Streaming potential dependence on water‐content in Fontainebleau sand

SUMMARY The electrokinetic potential results from the coupling between the water flow and the electrical current because of the presence of ions within water. The electrokinetic coefficient is well described in fluid‐saturated media, however its behaviour under unsaturated flow conditions is still discussed. We propose here an experimental approach to investigate streaming potential variations in sand at unsaturated conditions. We present for the first time continuous records of the electrokinetic coefficient as a function of water content. Two drainage experiments have been performed within a column filled with a clean sand. Streaming potential measurements are combined with water pressure and water content measurements every 10 cm along the column. In order to model hydrodymanics during the experiments, we solve Richards equation coupled with an inverse problem to estimate the hydraulic parameters of the constitutive relations between hydraulic conductivity, water pressure and water content. The electrokinetic coefficient C shows a more complex behaviour for unsaturated conditions than it was previously reported and cannot be fitted by the existing models. The normalized electrokinetic coefficient increases first when water saturation decreases from 100 to about 65–80 per cent, and then decreases as the water saturation decreases, whereas all previous works described a monotone decrease of the normalized electrokinetic coupling as water saturation decreases. We delimited two water saturation domains, and deduced two different empirical laws describing the evolution of the electrokinetic coefficient for unsaturated conditions. Moreover, we introduce the concept of the electrokinetic residual saturation, S r,ek w , which allows us to propose a new model derived from the approach of the relative permeability used in hydrodynamics.