It is now possible to fabricate networks of micro-channels that mimic the bifurcating structures found in biological vasculatures. The optimum ratio between the diameters of the parent and daughter branches in biological vascular systems can be described by Murray’s law. If the network consists of symmetric bifurcations, an important consequence of Murray’s law is that the tangential shear stress at the wall will remain constant throughout successive generations. This important hydrodynamic concept can be used to provide the basis for developing simple but elegant biomimetic design rules that can be applied to microfluidic networks with arbitrary cross-sectional geometries. The present paper shows how biomimetic networks of constant-depth rectangular and trapezoidal channels can be fabricated using standard photolithographic techniques. The design rule employed is based on the mean shear stress and is used to predict and control the stress distribution within the hierarchical network. The validation of the biomimetic design rule is obtained through a comprehensive series of computational fluid dynamic studies. A range of alternative biomimetic and hydrodynamic scaling principles are also discussed, including power and Reynolds number, that enable different parameters to be controlled in each successive generation.

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