Predicting streaming potentials in partially saturated porous media, a review of capillary-based models

In the last two decades, geophysical methods are emerging to characterize and monitor hydrosystems in the critical zone. The vadose zone is the compartment of the near surface where the pore space is saturated both by water and air, this yields a very complex and nonlinear behavior in terms of water distribution and dynamics. The combination of electrical resistivity imaging and streaming potential have shown their potential to study this compartment. The streaming potential is particularly interesting as it is directly linked to the water flow and therefore offers a way for in situ monitoring. Nevertheless, the use of appropriate petrophysical relationships is required to quantitatively relate the streaming potential signals to the water flow, i.e., to model the electrokinetic coupling phenomena. During the last decade, the development of capillary-based models opened large perspectives to model flow, transport, and coupling in partially saturated porous media. In this contribution, we propose a critical comparison of existing electrokinetic coupling models, from the up-scaling approach they are based on to the capillary size distribution they consider to explain the streaming potential signal, or the shape of the capillaries they consider to explain complex features such as hysteresis.