Abstract
Electrokinetic coupling between pore-fluid flow and electric field arising from the electrical double layer (EDL) has many applications in geoscience. In this study, we extended the formulas for the dynamic electrokinetic coupling coefficient (ECC) to arbitrary scaled capillaries. These two ECC formulas for the cylindrical and slit apertures, respectively, were derived without the thin or thick EDL assumption used in previous studies, relating to the normalized radius (the ratio of capillary radius to Debye length). By the identical ECC formulas for streaming current and electroosmosis effects, it is confirmed that Onsager’s reciprocity is generally satisfied for arbitrary scaled and shaped apertures. This ECC tends to the results using the thick and the thin EDL assumptions respectively with the decrease and increase of the normalized radius. It is shown that the relative error is less than 10.0% if the normalized radius is less than 0.8 and is larger than 20, respectively. Otherwise, the thick and the thin EDL assumptions are inapplicable. The high-frequency limit phase of this ECC increases from 45 o to 90 o with the decrease of the normalized radius, rather than that remains at 45 o under the thin EDL assumption. The linear approximation for solving the Poisson-Boltzmann equation influences the electric potential in the EDL and the ECC, which increases with the decrease of the normalized radius. If the normalized radius is larger than 7, the error is within 5.0% even though the linear approximation has been mathematically invalid when the salinity is 0.001 mol/L and zeta potential is -150 mV.
Highlights
Pore-fluid flow and electric field are coupled in fluid-filled porous media due to the electrical double layer (EDL) with excess charges
We have considered two different cross-sectional shapes, which are the cylindrical capillary and the capillary slit, these electrokinetic coupling coefficient (ECC) formula can be extended to porous media with circular apertures and flat fractures, respectively
We have proved that the Onsager reciprocity of the streaming current and electroosmosis ECCs is satisfied for arbitrary capillary/pore scales and cross-sectional shapes
Summary
Pore-fluid flow and electric field are coupled in fluid-filled porous media due to the electrical double layer (EDL) with excess charges. An applied electric field forces the excess charges to move, thereby driving pore fluid flow, which is referred to as the electroosmosis effect [Wiedemann, 1852]. These electrokinetic phenomena have various applications in geophysical exploration [e.g. Hu et al, 2000, 2002; Dupuis et al, 2009; Sava and Revil, 2012; Guan et al, 2013, 2015; Monetti et al, 2014; Zyserman et al, 2015], hydrogeophysics [e.g. Jouniaux and Zyserman, 2016] More introductions to electrokinetic phenomena and their applications in geosciences are available in some tutorials [e.g. Jouniaux and Zyserman, 2016]
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