‘Sneezing’ plants: pathogen transport via jumping-droplet condensation

Abstract

We show that condensation growing on wheat leaves infected with the leaf rust fungus, Puccinia triticina, is capable of spontaneously launching urediniospores off the plant. This surprising liberation mechanism is enabled by the superhydrophobicity of wheat leaves, which promotes a jumping-droplet mode of condensation powered by the surface energy released from coalescence events. We found that urediniospores often adhere to the self-propelled condensate, resulting in liberation rates of approximately 10 cm⁻² h⁻¹ for leaves infected with rust. Urediniospores were catapulted up to 5 mm from the leaf’s surface, a distance sufficient to clear the laminar boundary layer for subsequent dispersal even in gentle winds.

1. Introduction

The spread of plant pathogens through the atmosphere involves processes of liberation (take-off and ascent), drift (passive horizontal transport) and deposition (descent and landing) [1,2]. Liberation is influenced by various ecological and environmental factors that dictate the timing and mechanism of release, drift is associated with the passive, directed movement away from the ground surface in turbulent air currents and deposition involves descent and landing at a new destination [1]. Knowledge of these processes may assist growers and producers in making rational and informed management decisions, for example the application of a fungicide to control a specific plant pathogen [3–5].

Wheat represents about one quarter of the world’s food supply [6], and plant pathogens threaten the global productivity of this staple food crop [7]. Wheat losses to plant diseases are extremely costly to food security because these crop losses are realized after most input costs and management decisions have been made. One of the most devastating diseases of wheat is leaf rust caused by the fungus Puccinia triticina. The liberation and dispersal of urediniospores of P. triticina (among others) have been attributed to wind [8] and rainsplash [9,10].

Wheat leaves are known to exhibit a superhydrophobic surface wettability [11]. Previous studies have demonstrated that properly engineered superhydrophobic surfaces can enable jumping-droplet condensation via a two-step process. First, nanoscale embryos nucleate within the surface roughness but inflate into large-angle micro-droplets whose outer contact line exhibits the suspended Cassie state [12–14]. Second, these low-adhesion micro-droplets coalesce during natural growth, which converts surface energy into kinetic energy by virtue of the expanding liquid bridge breaking symmetry as it impacts the substrate [15–17]. Jumping-droplet condensation has been observed on engineered superhydrophobic surfaces [12–15,18], cicada wings [19], lotus leaves [20], geckos [21] and water strider legs [22].

Previous studies of jumping-droplet condensation were confined to exotic organisms such as lotus leaves; here, we show that jumping-droplet condensation occurs on the leaves of the common wheat plant. For diseased leaves, we demonstrate that jumping-droplet condensation is an important liberation mechanism for pathogenic spores. The jumping dynamics are sufficient to propel the spores beyond the laminar boundary layer, enabling subsequent dispersal by gentle winds. While recent reports have demonstrated that jumping droplets can remove dust or pollen from a superhydrophobic surface [19–21], the scope was limited to the self-cleaning of the individual organism. Here, we instead reveal the ironic twist of liberating particles in the new context of pathogenic material: jumping droplets can free spores from a given leaf, but subsequent dispersal can spread the disease across the crop. Spores are conventionally sorted into two different types: those actively ejected and those released by strong winds [23]. Our findings show that both types are simultaneously possible in a complementary fashion, with jumping-droplet ejection dominating in gentle conditions while wind-induced vibration/shear can remove spores in gusty conditions.

2. Material and methods

2.1. Cultivating wheat leaves

A seed mix of susceptible winter wheat lines (Massey, and testing line VA-135) were provided by the Griffey lab at Virginia Tech. This was used to grow wheat plants in a Conviron growth chamber (Model PCG 20) with the following settings: long day 12/12 h, light intensity 120 μmol m⁻² s⁻¹, temperature 24°C and a relative humidity of 50%. Urediniospores of P. triticina ( = P. triticina Roberge ex Desmaz. f. sp. tritici) race TCRKG were maintained at −80°C and conditioned in a 1.5 ml Eppendorf tube at 45°C in a hot water bath for 5 min. The tube was agitated twice during the incubation. The 1.5 ml tube was then placed, lid open, in an upright 50 ml Falcon tube with a moistened paper towel for 3 h. Following this humidity treatment, spores were suspended in a 50 ml conical tube in 30 ml of sterile water with 0.1% Tween 20 as a surfactant (Fisher Scientific) and aerosolized with a Prevail atomizer unit (Chicago Aerosol) onto six week old wheat plants. Inoculated plants were incubated in the dark at 100% humidity (136 DL dew chamber, Percival Scientific) for 24 h at 18°C to encourage infection, and then removed back to controlled growth conditions for disease development. Symptoms of leaf rust (the development of brown/orange lesions) and signs of the fungus (uredinia bearing urediniospores on the leaf surface) appeared within 7–12 days.

