- Open Access
Deviation of linear relation between streaming potential and pore fluid pressure difference in granular material at relatively high Reynolds numbers
Earth, Planets and Space volume 58, pages1045–1051(2006)
We conducted streaming potential measurements on the packing of glass beads, and investigated the deviation of streaming potential from the Helmholtz-Smoluchowski (H-S) equation. The H-S equation was originally derived on the assumption of laminar flows. Studies using a capillary have shown that the H-S equation is valid for turbulent flows in so far as the viscous sublayer is thicker than the electrical double layer and the entrance effect is negligible. Although the streaming potential in porous media has been reported to deviate from the H-S equation for turbulent flows, its mechanism is still poorly understood. We measured the fluid flux and the streaming potential as a function of the pore fluid pressure difference. The fluid flux begins to deviate from Darcy’s law at Reynolds number >3, and the streaming potential begins to deviate from the linear relation at larger Reynolds numbers. When the flow is fast, the fluid inertia separates the boundary layer from the solid surface and induces the counter flows. The fluid in the counter-flow region is separated from the circulating fluid, and ions there cannot contribute to the convection current. We think that this results in a lower streaming potential than expected from the H-S equation.
Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, 1972.
Bernabé, Y., Streaming potential in heterogeneous networks, J. Geophys. Res., 103, 20827–20841, 1998.
Bernabé, Y. and A. Revil, Pore-scale heterogeneity, energy dissipation and the transport properties of rocks, Geophys. Res. Lett., 22, 1529–1532, 1995.
Bocquet, P. E., C. M. Sliepcevich, and D. F. Bohr, Effect of turbulence on the streaming potential, Ind. Eng. Chem., 48, 197–200, 1956.
Brož, Z. and N. Epstein, Electrokinetic flow through porous media composed of fine cylindrical capillaries, J. Colloid Interface Sci., 56, 605–612, 1976.
Guéguen, Y. and V. Palciauskas, Introduction to the Physics of Rocks, Princeton University Press, 1994.
Hashimoto, T. and Y. Tanaka, A large self-potential anomaly on Unzen volcano, Shimabara peninsula, Kyushu island, Japan, Geophys. Res. Lett., 22, 191–194, 1995.
Ishido, T. and H. Mizutani, Experimental and theoretical basis of electrokinetic phenomena in rock-water systems and its applications to geophysics, J. Geophys. Res., 86, 1763–1775, 1981.
Jednačak, J., V. Paravdić, and W. Haller, The electrokinetic potential of glasses in aqueous electrolyte solutions, J. Colloid Interface Sci., 49, 16–23, 1974.
Johnson, D. L., J. Koplik, and L. M. Schwartz, New pore-size parameter characterizing transport in porous media, Phys. Rev. Lett., 57, 2564–2567, 1986.
Jouniaux, L. and J.-P. Pozzi, Permeability dependence of streaming potential in rocks for various fluid conductivities, Geophys. Res. Lett., 22, 485–488, 1995.
Kurtz, R. J., E. Findl, Al B. Kurtz, and L. C. Stormo, Turbulent flow streaming potentials in large bore tubing, J. Colloid Interface Sci., 57, 28–39, 1976.
Landau, L. D. and E. M. Lifshitz, Fluid mechanics, 2nd edn., Pergamon Press, 1980.
Lorne, B., F. Perrier, and J.-P. Avouac, Streaming potential measurements, 1. properties of the electrical double layer from crushed rock samples, J. Geophys. Res., 104, 17857–17877, 1999.
Revil, A., the hydroelectric problem of porous rocks: thermodynamic approach and introduction of a percolation threshold, Geophys. J. Int., 151, 944–949, 2002.
Revil, A. and P.W. J. Glover, Theory of ionic-surface electrical conduction in porous media, Phys. Rev. B., 55, 1757–1773, 1997.
Revil, A. and P. W. J. Glover, Nature of surface electrical conductivity in natural sands, sandstones, and clays, Geophys. Res. Lett., 25, 691–694, 1998.
Revil, A. and P. A. Pezard, Streaming electrical potential anomaly along faults in geothermal areas, Geophys. Res. Lett., 25, 3197–3200, 1998.
Revil, A., L. M. Cathles III, S. Losh, and J. A. Nunn, Electrical conductivity in shaly sands with geophysical applications, J. Geophys. Res., 103, 23925–23936, 1998.
Rutgers, A. J., M. de Smet, and G. de Myer, Influence of turbulence upon electrokinetic phenomena, Trans. Faraday Soc., 53, 393–396, 1957.
Scheidegger, A. E., The Physics of Flow through Porous Media, The Macmillan Company, 1957.
Shaw, D. J., Introduction to Colloid and Surface Chemistry, 3rd edn., Butterworths, 1980.
Stewart, P. R. and N. Street, Streaming potential and turbulence, J. Colloid. Sci., 16, 192–194, 1961.
Tuman, V. S., Streaming potential at very high differential pressures, J. Appl. Phys., 34, 2014–2019, 1963.
Turcotte, D. L. and G. Schubert, Geodynamics-Applications of Continuum Physics to Geological Problems, John Wiley and Sons, 1982.
Wong, P.-Z., Conductivity, permeability, and electrokinetics, in Methods in the Physics of Porous Media, edited by P.-Z. Wong, Academic Press, 1999.
About this article
Cite this article
Watanabe, T., Katagishi, Y. Deviation of linear relation between streaming potential and pore fluid pressure difference in granular material at relatively high Reynolds numbers. Earth Planet Sp 58, 1045–1051 (2006) doi:10.1186/BF03352609
- Streaming potential
- Helmholtz-Smoluchowski eauation
- turbulent flow
- Reynolds number