How fast does a droplet flow along a fibre?

The answer to this question has been preoccupying scientists at the University of Liège in Belgium, and it could improve the design of fog or cloud nets - water capture structures that can extract this precious resource from dry air.

Many plant species from desert regions have developed ingenious strategies to capture water from the air, ensuring their survival. Recently, researchers have focused on understanding the fundamental mechanisms of water transport, intending to reproduce and improve them, especially for facilitating the collection of atmospheric moisture in deserts.

A recent study sought to better grasp the factors influencing the movement of these precious droplets. To do this, scientists tracked in real-time, the characteristics and dynamics of these droplets as they slid along individual fibres or bundles of fibres.

"Following a droplet as it descends along a vertical fibre, under the influence of gravity presents a complex experimental challenge: how to track a droplet over several metres of thread?" explained Matteo Léonard, a researcher at the Group of Research & Applications in Statistical Physics (GRASP) and the study's lead author.

To address this problem, researchers devised a clever device in their laboratory.

"Instead of following the fall of a droplet, we set the fibre in motion, so that its speed is exactly equal and opposite to that of the droplet. This way, the droplet remains 'stationary' in front of the camera," Léonard said.

With this challenge overcome, the researchers first used fibres of different diameters. They observed that droplets had a lower speed at a given volume when the fibres were thicker, as predicted by theory.

Subsequently, researchers created bundles of fibres, by tying the ends of two or more fibres together and applying slight torsion to ensure contact between all the fibres.

"This configuration created a bundle of fibres with grooves, similar to the braiding of strands in a rope, which resulted in grooves appearing on the cord," explained Leonard.

In this configuration, researchers observed the same behaviours as with single fibres: as the number of fibres in the bundle increased, the overall diameter of the bundle increased, resulting in lower speed at a given volume. This predictable behaviour, however, concealed a more complex phenomenon.

Indeed, how would the droplet behave when both fibre configurations - single strand and bundle - have the same diameter - a fibre with 0.28mm diameter versus two fibres of 0.14mm diameter? Since the hindrance of the phenomenon is dissipation - friction within the liquid and between the liquid and the fibre, it might be expected that both cases would yield identical results, because the contact surface between the liquid and the fibre is the same in both cases.

"Not at all," says Léonard. "We observed that the droplet on the bundle of fibres was faster over the same distance travelled. It also lost the most volume."

The researchers believe that in this configuration, the droplet loses volume because it tends to fill the grooves with its own volume, thereby creating a liquid rail on which it slides more efficiently and thus faster.

The results of this study could make a significant contribution to the design of structures for atmospheric water collection. Access to fresh water is a major challenge for humanity due to water shortages for two-thirds of the world's population and devices that extract moisture from air can use the natural elements to deliver water in even the most water stressed regions.

This research could potentially improve the efficiency of cloud or fog nets - screens of fibres used by people in arid and semi-arid areas to capture water from the atmosphere as condensation, at a low cost.

Furthermore, this research highlights the growing importance of substructures regularly observed in organisms living in desert environments. These substructures, such as micro-grooves or micro-hairs, demonstrate nature's ingenuity in capturing and transporting water, inspiring future technological innovations.

The results of this study are featured in the journal Physical Review Fluids.