Fluid flow through ramified structures

We investigate the fluid flow through two-dimensional ramified structures b y direct simulation of the Navier-Stokes equations. We show that for trees with n generations, the flow distribution strongly depends on the Reynolds number Re. Specifically, for a tree without loops the flow becomes highly h eterogeneous at high Re. For a tree with loops, on the other hand, the how distribution tends to be more uniform at increased Re conditions. We show t hat these apparently contradictory behaviors have the same origin, namely, the effect of inertia on the momentum transport in the channels of the rami fied geometry. In order to simulate the propagation of the flow imbalance t hroughout the tree without loops, we develop a simple model that incorporat es the basic fluid dynamics features of the system. For large trees, the re sults of the model indicate that the distribution of flow at the outlet bra nches can be described by a self-affine landscape. Finally, we argue that t he nonuniform partitioning of flow found for the structure without loops ma y contribute to the morphogenesis and functioning of the bronchial tree. [S 1063-651X(99)18210-2].