a fluid dynamics-based modified murray law for hierarchical vein networks in lotus leaves: geometry, transport mechanism and biological implications

Lotus leaf is famous for its so-called lotus effect, which has evoked many advanced biomimetic designs, especially for surface’s wetting properties, its tree-like veins are also a source of brilliant innovations. the geometry of the veins is similar to that of blood vessels, where murray’s law can elucidate the branched structure. however, the law is not valid for the lotus’ vein structure. here we find a new law to reveal the geometry, and its biological understanding is elucidated, furthermore murray’s law is a special case of the new found law. our findings may be of great biological and technological importance, especially in plant ecology, urban traffic planning, watershed planning, and chemical engineering.