Poromechanics of Compressible Charged Porous Media Using the Theory of Mixtures

Abstract

Osmotic, electrostatic, and/or hydrational swellings are essential mechanisms in the deformation behavior of porous media, such as biological tissues, synthetic hydrogels, and clay-rich rocks. Present theories are restricted to incompressible constituents. This assumption typically fails for bone, in which electrokinetic effects are closely coupled to deformation. An electrochemomechanical formulation of quasistatic finite deformation of compressible charged porous media is derived from the theory of mixtures. The model consists of a compressible charged porous solid saturated with a compressible ionic solution. Four constituents following different kinematic paths are identified: a charged solid and three streaming constituents carrying either a positive, negative, or no electrical charge, which are the cations, anions, and fluid, respectively. The finite deformation model is reduced to infinitesimal theory. In the limiting case without ionic effects, the presented model is consistent with Blot’s theory. Viscous drag compression is computed under closed circuit and open circuit conditions. Viscous drag compression is shown to be independent of the storage modulus. A compressible version of the electrochemomechanical theory is formulated. Using material parameter values for bone, the theory predicts a substantial influence of density changes on a viscous drag compression simulation. In the context of quasistatic deformations, conflicts between poromechanics and mixture theory are only semantic in nature.