It is well-known that Ag–Au bimetallic nanoplates have attracted significant research interest due to their unique plasmonic properties and surface-enhanced Raman scattering (SERS).

Streaming potential is the result of coupling between a fluid flow and an electric current in porous rocks. The modified Helmholtz–Smoluchowski equation derived for capillary tubes is mostly used to determine the streaming potential coefficient of porous media. However, to the best of our knowledge, the fractal geometry theory is not yet applied to analyse the streaming potential in porous media. In this article, a fractal model for the streaming potential coefficient in porous media is developed based on the fractal theory of porous media and on the streaming potential in a capillary. The proposed model is expressed in terms of the zeta potential at the solid−liquid interface, the minimum and maximum pore/capillary radii, the fractal dimension, and the porosity of porous media. The model is also examined by using another capillary size distribution available in published articles. The results obtained from the model using two different capillary size distributions are in good agreement with each other. The model predictions are then compared with experimental data in the literature and those based on the modified Helmholtz–Smoluchowski equation. It is shown that the predictions from the proposed fractal model are in good agreement with experimental data. In addition, the proposed model is able to reproduce the same result as the Helmholtz–Smoluchowski equation, particularly for high fluid conductivity or large grain diameters. Other factors influencing the streaming potential coefficient in porous media are also analysed.

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Summary In reservoir and environmental studies, the geological material characterization is often done by measuring its electrical conductivity. Its main interest is due to its sensitivity to physical properties of porous media (i.e. structure, water content, or fluid composition). Its quantitative use therefore depends on the efficiency of the theoretical models to link them. In this study, we develop a new physically based-model that takes into account the surface conductivity for estimating electrical conductivity of porous media under partially saturated conditions. The proposed model is expressed in terms of electrical conductivity of the pore fluid, water saturation, critical water saturation and microstructural parameters such as the minimum and maximum pore/capillary radii, the pore fractal dimension, the tortuosity fractal dimension and the porosity. Factors influencing the electrical conductivity in porous media are also analyzed. From the proposed model, we obtain an expression for the relative electrical conductivity that is consistent with other models in literature. The model predictions are successfully compared with published experimental data for different types of porous media. The new physically based-model for electrical conductivity opens up new possibilities to characterize porous media under partially saturated conditions with geoelectrical and electromagnetic techniques.