Toward an optimal design principle in symmetric and asymmetric tree flow networks

• Published in: Journal of theoretical biology 2016-01, Vol.389, p.101-109
• Main Author: Miguel, Antonio F.
• Format: Article
• Language: English
• Subjects: Animals; Arteries - physiology; Asymmetric branching; Blood Vessels - physiology; Capillaries - physiology; Constructal law; Coronary Vessels - physiology; Dogs; Hess–Murray law; Humans; Hydrodynamics; Lung - blood supply; Lung - physiology; Models, Cardiovascular; Newtonian flow; Non-Newtonian flow; Obstructed tubes (vessels); Optimal design; Rheology; Shear Strength; Stress, Mechanical; Symmetric branching; Tree-shaped flow networks
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2015.10.027

Fluid flow in tree-shaped networks plays an important role in both natural and engineered systems. This paper focuses on laminar flows of Newtonian and non-Newtonian power law fluids in symmetric and asymmetric bifurcating trees. Based on the constructal law, we predict the tree-shaped architecture that provides greater access to the flow subjected to the total network volume constraint. The relationships between the sizes of parent and daughter tubes are presented both for symmetric and asymmetric branching tubes. We also approach the wall-shear stresses and the flow resistance in terms of first tube size, degree of asymmetry between daughter branches, and rheological behavior of the fluid. The influence of tubes obstructing the fluid flow is also accounted for. The predictions obtained by our theory-driven approach find clear support in the findings of previous experimental studies. •Fluid flow in symmetric and asymmetric tree-shaped flow networks is studied.•Flows of Newtonian and non-Newtonian are studied.•Scaling laws for optimal sizes of symmetric bifurcations are proposed.•Scaling laws for optimal sizes of asymmetric bifurcations are proposed.•Hess–Murray׳s law is justified and extended.