2.2. Experimental set-up

For condensation experiments on the wheat leaves, a Peltier stage (Linkam, Model T95-PE) was used to control the surface temperature. A section of a wheat leaf was thermally bonded to the Peltier element with a thin coating of thermal grease (Thermalcote, Part No. 251 G, k = 0.765 W m⁻¹ K). For spore counting experiments, acrylic spacers were placed on two sides of the Peltier element such that another (longer) piece of acrylic could bridge the gap. Water-sensitive paper (Syngenta, Part No. 347456, original size 76 mm × 26 mm) was adhered to the underside of the bridging acrylic by taping its outer edges, such that the gap between the wheat leaf and paper was either 1.5 mm, 3 mm or 5 mm. The experiment was run for 1 h by chilling the Peltier stage down to 0°C, during which condensation readily grew on the surface of the leaf. The paper was then removed from the set-up and placed under a microscope to quantify the adhered spores.

2.3. Contact angle measurements

The contact angles of 10 μl droplets deposited on wheat leaves were measured on a goniometer (ramé-hart, Model 590) using the shrink–swell method.

2.4. Imaging

We made use of the Vision Research Phantom v711 high-speed colour camera, which is capable of recording up to 7500 frames per second at full 1280 × 800 resolution. The high-speed camera was mounted on an optical microscope (Nikon, Eclipse LV150) for top-down imaging. A 20 × Mitutoyo objective lens (Part No. 378-810-3) was used for counting the number of spores. The top-down perspective was useful for obtaining statistical information on the dispersal rates of fungal spores over time due to jumping droplets. For side-view imaging of the jumping droplets, the high-speed camera was attached to either a macro lens (Canon, MP-E 65 mm, 1–5 × mag) or a long-distance microscope (Infinity Infiniprobe TS-160, 1–16 × mag).

2.5. Mechanical vibration

A 5 cm long segment was cut from a typical sporulated wheat leaf and taped to a flat stage fixed to a mechanical wave driver (PASCO, SF-9324). The amplitude and frequency of the driver were controlled using a function generator (Agilent, 33210A) along with a power amplifier (KROHN-HITE 7500). The frequency of vibration was gradually increased to find the critical frequency required to detach spores from the leaf surface.

2.6. Air flow

Wind tunnel experiments were conducted in an Airtech X-Stream wind tunnel (Model 57889). For a given velocity of the air flow, a 5 mm segment of a sporulated wheat leaf was double-sided taped on a laboratory jack and left inside the wind tunnel for 5 min.

3. Results

The jumping-droplet mechanism of spore liberation requires a natural dew cycle on a superhydrophobic surface, as conceptualized in figure 1 for the case study of wheat leaves. On healthy wheat leaves, the advancing and receding apparent contact angles were θ_A = 127 ± 5° and θ_R = 117 ± 3°, respectively, while droplets on the central region of diseased leaves exhibited a more hydrophobic θ_A = 144 ± 6° and θ_R = 138 ± 9° (figure 2a). These contact angles are at the very low end of the superhydrophobicity spectrum, as most superhydrophobic surfaces exhibit θ_A > 150° [24]. However, these contact angles are highly dependent upon the size of the droplets, as micrometric condensate can exhibit larger angles. Regardless, the low contact angle hysteresis of θ_A − θ_R ≤ 10° indicates that air pockets are trapped beneath the deposited droplets to promote the low-adhesion (Cassie state), which satisfies the second (and more important) criteria for superhydrophobicity [24]. For the diseased wheat leaves in particular, the wettability was found to be heterogeneous, with either end of the leaf being less hydrophobic: θ_A = 120 ± 20° and θ_R = 100 ± 30°.

Figure 1.

Jumping-droplet mechanism of spore liberation. (a) Schematic of the liberation of rust spores via the coalecence-induced self-propulsion of dew droplets growing on diseased wheat leaves. The self-propulsion is predominantly out-of-plane, resulting in the spore-laden droplets clearing the boundary layer for dispersal in the wind. (b) False-coloured ESEM micrograph of a sporulated wheat leaf. The radius of a typical P. triticina spore is r_s = 8.0 ± 1.9 μm. (Online version in colour.)

