Capillary trees for passively pumping water

Abstract

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 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 location 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 CS as a local indicator to determine the geometrical parameters of each conduct that allow to sustain the overall mass flow rate. 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’s law. The superiority of dendritic architectures in the roots and canopy branches of the capillary trees is demonstrated.

The Fastest Capillary Flow in Root-like Networks under Gravity

“…Such results are also supported by previous literature. 32,39,42 Furthermore, the capillary flow in the variable-diameter rootlike network is faster than that in equal-diameter root-like networks at 20 mm ≤ l ≤ 50 mm, because there is less viscous resistance in the variable-diameter network than the equaldiameter network with d 0 = d 1 = 0.05 mm and is subjected to higher capillary pressure than the equal-diameter network with d 0 = d 1 = 0.01 mm. Therefore, it is possible to obtain a faster capillary flow in root-like networks depending on the appropriate combination of structure parameters.…”

“…Lee studied the effects of structural parameters on dewatering rate in artificial trees driven by capillary force and proposed that the increasing conduit diameter will enhance water flux. Recently, Zhang and Lorente , analyzed the capillary flow in steady state and obtained the maximum mass flow rate in root-like networks that are generated iteratively or randomly.…”

The growth of capillary networks by branching for maximum fluid access

“…( 3)). Yet, our previous work 33 showed that in capillary networks the exponent γ in Eq. ( 3) diverges from the value 3 when the channels are in the vicinity of the network outlet.…”

Capillary efficiency study in leaf vein morphology inspired channels

“…To study the effect of α apex on capillary flow, this study establishes several capillary channel models with wedge features given the same channel length and projection area [49]. The α apex is adjusted by changing the inlet and outlet widths as shown in table 4.…”