Strain-Gradient Poromechanical Description of Unsaturated Porous Materials
Giulio Sciarra · 2013
Fluid infiltration is typical of many physical phenomena including, among others, geologic CO2 sequestration, rainfall induced infiltration, drying and desiccation. All of these phenomena are interesting to be studied, per se, but also because of the macroscopic occurrences which they trigger (for instance, CO2 displacement in aquifers, capillary trapping, drying, desiccation cracking or wetting collapse). Apparently, the infiltrating fluid is different for each of these phenomena. However, the common aspects rely on the role of capillarity in the characterisation of the partially saturated porous material. Several mathematical models have been proposed which attempt to simulate these mechanisms through suitable upscaling procedures and, consequently, at a characteristic scale much larger than that of capillarity. On the other hand, the so-called phase-field models are less common. Following Coussy's approach to a thermodynamically consistent deduction of poromechanics, and extending some previous results by the author, an enhanced poromechanical model involving gradients of strain and saturation degree is presented and discussed. Preliminary results for a biphasic van der Waals-like fluid flowing through a rigid matrix are presented aiming at capturing fingering during desiccation.