Figure 2.

(a) Advancing and receding contact angles as measured on diseased and healthy wheat leaves. Results correspond to an average of three separate trials, and error bars represent a standard deviation. (b) Self-assembly of spores on the surface of a wheat leaf. In particular, agglomerates of spores are visible near the bottom portion of the droplet where the light is reflected. (c) A 50 μm diameter satellite droplet condenses atop the interface of a spore-laden 300 μm droplet, without coalescing. (Online version in colour.)

Interestingly, the urediniospores themselves were found to be hydrophobic. While droplets could not be directly deposited on the microscopic urediniospores, their wettability could instead be inferred from condensation experiments. Urediniospores were observed to aggregate at the free interface of a condensing liquid droplet (figure 2b), indicating that the spores are not hydrophilic. In other words, hydrophobic spores will more strongly deform the local interface in order to meet their contact angle requirements, leading to curvature-induced forces that aggregate the particles. Secondly, condensate was sometimes observed to nucleate and grow as satellite droplets atop the spore–laden interface of a mother droplet, rather than immediately coalescing (figure 2c). This is suggestive of the spores promoting two separate liquid interfaces on either side, which is only possible for hydrophobic contact angles. We note that this observation of satellite droplets has also been observed when condensing on a bed of hydrophobic particles (i.e. liquid marbles) [25]. The fact that these spores are hydrophobic explains why the contact angles of water were actually larger on the centre of a diseased leaf compared with a healthy leaf.

In figure 3a, we show that jumping-droplet condensation occurs on the leaves of the common wheat plant. The condensation was formed by thermally bonding a healthy leaf section (2 cm × 2 cm) on a Peltier stage set to T_w = 0°C for ambient conditions of T_∞ = 21 ± 6°C and $H=55\pm 17\text{\%}$. Side-view microscopy was obtained using a high-speed camera (Phantom v711) attached to a 5 × magnification lens (Canon MP-E). Microscopic dew droplets were observed to exhibit quasi-spherical apparent contact angles, larger than that of the macroscopic deposited droplets, to facilitate the jumping upon coalescence. We attribute the enhanced superhydrophobicity of the condensed droplets to the non-homogeneity of the leaf’s surface, such that smaller droplets can avoid local hydrophilic features that are inescapable to larger droplets.

Figure 3.

Dynamics of jumping-droplet condensation on healthy and diseased wheat leaves. (a) High-speed time-lapse photography of a coalesced dew droplet (final radius R ≈ 78 μm) jumping from a healthy leaf. The total time of the time-lapse arc is t ≈ 26.7 ms. (b) First confirmation that jumping droplets can liberate spores from a pustule of the rust P. triticina on a wheat leaf. Time-lapse images show a droplet (R ≈ 36 μm) jumping several millimetres off the surface and falling back down over a time t ≈ 40 ms. Inset shows an orange urediniospore, roughly 10 μm in diameter, that is carried by the jumping droplet. (c) Top-down microscopy of three spores being liberated by jumping droplets. From the second to the fourth frames, a dew droplet vertically jumps off the leaf surface due to coalescence. A comparison between the first and last frames shows that the jumping droplet removed the spores from the leaf’s surface within 2 ms. Scale bar represents 100 μm. (d) Jumping velocity plotted against the final radius of the jumping droplet. The solid and dotted lines in figure 3d correspond to equation (3.2) for no spore (n = 0) and one spore (n = 1), respectively. (Online version in colour.)

Repeating the side-view imaging with a rusted wheat leaf, we were able to directly observe spores adhering to jumping droplets as they ejected from the surface (figure 3b). Rather than being encapsulated within a jumping droplet, the hydrophobic P. triticina spores tended to remain at the droplet’s free surface even during jumping. The limited magnification and side-view perspective does leave some room for doubt that the orange pixels could be a lighting effect, rather than liberated spores. More conclusive evidence was therefore obtained by switching to a top-down optical microscope, where the spores could be directly observed on the leaf’s surface prior to their jumping-induced transport (figure 3c).

