Leaf water shedding: Moving away from assessments based on static contact angles, and a new device for observing dynamic droplet roll‐off behaviour

Leaf wettability and drainage characteristics of different taxa are often hypothesised to have emerged as a result of evolutionary selection, perhaps to limit the duration of leaf wetness, or to direct water toward efficiently to the soil and root system, rather than suffering loss to evaporation. Methods for quantifying leaf wetting and drainage are however not well‐developed. The present work describes a low‐cost, electro‐mechanical tilting table intended to facilitate precise and reproducible measurements of droplet shedding from leaves, describe by the roll‐off angle αroll. The new tilting table uses widely‐available components (microcontroller, stepper motor and driver, liquid‐crystal display (LCD) and custom operating code) to achieve controlled tilting through the range 0° to >90° at user‐controlled rates of tilting. It is suitable for field use, such that leaf specimens can be tested within minutes of collection. Water shedding tests on juvenile leaves from Homolanthus populifolius, native to the wet tropics of northern Queensland, Australia, show that testing of whole leaves (rather than small excised samples) reveals quite complex behaviour in which the open leaf surface is hydrophobic but major adaxial veins are strongly hydrophilic and can trap droplets. These can remain attached to the leaf at inclinations beyond vertical. Moreover, the apparent droplet roll‐off angles are dependent on the tilt speed applied. Droplet roll‐off tests used to characterise the propensity for leaf wetting or water shedding require controlled and reproducible experimental conditions, and a device suitable for studying the whole intact leaf surface. Preliminary results on H. populifolius show complex adaxial leaf surface characteristics, with mixed hydrophobic and hydrophilic components. This suggests that overall propensity to retain or shed water droplets is likely to depend on the size and intensity of rain or canopy drip from above. This makes the inferring of evolutionary costs or advantages more challenging and more likely to co‐vary with regional environmental conditions.


| INTRODUC TI ON
Leaf drip, splash and drainage are key processes in the movement of water through vegetation canopies, including crop plants, shrublands and forests.They influence the amount of water that can be retained on leaves, and hence the magnitude of canopy interception and the duration of leaf wetness.Leaf wettability, described by measures of hydrophilicity or hydrophobicity, primarily of the adaxial surface, is thought to reflect the tendency for leaf water retention or drainage.
On hydrophobic surfaces, small droplets adopt an almost spherical form (Figure 1b).Despite its wide use, α fails to capture the rolling or sliding behaviour of droplets that is the central process of leaf water shedding.This has been shown by several studies in which, despite values of α in the hydrophobic or superhydrophobic range, droplets were found to remain 'pinned' on leaf surface structures, such that they did not move, and the leaf did not drain, if the leaf was tilted vertically or even inverted.Hagedorn et al. (2017) studied soybean leaves (Glycine max L.), establishing α = 162.4°but α roll = 20.9°.The latter is quite steep, compared for instance with lotus leaf (Nelumbo nucifera), for which α > 160° (similarly super-hydrophobic) but α roll = 3° (Extrand & Moon, 2014;Yi et al., 2019).Guo et al. (2019) examined eucalyptus leaves from several species (notably E. dolorosa) and found α > 150° (again, super-hydrophobic), though droplets would adhere so strongly that the leaf could be tipped upside-down without droplets becoming dislodged (tilt angle = 180°).Prajapati and Rowthu (2022) found that on banana leaves (Musa spp.), despite an adaxial α = 130° (strongly hydrophobic), droplets became pinned against ridges on the leaf, even at tilt angles of 90°.In yet other studies, a large value of α has indeed been matched by the expected correspondingly small value of α roll .
These results suggest that when whole leaves are considered, α and α roll may be only weakly related, or indeed virtually independent, in some taxa.The existence of a relationship between α and α roll remains in need of checking on a wider range of taxa and leaf characteristics.
It seems appropriate, particularly in ecohydrological studies, to place more emphasis on the leaf droplet roll-off angle, α roll , since this is the leaf inclination at which a small sessile droplet begins to move across a leaf as it is tilted away from horizontal, perhaps as a leaf droops during rainfall, under the growing weight of retained droplets.Thus, α roll may be more easily interpreted in terms of the likelihood or completeness of leaf drainage than can the static contact angle α.Lenz et al. (2022) provide a fuller list of relevant studies than can be included here.

