Asymmetric Flow in Symmetric Branched Structures

Abstract

We investigate the fluid flow through a cascade of bifurcations by direct simulation of the 2D Navier-Stokes equations. We show that, for a fully symmetric tree with $n$ generations ( $n\ensuremath{\ge}3)$, the flow distribution becomes significantly heterogeneous at an increased Reynolds number. We develop a binary tree model and find that the distribution of flow at the outlet branches can be described by a self-affine landscape, with a self-affine exponent $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.9$ for the human lung. We suggest that the asymmetric flow occurring in symmetric branched structures may be important both for the morphogenesis of the bronchial tree, and for its functioning during inspiration.