Authors:
Yuri P. Rybakov,Nataliya V. Semenova,DOI NO:
https://doi.org/10.26782/jmcms.2019.03.00040Keywords:
Darcy's Law, Filtration,Porous Medium,Transverse Diffusion,Abstract
The liquid flow in a porous medium is considered for the axially-symmetric case. The generalization of the Darcy's filtration law is suggested and the explanation of the so-called "near-wall" effect is given. The filtration efficiency is estimated for filters of two possible geometries: cylindrical and radial ones. As an illustration we consider also the case of the cylindrical filter with a bi-layer filling.Refference:
I.Bear J. (1988). Dynamics of Fluids in Porous Media. Dover Publications, Mineola.
II.Cheremisinoff N.P., Azbel D.S. (1998). Liquid Filtration. Butterworth-Heinemann, Boston.
III.Darcy H. (1856). Les FontainesPubliques de la Ville de Dijon. Dalmont, Paris.
IV.Dullien F.A.L. (2012). Porous Media: Fluid Transport and Pore Structure. Academic Press, San Diego.
V.Fara H.D., Sheidegger A.E. (1961). Statistical geometry of porous media. Journal of Geophysical Research, 66: 3279-3284.
VI.Harlemaii D.R.F., Rumer R.R. (1963). Longitudinal and lateral dispersion in an isotropic porous medium. Journal of Fluid Mechanics, 16(3): 385-394.VII.Josselin de Jong G. (1958). Longitudinal and transverse diffusion in granular deposits. Transactions of American Geophysical Union, 39: 67-74.
VIII.Kim S., Karila S.J. (1991). Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann, Boston.
IX.Knudsen W.C. (1962). Equations of fluid flow through porous media –incompressible fluidof varying density. Journal of Geophysical Research, 66(4): 1185-1197.
X.Lukerchenko V.N., Maslov D.N., Rybakov Yu.P. Shabalina T.M., Shikin G.N., Yanushkevich V.A. (2013). Electric circuit model of hydrodynamic flows in a porous medium. In “Mathematical Models of Nonlinear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere”, Nadykto A.B., ed., Uvarova L.A., ed. Nova Science Publishers, Hauppage, New York, Chapter 14, pp. 217-224.
XI.Nield D.A., Bejan A. (1999). Convection in Porous Media. Springer-Verlag, New York.
XII.Pinder G.F., Gray W.G. (2008). Essentials of Multiphase Flow and Transport in Porous Media. John Wiley & Sons, Inc., New York.
XIII.Polubarinova-Kochina P.Ya. (1960). Theory of Ground Water Movement. Princeton University Press,Princeton. XIV.Saffman P.G. (1959). A theory of dispersion in a porous medium. Journal of Fluid Mechanics, 6: 321-349.
XV.Sahimi M. (2011). Flow and Transport in Porous Media and Fractional Rock. John Wiley & Sons, Inc., New York.
XVI.Sheidegger A.E. (1960). The Physics of Flow Through Porous Media. MacMillan, New York.XVII.Sheidegger A.E. (1961). General theory of dispersion in porous media. Journal of Geophysical Research, 66: 3273-3278.
XVIII.Sheidegger A.E. (1964). Statistical hydrodynamics in porous media. Journal ofApplied Physics, 25(8): 997-1001.
XIX.Vafai K. (2015). Handbook of Porous Media. CRC Press, Taylor & Francis Group, Boca Raton.
XX.Whitaker S. (1966). The equations of motion in porous media. Chemical Engineering Science, 21: 291-300.
XI.Whitaker S. (1986). Flow inporous media I: A theoretical derivation of Darcy’s law. Transport in Porous Media, 1: 3-25.
XXII.Whitaker S. (1996). The Forchheimer equation: A theoretical development. Transport in Porous Media, 25: 27-61.
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