The initial velocity of jumping droplets was captured using side-view high-speed microscopy for both healthy and diseased wheat leaves (figure 3d). When two droplets of radii R merge together, a perfect conversion of excess surface energy to kinetic energy predicts a jumping velocity of $v=\sqrt{3(2-2^{2/3})}{(\gamma /\rho R)}^{1/2}$, where γ ≈ 75.7 mN m⁻¹ and ρ ≈ 1000 kg m⁻³ are the surface tension and density of water at 0°C. However, this predicted value exceeds the experimentally observed jumping rates by a factor of 5 [18]. Mouterde et al. have recently shown that this apparent discrepancy can be resolved by invoking a conservation of momentum argument [26,27]:

$$v=\frac{{ϵ}^{5/2}}{2{(1+{ϵ}^3)}^{5/6}}{\left(\frac{\gamma }{\rho R_{\mathrm{f}}}\right)}^{1/2},$$ 3.1

where R_f is the post-merged radius and ε = r/R is the degree of asymmetry between merging two droplets of radius R and r (R > r). Using this new approach yields the proper pre-factor of about 0.2 even for a perfectly symmetric merging (ε = 1). The rest of the energy is primarily dissipated as droplet oscillations inherent to the hydrodynamics of jumping [16,17]. The measured initial jumping velocities obeyed equation (3.1) across an order of magnitude of values for the droplet size with an average asymmetry of ε = 0.7. The moderate scatter in experimental values of v about equation (3.1) may also be attributed to the possibility of coalescence events involving more than two droplets [28] and losses due to adhesion of the liquid with the solid, which might be non-negligible on the wheat surface.

Droplets jumping from sporulating leaves did not exhibit any noticeable changes in velocity compared to healthy leaves, indicating that the spores do not appreciably impact the hydrodynamics of droplet self-propulsion (figure 4). Using side-view high-speed imaging, trajectories of jumping droplets in the z–x plane were obtained (figure 4a,d). It was observed that these lateral trajectories can exceed 2 mm in the absence of any appreciable wind. A typical wheat leaf is only about 5 mm in width, suggesting that most droplets are capable of vaulting beyond the leaf’s edge regardless of the wind conditions.

Figure 4.

Trajectories of jumping droplets. (a–c) Trajectories of the centre of mass of jumping droplets on a healthy leaf. (d–f) Analogous trajectories for droplets jumping from diseased leaves. The field-of-view of the microscopes were limited to about 2.5 mm and we restricted ourselves to cases where the peak and subsequent falling of a jumping droplet were visible. Bends in the trajectories of droplets are associated with the rotation of the droplets as well as drag forces. (Online version in colour.)

The z-coordinate (figure 4b,e) and x-coordinate (figure 4c,f) of jumping droplets were plotted as a function of time. Combining this information yields the values of v_x = dx/dt and v_z = dz/dt for all times. These velocities were then used to obtain $v={(v_z^2+v_x^2)}^{1/2}$ as a function of time for every jump. The initial value of v for each jump is used as the jumping velocity in figure 3d. Droplets that moved out of focus early in a jump, due to appreciable movement in the y-direction, were not considered in our analysis.

To understand why the addition of a spore does not affect the ballistics of jumping microdroplets, we re-derive equation (3.1) with the larger droplet containing n spores of size r_s (see electronic supplementary material, figure S1 and §1 for a complete derivation). Defining R_f to be the post-merged radius of the jumping droplet including any spores, $R_{\mathrm{f}}^3\approx R^3+r^3+n{r}_{\mathrm{s}}^3$. Assuming the spore density is comparable to water and that the effects of the spores on the interfacial area cancels out before and after merging, we obtain a modified version of equation (3.1):

$$v_s={(1-\frac{n{r}_{\mathrm{s}}^3}{R_{\mathrm{f}}^3})}^{5/6}v.$$ 3.2

Note that in the absence of any spores (n = 0), equation (3.2) becomes equation (3.1). In figure 3d, the dotted line corresponds to equation (3.2) for one spore. It will be later shown that most of the spore-laden jumping droplets carried one urediniospore (figure 5d). Equation (3.2) shows that jumping with spores is equivalent to jumping on healthy leaves, unless the droplet is beneath a critical size of about R_f ≈ 10 μm where the cubic term $r_s^3/R_{\mathrm{f}}^3$ causes a sharp decrease in v_s as R approaches the spore size. This crossover in regimes was not observed experimentally due to the fact that on a moderately superhydrophobic surface condensate does not inflate to a sufficiently large contact angle required for jumping until growing to at least 10 μm in size [14].

Figure 5.

