Microstructure evolution and fluid transport in porous media: a formal asymptotic expansions approach

This paper investigates the effects on the behavior of a saturated porous material of an evolving microstructure induced by the mass exchange between the solid and the fluid phases saturating the porous network, using two-scale asymptotic expansions. A thermodynamically consistent model of the fluid physics flowing through the porous network is proposed first, describing microstructure variations to be captured implicitly via the level set method. The two-scale asymptotic expansions method is then applied to obtain an upscaled model capable to account for mass transfer. This last is proven to depend not only on the gradient of the macroscopic forces, such as the fluid pressure and the chemical potential, but also on the average velocity of the solid–fluid interface. Numerical simulations are carried out using the finite element method in order to evaluate the relative weight of the new terms introduced.