Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105
Magnetic Fluid Flows in Porous Media*
LI Ming-Jun**, CHEN Liang
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105
摘要The seepage law under a magnetic field is obtained by up-scaling the flow at the pore scale of rigid porous media, and the macroscopic equivalent model is also obtained. It is proved that the macroscopic mass flow depends on the macroscopic magnetic force and the gradients of pressure and of magnetic pressure, as Zahn and Rosensweig have described in their experiments. The permeability tensor is symmetric and positive.
Abstract：The seepage law under a magnetic field is obtained by up-scaling the flow at the pore scale of rigid porous media, and the macroscopic equivalent model is also obtained. It is proved that the macroscopic mass flow depends on the macroscopic magnetic force and the gradients of pressure and of magnetic pressure, as Zahn and Rosensweig have described in their experiments. The permeability tensor is symmetric and positive.
[1] Rosensweig R E 1997 Ferrohydrodynamics (Cambridge: Cambridge University)
[2] Borglin S E and George J 2000 Porous Media 41 61
[3] Zahn M and Ronald E 1980 IEEE Trans. Magn. 16 2
[4] Chen C Y and Wu H J 2005 Phys. Fluids 17 042101
[5] Chen C Y, Wu S Y and Miranda J A 2007 Phys. Rev. E 75 036310
[6] Geindreau C and Auriault J L 2001 C. R. Acad. Sci. Paris 329 t.11
[7] Geindreau C and Auriault J L 2002 J. Fluid Mech. 466 343
[8] Auriault J L 1991 Intl J. Engng Sci. 29 785
[9] Yamaguchi H 2008 Engineering Fluid Mechanics (Springer: Springer Science)
[10] Bensoussan A, Lions J L and Papanicolaou G 1978 Asymptotic Analysis for Periodic Structures (North Holland: NorthHolland Pub. Co.)
[11] Hornung U 1996 Homogenization and Porous Media (Hardcover: Springer)
[12] Sanchez-Palencia E 2000 Porous Media 41 61
2011, Vol. 28 
