Abstract of the paper ``Kozeny-Carman relations and image processing methods for estimating Darcy's constant'' with Stephen C. Blair

A natural connection is demonstrated between Kozeny-Carman relations for porous media and the image processing techniques which have recently been applied to the problem of estimating the parameters in such relations. We show that the specific surface area term in the Kozeny-Carman relation is best estimated from a smoothed version of the actual material surface and then demonstrate that to measure this image specific surface the magnification of a cross-section of the porous material should be chosen so that a typical correlation length for the sample corresponds to a distance comparable to 100 discrete picture elements. Under these conditions, the assumptions typically made in the derivation of a Kozeny-Carman relation are entirely compatible with the resolution constraints imposed by digitizing the image. Thus, although the measured image specific surface may be considerably smaller in magnitude than the true specific surface area of the material (due to resolution constraints), this smaller value is nevertheless the required input to the Kozeny-Carman relation. The argument is based on a known comparison theorem relating the permeabilities of two porous materials which differ only by the addition (without rearrangement) of solid to the one more porous.

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