Vladimir Mityushev and Pierre M Adler 2006 J. Phys. A: Math. Gen. 39 3545 doi:10.1088/0305-4470/39/14/004
Vladimir Mityushev1 and Pierre M Adler2
Show affiliationsThe flow in and around a fracture modelled as a two-dimensional permeable lens immersed in an infinite porous medium of different permeability is analytically solved by means of conformal mapping and Fourier transform. When the lens is more permeable than the surrounding medium, singularities occur at angular points for flow parallel to the lens, while velocities vanish at these points for flow perpendicular to the lens. In the opposite case, when the lens is less permeable than the surrounding medium, singularities are exchanged and flows parallel and perpendicular to the lens are regular and singular, respectively. Predictions are successfully compared with data obtained by a numerical code.
47.56.+r Flows through porous media
30C20 Conformal mappings of special domains
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Issue 14 (7 April 2006)
Received 15 August 2005, in final form 30 January 2006
Published 22 March 2006
Vladimir Mityushev and Pierre M Adler 2006 J. Phys. A: Math. Gen. 39 3545
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