Branching in fluidic networks with permeable walls: an extension of Hess-Murray’s law

Abstract

The branching of fluidic networks becomes a subject of great interest due to its importance in understanding the behavior of branching networks in biology (cardiovascular and bronchial systems, river basins, the structure of plants and trees, etc..), as well as for the biomimetic design of engineering systems [1, 2]. The successive division of tubes and their hierarchical structure are distinctive features of tree-shaped networks. As the network progresses, tubes become smaller, both in length and diameter with the successive division of tubes. The design of these networks is generally assumed as being described by the Hess-Murray’s law. This paper addresses a fundamental issue of distributing a fluid flow in a network of vessels with permeable walls.