Quantifying liberated spores. (a) Schematic of experimental set-up to capture the spores carried off the wheat leaf by jumping dew droplets. Water-sensitive paper is placed a fixed height above a condensing wheat leaf. (b) Experimental micrograph of droplets and spores caught by the water-sensitive paper during jumping-droplet condensation. The blue regions represent the splatter pattern of the impacting jumping droplets, while spores carried by droplets are brownish red in colour. (c) Spores liberated per unit area of the wheat leaf per hour as captured by the water sensitive paper placed at heights of h = 1.5, 3 and 5 mm. (d) Frequency distribution of spores carried off by individual jumping droplets. We see that at any given height, more than 80% of the droplets jumping with spores have only one spore adhering to them. (Online version in colour.)

To quantify the rate of spore liberation from a diseased leaf surface, a small piece of water-sensitive paper was placed above a condensing leaf surface with the out-of-plane separation fixed by acrylic spacers of height h = 1.5, 3 or 5 mm (figure 5a and electronic supplementary material, figure S2). Wheat leaf samples, 1 cm × 3 cm, were inoculated with P. triticina in the same manner as the previous experiments and were held at T_w = 0°C to induce jumping-droplet condensation. The ambient conditions ranged from T_∞ = 20–30°C and $H=50\text{–}60\text{\%}$ depending on the day. After exactly 1 h of condensation, the opposing paper was removed and analysed under a microscope to quantify jumping-droplet impact events (blue splatter) and transported spores (red), as shown in figure 5b and electronic supplementary material, figure S3. It was confirmed via side-view microscopy that the condensation never came close to large enough to ‘bridge’ across the millimetric gap, such that all water and spores on the paper correspond to jumping droplets crossing the gap. To ensure repeatability of the results, three different sporulating leaves were used. Three sections were cut from each leaf, such that all three spacer heights were tested for each leaf.

The mean rates of spore liberation were 56 ± 28 cm⁻² h⁻¹ across the 1.5 mm gap, 67 ± 63 cm⁻² h⁻¹ for the 3 mm gap and 21 ± 16 cm⁻² h⁻¹ for the 5 mm gap (figure 5c, see the ‘Spore-Counting Experiments’ section in the electronic supplementary material for more details). As expected, fewer spores were able to traverse the 5 mm gap compared to the 1.5 mm or 3 mm gaps, although it is impressive that an appreciable amount of spores were still able to travel this far given the large viscous drag exerted on jumping droplets [29]. Despite the large degree of heterogeneity in the results, it was consistently found across multiple wheat plants that condensation was able to liberate spores at rates of $\mathcal{O}(10)$ cm⁻² h⁻¹ and propel them at least 1.5–5 mm from the surface. Assuming a total wheat leaf area of 10 cm² and a natural dew cycle of 1 h d⁻¹, about 100 urediniospores could be liberated by jumping-droplet condensation each day per diseased leaf. About 75% of jumping droplets contained just a single urediniospore, with the remainder carrying up to 11 (figure 5d).

For spores located on the underside of a leaf, or for vertically oriented leaves, the jumping-droplet effect is only needed to detach the spores from the leaf surface. After this initial liberation, gravity and/or wind can facilitate the subsequent dispersal of the spores. However, for spores on the top face of a leaf, jumping droplets must propel spores beyond the laminar boundary layer for wind-induced pathogen transport to be possible. Otherwise, the jumping-droplets (and spores) would simply fall back to the same leaf in a slightly different location. The thickness of a laminar boundary layer at a distance x downwind from the leading edge of a horizontal leaf can be estimated as

$$\delta \sim {\left(\frac{\nu x}{U}\right)}^{1/2},$$ 3.3

where ν = 1.5 × 10⁻⁵ m² s⁻¹ is the air’s kinematic viscosity and U is the wind speed. Typical wind speeds are U ≈ 0.01–10 m s⁻¹. Taking the width of the leaf, which is typically 5 mm, as the characteristic length scale, we obtain a boundary layer of thickness of δ ≈ 0.086–2.7 mm. Given our findings that jumping droplets can launch spores up to 5 mm from the surface, it seems that they can liberate spores beyond the boundary layer for virtually any wind speed. Once clear of the boundary layer, jumping droplets of typical radius R_f ≈ 30 μm should be able to suspend in winds as slow as U ∼ 0.1 m s⁻¹ for subsequent long-range dispersal.

