An effective excess charge model to describe hysteresis effects on streaming potential

Abstract

Streaming potentials are produced by the coupling between the water flow and the electrical current generated by the drag of electrical charges within the pore water of the media. This electrokinetic coupling is strongly influenced by the hydraulic properties that control groundwater flow (permeability, saturation and pressure head). Under unsaturated conditions, hydrogeologic studies have widely established that the relationships of permeability and saturation with pressure head are different for drainage and imbibition experiments. The hysteresis phenomenon present on these properties produces a hysteretic behaviour on the streaming potential which has been recently observed in experimental data. Hysteresis can be explained by the presence of irregularities in the pore geometry of the media which affects the water flow and, therefore, the excess charge density that is effectively dragged by the flow. In this study, we present a physically-based analytical model to describe the hysteresis phenomenon in the estimates of the effective excess charge density. Under the assumptions of a porous medium represented by a bundle of tortuous capillary tubes with throats and a fractal pore size distribution, hysteretic curves are obtained for the effective excess charge density as a function of pressure head using a flux averaging technique. These analytical expressions are closed-form and depend on the medium petrophysical and chemical properties. The predictions of the proposed model are consistent with laboratory data from drainage-imbibition experiments. These results open up exciting possibilities for studies involving water movement and processes in the vadose zone.