coupling mechanisms stemming from the intrinsic characteristics of the constituents. In this context, the model under consideration consists of a fluid-saturated solid matrix carrying volume-free fixed negative charges, while the pore fluid is given by a mixture of a liquid solvent and the cations and anions of a dissolved salt. Based on the well-founded Theory of Porous Media (TPM), use is made of the assumption of quasi-static processes. The governing equations are given by the volume balance of the fluid mixture governed by the hydraulic pressure, the concentration balance governed by the cation concentration, the overall momentum balance governed by the solid displacement and the electrical continuity equation governed by the electrostatic force. Furthermore, the mechanical solid extra stress is described by an extended neo-Hookean material law, while the viscous fluid flow follows an extended Darcy’s law, which includes the gradients of the ion concentrations and the electrical potential. Furthermore, the ion diffusion is described by an extended Nernst-Planck equation. Finally, the model is implemented into the FE tool PANDAS by use of a mixed finite element scheme. The presented examples proceed from boundary conditions depending on internal variables such that certain stabilisation techniques are needed.