| Experimental determination of α roll
No standardised, flexible method for measuring α roll has emerged.
Thus, using very small droplets in the 2-10 μL range will over-estimate the value of α roll that would apply to larger droplets, such as drips from foliage higher in the plant canopy, that may reach 5, 6 and 7 mm diameter (Levia et al., 2017), or equivalently droplet volumes of 65.4 μL, 113.1 μL and 179.6 μL respectively.Droplets of this size would undergo roll-off at much lower tilt angles than would the very small droplets often used in the measurement of α roll .Thus, to build a more complete understanding of roll-off angles in nature, tests need to include larger droplets, and, ideally, a range of droplet sizes spanning those found on foliage in the environment.
Generally, when the rate of tilting has been reported, it has been very slow.For instance, a rate of 60° min −1 was adopted by Mandsberg and Taboryski (2017), Guo et al. (2019) and Prajapati and Rowthu (2022), whilst Yao et al. (2020) adopted the slower rate of 30° min −1 .In some studies, no tilting rate has been specified (Extrand & Moon, 2014;Fritsch et al., 2013;Hagedorn et al., 2017).Owing to the lack of attention to the rate of tilting, it has not become clear whether this aspect of the measurement procedure alters the measured value of α roll .
Finally, it is worth noting that in many determinations of α roll , small pieces of leaf are excised, rather than examining the entire in-tact leaf surface.For instance, Extrand and Moon (2014) and Hagedorn et al. (2017) used cut leaf pieces of 1 cm 2 .This excludes the possible influence of venation and other macroscopic leaf surface features.There is a need for a device that can allow speedy testing of whole leaf specimens and so permit the study of oblique or transverse roll-off across whole leaves, as well as roll-off in the direction from petiole to leaf tip.It is likely that many leaf surfaces have macroscopic features affecting droplet roll-off that cannot be properly captured from a 1 cm 2 cut fragment.A suitable device would allow rapid testing of whole leaf specimen in various orientations, such that a moving droplet crossed leaf surface structures at various angles.The orientation of droplet drainage has been shown to result in wide variations in α roll .Prajapati and Rowthu (2022) for instance showed that ridges on banana (Musa spp.) resulted in free drainage for droplets moving parallel to the ridges but droplets became pinned when drained normal to the ridges, even when the leaves were tilted to 90° from horizontal.Guo and Liu (2007) and Lee et al. (2013) drew attention to a similar phenomenon on rice leaves (Oryza sativa), in which drainage down the leaf parallel to small ridges resulting from vascular bundles was much freer than transverse drainage.Evidently, the orientation of the leaf during determination of α roll is significant and should not be excluded from study.

| A small, portable tilting table for studies of leaf droplet roll-off angle
The objective of the work reported here was to develop a motorised tilt table suitable for carrying out more standardised and controlled lab or field-based study of leaf droplet water-shedding and roll-off angles.In tilt tests of rock sliding on fracture surfaces, motorised tilt tables have become accepted as the best form of apparatus (Alejano et al., 2018) and it is desirable for similar standardisation in leaf water droplet roll-off tests, and for the possible influence of tilt rate to be investigated.Such a device should permit exact rates of tilting to be reproducible in replicate experiments where other test conditions, such as droplet size and direction of drainage, are varied.The design criteria for the device described below included the following: 2. Robust, compact and portable, and able to be taken into the field.
4. Motorised, with smooth tilting action covering the range 0° to >90°, and adjustable, precisely-controlled, tilting speed. 5. Tilting speed to be user-adjustable, and indicated on a small LCD.
6. Instant motor stop when roll-off is observed, with display of the corresponding angle on a small LCD.
7. Suitable tilting table surface to which leaf specimens could be held using map pins.
8. Waterproof control electronics, based on proven and readilyavailable components.9. Completely re-programmable via a laptop if required (e.g. to change units from degrees of tilt to % or radians, or to alter default tilt rate settings) but able to work as a free-standing device.
The above goals were realised in a device employing a stepper motor and programmable control electronics, and a hinged table to which leaf specimens could be attached.Tilting rate was adjustable, and the angular resolution was 0.01°.Schematic diagrams, together with technical, calibration and operating details, and a brief video of the tilting table in operation, are provided in the Supporting Information.

