Fractal-like tree networks increasing the permeability

Abstract

The effective permeability of composites embedded with self-similar fractal-like tree networks is studied. The effective permeability tensor of the composites is derived and is found to be related to microstructures of the networks. The present results show that the larger the ratio of successive branching channel diameters, the higher the effective permeability; the higher the relative surface porosity of the tree networks and matrix, the higher the effective permeability; the denser the tree networks, the lower the effective permeability; the longer the branches, the lower the effective permeability. It is found that the dimensionless effective permeability of composites scales as the diameter exponent by K+(e,y) approximately beta alpham, with alpha approximately 4. It is also found that when m>1 and nbeta4/gamma<1, the effective permeability K+(e,y) scales as the iteration m, ln K+(e,y)/m approximately ln (nbeta4/gamma). The fractal-like tree networks can significantly increase the effective permeability of the composites compared to the traditional parallel nets under properly chosen structural parameters.