Streaming potentials of granular media: Influence of the Dukhin and Reynolds numbers
Abstract
Laboratory experiments are performed to understand the controlling parameters of the electrical field associated with the seepage of water through a porous material. We use seven glass bead packs with varying mean grain size in an effort to obtain a standard material for the investigation of these electrical potentials. The mean grain size of these samples is in the range 56–3000 μm. We use pure NaCl electrolytes with conductivity in the range 10−4 to 10−1 S m−1 at 25°C. The flow conditions cover viscous and inertial laminar flow conditions but not turbulent flow. In the relationship between the streaming potential coupling coefficient and the grain size, three distinct domains are defined by the values of two dimensionless numbers, the Dukhin and the Reynolds numbers. The Dukhin number represents the ratio between the surface conductivity of the grains (due to conduction in the electrical double layer coating the surface of the grains) and the pore water electrical conductivity. At high Dukhin numbers (≫1) and low Reynolds numbers (≪1), the magnitude of the streaming potential coupling coefficient decreases with the increase of the Dukhin number and depends on the mean grain diameter (and therefore permeability) of the medium. At low Dukhin and Reynolds numbers (≪1), the streaming potential coupling coefficient becomes independent of the microstructure and is given by the well-known Helmholtz-Smoluchowski equation widely used in the literature. At high Reynolds numbers, the magnitude of the streaming potential coupling coefficient decreases with the increase of the Reynolds number in agreement with a new model developed in this paper. A numerical application is made illustrating the relation between the self-potential signal and the intensity of seepage through a leakage in an embankment.
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