MIT10_626S11_lec34

MIT10_626S11_lec34 - VI Porous Media Lecture 34 Transport...

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Unformatted text preview: VI. Porous Media Lecture 34: Transport in Porous Media MIT Student 1. Conduction In the previous lecture, we considered conduction of electricity (or heat conduction or mass diffusion) in a composite medium, where each component has a nonzero conductivity. In a porous medium, we focus on one “pore phase” and assign zero conductivity to the “matrix phase”. From the notation of the previous lecture, 1 = = ¡ 1 = = ¡ ¡ℎ = 0, > 1 ¢ Note: the Hashin-Shtrikman and Wiener lower bounds are zero, since any volume fraction of nonconductive material can be distributed so as to completely block conduction through the porous medium (i.e. if there is no percolating path of the conductive phase). The upper bounds are £ ¢¤¥¤¦ = 1 1 = ¡ ¡ 1 2 1 2 § 1 − ¨ £ = 1 1 − 2 1 + 1 = © − 2 − ª = © 2 − ª ¡ ¡ Percolation model (which assumes isotropic media) gives ¤¦« ~ § − « ¨ ¬ For just above the critical point « , where the exponent t=2 is believed to have a universal value for any 3D model. A simple form which captures this effect is ¤¦« ≅ ­ ® 1 − − « « ¯ 2 , ,0 « ≤ ≤ ≤ ≤ 1 « Lecture 34 10.626 Electrochemical Energy Systems (2010) Bazant since →...
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MIT10_626S11_lec34 - VI Porous Media Lecture 34 Transport...

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