Formulation of capillary hysteresis with internal state variables

A thermodynamically consistent framework is proposed for modeling the hysteresis of capillarity in partially saturated porous media. Capillary hysteresis is viewed as an intrinsic dissipation mechanism, which can be characterized by a set of internal state variables. The volume fractions of pore fluids are assumed to be additively decomposed into a reversible part and an irreversible part. The irreversible part of the volumetric moisture content is introduced as one of the internal variables. It is shown that the pumping effect occurring in a porous medium experiencing a wetting/drying cycle is thermodynamically admissible. A generic evolution equation for internal variables is developed. By virtue of the notion of the bounding surface plasticity, a model of capillary hysteresis is developed, which is capable of predicting all types of (primary, secondary, and higher-order) scanning curves within the boundary loop. Provided that the main wetting curve and the main drying curve have been experimentally determined, the proposed model requires only one additional parameter to describe all the scanning curves. The model predictions are compared with experimental measurements found in the literature, showing that the new model is capable of describing the capillary hysteretic phenomena in a variety of partially saturated porous materials.