Abstract

The effective medium theory is extended to include anisotropic regular lattices regardless of their connectivity structure. Anisotropy is introduced by a lattice "decoration" process in which "conductances" of bonds aligned with different lattice directions are drawn from different probability density functions. Details of pore space and transport process are subsumed in the bond conductances. The key ingredient of the theory is a node-to-node resistance in the "anisotropic effective medium" from which the lattice effective bond conductance is determined. Node-to-node resistances of a number of two- and three-dimensional lattices are catalogued. The results accord with those of Bernasconi (1974) for square and simple cubic lattices. The relationship between effective bond conductance and macroscopic permeability (the hydraulic analog of d.c. conductivity) is discussed. Bond-percolation of the anisotropic effective medium permeability is compared with that according to Monte Carlo calculations on large two- and three-dimensional lattices. The effective medium theory is accurate to 5% except near the conduction threshold of three-dimensional lattices. The theory should prove useful for other anisotropic properties, such as capillary dispersivity, molecular diffusivity, thermal conductivity, and dynamic permeability (the hydraulic analog of a.c. conductivity).