The scaling laws of transport properties for fractal-like tree networks

摘要

The scaling laws of transport properties are very important for understanding the transport mechanisms of the fractal-like tree networks, which have received extensive attention recently. In this paper, we analyze the transport properties including electrical conductivity, heat conduction, convective heat transfer, laminar flow, and turbulent flow in the networks and also derive the scaling exponents of the transport properties in the networks. We show that the scaling laws are different for different transport processes and the scaling exponents are sensitive to microstructures of the networks. The models and results we present here may shed light on the transport mechanisms of the networks such as the natural systems, nanotube networks, microelectronic cooling networks, organisms, fracture networks in oil/water reservoirs, seepage flow in porous networks/media, etc., and might provide guidance for design of composites with the tree structures.