Passive water ascent in a tall, scalable synthetic tree

Abstract

the transpiration cycle in trees is powered by a negative water potential generated within the leaves, which pumps water up a dense array of xylem conduits. Synthetic trees can mimic this transpiration cycle, but have been confined to pumping water across a single microcapillary or microfluidic channels. Here, we fabricated tall synthetic trees where water ascends up an array of large diameter conduits, to enable transpiration at the same macroscopic scale as natural trees. An array of 19 tubes of millimetric diameter were embedded inside of a nanoporous ceramic disk on one end, while their free end was submerged in a water reservoir. After saturating the synthetic tree by boiling it underwater, water can flow continuously up the tubes even when the ceramic disk was elevated over 3 m above the reservoir. A theory is developed to reveal two distinct modes of transpiration: an evaporation-limited regime and a flow-limited regime.

Modeling transpiration in synthetic trees

“…The effective nanopore radius of the disk, when not varied continuously, was either r p = 1 nm, 10 nm, or 100 nm. The porosity and tortuosity of the nanopores were fixed to = 0.32 and τ = 3.5, respectively, again in consonance with recent experimental reports [31,32] . This resulted in a permeability of k = 1 .…”

“…1 . The inner radius of each tube was fixed at r t = 1.59 mm and the number of tubes was fixed at N = 19, consistent with the tubes used in recent reports that experimentally validated the con- cept of a scalable synthetic tree [31,32] . The vertical height of the tube array, spanning from the free surface of the lower reservoir to the nanoporous leaf, was varied as either H = 10 m, 100 m, or 1,0 0 0 m. The cross-sectional area of the nanoporous disk (i.e.…”

“…The local humidity is now higher than that of the ambient, such that the Kelvin and Laplace pressures acting at the menisci are not known a priori. A recent report showed that the Kelvin and Laplace pressures, and by extension the local humidity, could be estimated by measuring the transpiration rate and invoking conservation of mass for a tree with a known hydraulic resistance [31] .…”

Transpiration-powered desalination water bottle

“…For any synthetic tree operating at steady-state, the mass flow rate of liquid water is rate-limited by the mass flow rate of evaporation from the leaf. 43 In other words, for mass to be conserved at equilibrium:…”

“…37,[40][41][42] However, in 2020 a scalable synthetic tree was demonstrated by connecting 19 plastic tubes in parallel between a water reservoir and a ceramic leaf. 43 In 2021, follow-up works used a solar lamp to boost the evaporation rate of the synthetic leaf and re-condensed the water in a solar still 44 and modeled how the transpiration rate depends on the ambient environment, heat input, and tree geometry. 45 While most synthetic trees have replenished their water from a freshwater reservoir, Wang et al recently used a saltwater reservoir to demonstrate capillary-driven reverse osmosis at the intake of the system.…”