Capillary trees for passively pumping water

Capillary flows are an attractive feature for passive water harvesting as they require no external driving force to pull the fluid out within the capillary network. Here we analyze the architecture of capillary flow networks in a steady state, and the impact of the network morphology on the maximum mass flow rate that can be extracted for a fixed network volume and fixed network footprint. We develop a search algorithm to test the possible locations of all the junction and bifurcation nodes and the changes in diameter ratios with the objective of obtaining the maximum mass flow rate from the network. We define the capillary strength as a local indicator to determine the geometrical parameters of each channel that allow the overall mass flow rate to be sustained. It is shown that the diameter ratio of connected tubes for maximum mass flow rate depends on the distance from the network outlet, and therefore does not follow the Hess-Murray law. The superiority of dendritic architectures in the roots and canopy branches of capillary trees is demonstrated.

Automated summary

In this study, the architecture of capillary flow networks in a steady state is analyzed, and the impact of network morphology on maximum mass flow rate is investigated. A search algorithm is developed to determine the optimal parameters. The results demonstrate the superiority of dendritic structures in the roots and canopy branches of capillary trees.