| The test plant-Homalanthus populifolius
Preliminary tests of the tilt table were carried out on whole juvenile leaves of the Queensland poplar, Homalanthus populifolius, commonly known as the 'bleeding heart' owing to the bright red colour of its senescent leaves.H. populifolius is an Australian native rainforest tree that grows to about 8 m.Casual observation had suggested that the juvenile leaves are markedly hydrophobic, though mature leaves are much less so.Apart from droplets pinned on veins (Figure 1c), the adaxial surface of juvenile leaves frequently appears quite dry even following days of rain.Leaf length and breadth are typically 5-10 cm.Leaves of H. populifolius have a pinnate-reticulate pattern of venation, the primary vein network being pinnate and the major lateral veins networked by much smaller reticulate venation.Leaves were collected within 100 m of a field laboratory on the Atherton Tableland in far northern Queensland, Australia, to which they were carried in a sealed plastic container, and tests performed within 5 min of collection.
Fieldwork was conducted on private land with the permission of the owner.

| Mounting of leaf specimens
The tilting table was surfaced with a sheet of EVA (ethylene vinyl acetate) foam, available in the form of inexpensive flooring tiles.Leaves were attached using map pins adjacent to the leaf margins-the leaves were not punctured.Leaves are not planar, so this mounting method permits undulations in the leaf to remain, in contrast to the use of double-sided tape to attach excised pieces of leaf that are held flat.
Water droplets were placed on the test leaf specimens using a 5-50 μL adjustable laboratory micropipette.Initial locations for droplet placement were on the open leaf surface, away from veins, in all experiments.Droplet sizes of 10, 20 and 50 μL were tested.Local rainwater from the field area, collected in washed plastic containers, was used in all experiments.This was done for better correspondence with local conditions, than the use of distilled or deionised water, which is common in leaf wettability studies (e.g.Extrand & Moon, 2014).The field location was not far from the coastline, and dissolved salts from condensation nuclei could be expected in rain.
Such solutes can influence surface tension, and hence potentially water shedding behaviour.

| Tilt rate and tilt angle
A power function relationship, having r 2 = 0.999, was established between the frequency of step pulses fed to the motor and the rate of tilt (α rate ) in degrees per minute (Figure 2a).The device was readily able to generate tilt speeds from tens of degrees per minute to hundreds of degrees per minute.The power function regression model was: in which α rate is expressed in degrees per minute, and motor pulses provided by the stepper motor controller are expressed by their duration in μs.
A similar relationship, having r 2 = 0.998 was established between the number of step pulses fed to the motor and the resulting tilt angle in degrees, as measured by the digital inclinometer (Figure 2b).This relationship was only applied for angles of tilt of up to 90°, though in some experiments, the tilt table was allowed to overturn to observe whether droplets would remain suspended.The linear regression model was: in which the tilt angle is specified in degrees and the number of motor pulses, N, is dimensionless.

| Droplet size and roll-off angles
Roll-off tests were carried out with droplets of 10, 20, and 50 μL volumes.These tests were carried out on single leaves of H. populifolius.Repeated tests on the same leaf specimen and from the same initial droplet position was possible because the leaf surface remains dry after each test, owing to complete droplet roll-off, and the tilt table device permits tests to be completed rapidly and in quick succession.

| Effect of leaf venation on droplet adhesion or roll-off
During tilt tests (and also from opportunistic observations made on plants in situ at rainforest locations during periods of rain) it became clear that the leaf surface along major veins was not hydrophobic.This was indicated by a clear tendency for droplets to roll down the sloping leaf surface but come to rest on a vein, or at the junction of main and secondary veins.The adhesion of the droplet to the surface of a vein can clearly been seen through the clear water droplet shown in Figure 1d.When tilted, droplets lodged in such locations deformed (Figure 1c) to exhibit widelydifferent advancing and receding contact angles, but did not roll.
In some cases, test leaves could be tilted to beyond 90° with the droplet still attached to the vein surface.Roll-off angles for droplets pinned to veins of up to 60°-80° were recorded, depending on the test droplet size (Table 1).For both 20 and 50 μL droplets, much larger α roll was found for droplets lodged on veins than for droplets of the same size deposited on the open leaf surface away from veins.Generally, α roll from the mid-vein was more than twice those recorded on the open leaf surface, for which α roll was generally <10° for 50 μL droplets.

