TRANSPORT PROCESSES IN FRACTALS .6. STOKES-FLOW THROUGH SIERPINSKI CARPETS

The Stokes flow of a Newtonian fluid is calculated inside a porous medium that is spatially periodic, the unit cell being a fractal named a Sierpinski carpet. Complete results are given for the longitudinal permeability. A scaling argument and complete numerical calculations provide two exponents of the power law that differ by only 2 per-cent when the construction stage is large; in this limit, the scaling argument provides the same result as the classical Carman equation. The agreement between these two results may be fortuitous and thus has to be considered with caution. Various comments and extensions to three-dimensional media such as the Menger sponge are also presented.