Constant depth microfluidic networks based on a generalised Murry's law for Newtonian and power-law fluids

Microfluidic bifurcating networks of rectangular cross-sectional channels are designed using a novel biomimetic rule, based on Murray’s law. Murray’s principle is extended to consider the flow of power-law fluids in planar geometries (i.e. of constant depth rectangular cross-section) typical of lab-on-a-chip applications. The proposed design offers the ability to control precisely the shear-stress distributions and to predict the flow resistance along the network. We use an in-house code to perform computational fluid dynamics simulations in order to assess the extent of the validity of the proposed design for Newtonian, shear-thinning and shear-thickening fluids under different flow conditions.