| The effect of tilt rate on roll-off angle
As noted above, whether the rate of tilting affects α roll remains unclear, since there has not been a suitable device with which to explore this question.This was tested using a single H. populifolius leaf.A junction of two veins was found to be a location to at which drops deposited on the leaf would rapidly settle, and repeated roll-off angle tests were carried out by placing 20 μL droplets at this same location for each replicate test.The marked hydrophobicity of the test leaf ensured that no residual water remained on the leaf after each of 12 successive tilt tests that were carried out over a period of about 5 min.The results (Figure 3) showed that at the fastest tilt rate, the roll-off angle was 7.9°, but this rose to 16.2° at the slowest tilt rate.Thus, droplets were apparently more (1)  = , () −.
stable, and less prone to roll, if the leaf was tilted slowly.Ideally, this kind of test would be repeated using different droplet sizes and with different taxa.
The relationship between tilt rate and roll-off angle was fitted by an exponential regression model having r 2 = 0.93.The relationship was where α roll is expressed in degrees and α ratel is expressed in degrees per minute.

| DISCUSS ION
The device described here was found to facilitate quick determina- tions of leaf roll-off angle α roll , and to support tests using widely varying but controlled, constant tilt rates.The device has been robust (3) = .
− ., The variation of roll-off angle with droplet size is more straightforward to understand.Especially on strongly hydrophobic leaves such as the juvenile leaves of H. populifolius, large drops are inherently less stable than smaller droplets.Furthermore, small droplets could have most of their area of attachment to the leaf surface localised on a vein, where the surface seems to be hydrophilic.Such droplets would exhibit a diminished tendency to move, until a steeper angle of tilt was achieved.It would be informative to explore this further, and to find the largest droplet size that can be pinned to a vein.
Droplet rolling is only one aspect of water shedding on leaves, and splash must also be considered, because most water droplets arriving at the surface of a leaf would do so by falling and striking the leaf surface.There is an exception for fog droplets, which are far smaller, but which can coalesce on a suitable leaf surface to form larger droplets that are of sufficient size to run off the leaf as fog drip.The apparatus describe here might prove useful in drop collision experiments, to characterise the nature of splash on leaves sitting at different angles in relation to the trajectory of a falling drop.
Several additional areas of enquiry bearing on leaf wetting and water shedding, and that warrant further research, can be highlighted: 1. Droplets often arrive at the leaf surface after falling as rain or as drips from higher in the canopy.In both cases, there is an impact at the leaf surface, and this cannot be well represented by tilt-table tests using a sessile drop carefully placed droplet contact angle, hydrophilicity, hydrophobicity, leaf roll-off angle, leaf wettability F I G U R E 1 Droplets on leaves of Homolanthus populifolius.(a).Pendant drop pinned to a vein despite inclination of 70°.Note advancing angle larger than receding angle, and pinning of drop with only a small area of attachment to the vein.(b) 10 μL droplet on open leaf surface showing near-spherical form typical of hydrophobicity.(c) Small droplets (5-10 μL) on a leaf in situ following sustained drizzle.Note that virtually all droplets are pinned to veins.(d).View through the upper surface of a 50 μL droplet pinned to a vein.The narrow area of hydrophilic contact is clearly visible as a darkened area along the vein and its margins.
using a micropipette.How does splashing vary with the angle of incidence of the drop, and the water-shedding behaviour of the leaf surface?Do leaf surface structures such as veins exert a reduced influence on drop retention or shedding when the drop arrives in such an impact?2. It is unclear how frequently droplets adhere to structures on the leaf surface, such as veins, despite the bulk of the surface being hydrophobic.Do pinned droplets merge with others in collisions, and it is this process that in due course results in roll-off, when the droplet has become sufficiently large?How common is theF I G U R E 3The relationship between roll-off angle (α roll ) and the rate of tilting of the leaf specimen (α rate ).The dotted line is the exponential regression model shown in Equation (3).
Details of tilt table calibrations.(a)scatterplot of the tilting rate versus the duration of pulses send to the winding motor.Pulses at a higher frequency achieve more rapid tilting.The dotted line is the power-function regression model of Equation (1).(b) scatterplot showing measurements of tilt angle versus the number of stepper motor pulses sent to the winding motor.A strongly linear relation is evident.The dotted line is the linear regression model of Equation (2).Tests were carried out at a tilting rate of α roll = 160° min −1 .andreliable in testing to date, even in very wet monsoonal tropical conditions.The cost of the device is modest, at approx.A$100.There are other devices that can be applied to investigate droplet motion.
come to rest.However, if the tilting is faster, the rolling droplet may acquire sufficient momentum to roll through a nearby stable location, and continue to roll from the leaf.Other hypotheses may emerge from further research.