Microfluidic bifurcating networks for power-law fluids

Bifurcating networks are widely found in nature and are often responsible for controlling fluids that exhibit complex rheological behaviour. Examples are the vascular branching network that drives blood throughout the human body, the oxygen respiratory system in the human lungs and the bifurcating formations of xylem responsible for the distribution of water and other nutrients in plants and trees. Here, we take advantage of the biomimetic principles obtained by studying these natural systems to design fluid distribution networks for use in lab-on-a-chip devices. The novel biomimetic design rule we have recently proposed allows us to generate bifurcating microfluidic networks of rectangular cross-section for use with power-law and Newtonian fluids [1]. The design is based on Murray’s law, which was originally derived for blood flow in the vascular system, using the principle of minimum work. Murray [2] considered Newtonian fluid flows to predict the optimum ratio between the diameters of the parent and daughter vessels in networks with circular cross-section to obtain a uniform wall-shear stress along the network. In our study, we have extended the relationship to consider the flow of power-law fluids in planar geometries (i.e. geometries of rectangular cross-section with constant depth) typical of lab-on-a-chip applications. Furthermore, the design rule has been generalised to consider a range of shear-stress distributions via a branching parameter, offering the ability to precisely control the shear-stress distribution and predict the flow resistance along the bifurcating network.