Laws of non-symmetric optimal flow structures, from the macro to the micro scale

Many natural systems and engineering processes occur in which a fluid invades a territory from one entry point (invasion), or conversely is expelled from the territory through an outlet (drainage). In any such situation an evolutionary flow structure develops that bridges the gap between the micro-scale (diffusion dominant) and the macro-scale (convection dominant). The respiratory and circulatory systems of animals are clear examples of complex flow trees in which both the invasion and drainage processes occur. These flow trees display successive bifurcations (almost always non-symmetric) which allow them to cover and serve the entire territory to be bathed. Although they are complex, it is possible to understand its internal structuring in the light of Constructal Law. A scaling law for optimal diameters of symmetric bifurcations was proposed by Murray (1926), while Bejan and co-workers (2000-2006) added a new scaling law for channel lengths, and based scaling laws of tree shaped structures on theoretic...