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

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.