Theoretical foundation for conductivity scaling

Scaling of conductivity with the support volume of experiments has been the subject of many recent experimental and theoretical studies. However, to d ate there have been few attempts to relate such scaling, or the lack thereo f, to microscopic properties of porous media through theory. We demonstrate that when a pore network can be represented as a collection of hierarchica l trees, scalability of the pore geometry leads to scalability of conductiv ity. We also derive geometrical and topological conditions under which the scaling exponent takes on specific values 1/2 and 3/4. The former is consis tent with universal scaling observed by Neuman [1994], while the latter agr ees with the allometric scaling laws derived by West et al. [1997].