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BioMed Research International
Volume 2017, Article ID 5284816, 12 pages
https://doi.org/10.1155/2017/5284816
Research Article

Optimal Branching Structure of Fluidic Networks with Permeable Walls

1Department of Mechanical Engineering, Federal University of Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brazil
2Mechanical Engineering Graduate Program, University of Vale do Rio dos Sinos (UNISINOS), São Leopoldo, RS, Brazil
3Department of Physics, School of Science and Technology, University of Evora, Evora, Portugal

Correspondence should be addressed to Antonio F. Miguel; tp.aroveu@mfa

Received 1 January 2017; Revised 16 March 2017; Accepted 29 March 2017; Published 21 May 2017

Academic Editor: Kazunori Uemura

Copyright © 2017 Vinicius R. Pepe et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Biological and engineering studies of Hess-Murray’s law are focused on assemblies of tubes with impermeable walls. Blood vessels and airways have permeable walls to allow the exchange of fluid and other dissolved substances with tissues. Should Hess-Murray’s law hold for bifurcating systems in which the walls of the vessels are permeable to fluid? This paper investigates the fluid flow in a porous-walled T-shaped assembly of vessels. Fluid flow in this branching flow structure is studied numerically to predict the configuration that provides greater access to the flow. Our findings indicate, among other results, that an asymmetric flow (i.e., breaking the symmetry of the flow distribution) may occur in this symmetrical dichotomous system. To derive expressions for the optimum branching sizes, the hydraulic resistance of the branched system is computed. Here we show the T-shaped assembly of vessels is only conforming to Hess-Murray’s law optimum as long as they have impervious walls. Findings also indicate that the optimum relationship between the sizes of parent and daughter tubes depends on the wall permeability of the assembled tubes. Our results agree with analytical results obtained from a variety of sources and provide new insights into the dynamics within the assembly of vessels.