Flow facilitated hierarchical pattern formation in biological transport networks

From leaf venation patterns to blood vasculature, hierarchical networks of tubes are ubiquitous in nature. We study a model where tube radius grows in proportional to local fluid flow velocity, shear rate, or flux, and show that it may facilitate the formation of hierarchical network patterns, reminiscent of some biological networks. By tuning the model parameters we observe a phase transition from homogenization (where flow is uniform) to channelization (where flow is supported by a small subset of tubes).