Theory of porous media with the advection term and mass exchange between phases

Abstract

Earlier modeling approaches in the field of mixtures assumed the solid phase of the mixture was the predominant constituent and simplified the constitutive laws for the fluid phase. In the field of mixtures, it has been argued that methods such as the theory of poroelasticity are incapable of accurately capturing mass exchange between phases and stress and strain fields. Mass exchange between phases and accurate stress and strain variations of each phase are indispensable to many fields of study, such as bone remodeling, fault movement in rocks, and shock waves in soils. This study presents an alternative method for capturing the stress and strain fields of mixtures, focusing on the advection term in the balance of linear momentum and mass exchange for each phase. In addition, this extended theory has the potential for measuring the shear stress field of a viscous fluid component, considering complex boundary conditions, and modeling chemical reactions between mixture phases. The capability of the model has been evaluated by analyzing 2D and 3D examples, including a realistic bone remodeling scenario. Calculations have shown a maximum difference of 20% in the displacement fields. Thus, results clearly demonstrate the importance of considering the advection term and mass exchange between phases, as its application causes significant variations in the displacement and stress fields of the mixture. The developed model of this study can be considered as a general theory, which yields the classic poroelastic model with certain manipulations.