The ability to fabricate networks of micro-channels that obey the biological properties of bifurcating structures found in nature suggests that it is possible to construct artificial vasculatures or bronchial structures. These devices could aid in the desirable objective of eliminating many forms of animal testing. In addition, the ability to precisely control hydraulic conductance could allow designers to create specific concentration gradients that would allow biologists to correlate the behavior of cells. In 1926, Murray found that there was an optimum branching ratio between the diameters of the parent and daughter vessels at a bifurcation. For biological vascular systems, this is referred to as Murray’s law and its basic principle has been found to be valid in many plant and mammalian organisms. An important consequence arises from this law: when the successive generations consist of regular dichotomies, the tangential shear stress at the wall remains constant throughout the network. This simple concept forms an elegant biomimetic design rule that will allow designers to create complex sections with the desired hydraulic conductance or resistance. The paper presents a theoretical analysis of how biomimetic networks of constant-depth rectangular channels can be fabricated using standard photolithographic techniques. In addition, the design rule developed from Murray’s law is extended to a simple power-law fluid to investigate whether it is feasible to design biomimetic networks for non-Newtonian liquids. Remarkably, Murray’s law is obeyed for power-law fluids in cylindrical pipes. Although highly promising, the extension of the analysis to rectangular or trapezoidal channels requires much further work. Moreover, it is unclear at this stage whether Murray’s law holds for other non-Newtonian models.

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