Finally, control experiments were performed to compare how spore liberation by jumping-droplet condensation compares to the already-known mechanisms of vibration and wind shear. Sporulated leaves were fixed to a mechanical vibration stage and the speed of oscillation was gradually increased until spores were able to catapult from the surface (figure 6a,b). A critical vibrational speed of about v_v ≈ 0.6 m s⁻¹ was found, where v_v = 2πf A, f is the imposed frequency, and A is the peak amplitude measured by the side-view high-speed camera (electronic supplementary material, figure S4). The vertical adhesion force between a single dry spore (P. triticina) and a wheat leaf can be correlated with the minimum acceleration of the leaf to liberate spores as $F_{\mathrm{a}}\approx {\rho }_{\mathrm{s}}{r}_{\mathrm{s}}^3{(2\pi f_{\mathrm{c}})}^2{A}_{\mathrm{c}}$, where ρ_s ≈ ρ ≈ 1000 kg m⁻³ is the spore density, f_c = 60 Hz and A_c = 1.5 mm are the critical frequency and peak amplitude corresponding to spore liberation, respectively (figure 6b). Therefore, the adhesion force between spores and the leaf can be approximated as F_a ≈ 0.1 nN, which is a good agreement with that reported in [10].

Figure 6.

Comparison to spore liberation via vibration or wind shear. (a) Vibration of a sporulated leaf at f = 40 Hz and a peak-to-peak amplitude of 2A = 3.6 mm was not strong enough the detach any spores. (b) At a critical frequency of f = 60 Hz, some of the spores were catapulted from the leaf. (c) Top-down microscopy of a spore-laden leaf before (left) and after (right) subjecting to an 8 m s⁻¹ wind. Nearly all of the spores remained adhered to the leaf. (Online version in colour.)

Even with the best-case scenario of a leaf being perfectly perpendicular to a wind flow, this would require a wind speed of at least U ∼ 1 m s⁻¹ (see the electronic supplementary material, figure S5). A leaf was also placed within a wind tunnel, where liberation was characterized by comparing spore counts before and after subjecting the leaf to wind. For a typical wind speed of 8 m s⁻¹ [30], a subset of spore agglomerates were able to initially shear off the leaf’s surface, but the other agglomerates and nearly all of the isolated spores remained adhered (figure 6c and electronic supplementary material, figure S5). This is in agreement with a previous report [31]. The critical shear stress for spore detachment can be approximated as ${\rho }_{\mathrm{air}}(r_{\mathrm{s}}^2/{\zeta }^2)U_{\mathrm{c}}^2\approx 1$ mPa, where U_c = 8 m s⁻¹ is the empirical critical wind velocity and $r_{\mathrm{s}}^2/{\zeta }^2$ is a pre-factor to obtain the local wind velocity at the centre of a spore assuming a linear velocity gradient across the boundary layer.

In addition to dry dispersal, wind could also shear a spore-laden droplet from a wheat leaf (figure 7a). The wind shear must overcome the droplet’s lateral adhesion force, which can be approximated as [32]

$$F_{\mathrm{adh}}\approx \pi a\gamma (\cos {\theta }_{\mathrm{R}}-\cos {\theta }_{\mathrm{A}}),$$ 3.4

where a is the droplet’s contact radius with the surface. The contact radius can be expressed in terms of the spore-laden droplet’s radius of curvature: a = R_ssinθ_s, where $R_{\mathrm{s}}^3\approx R^3+n{r}_s^3$ accounts for both the volume of the pure liquid (of radius R) and adhered spores of quantity n and radius r_s, while θ_s ≈ (θ_A + θ_R)/2 is the average apparent contact angle of the sliding droplet. Making these substitutions into equation (3.4) and using trigonometric relations:

$$F_{\mathrm{adh}}\approx 2\pi \gamma (R_{\mathrm{s}}\sin {\theta }_{\mathrm{s}})\sin \frac{{\theta }_{\mathrm{A}}+{\theta }_{\mathrm{R}}}{2}\sin \frac{{\theta }_{\mathrm{A}}-{\theta }_{\mathrm{R}}}{2}\approx \pi \gamma (R_{\mathrm{s}}{\sin }^2{\theta }_{\mathrm{s}})\mathrm{\Delta }\theta ,$$ 3.5

where Δθ = (θ_A − θ_R). For large-angle droplets on non-wetting surfaces, the force exerted by the wind is approximately: $F_{\mathrm{wind}}\approx 1/2{\rho }_{\mathrm{air}}{U}^2(\pi R_{\mathrm{s}}^2)$. Solving for the critical wind speed, the spore-laden droplet will be removed when F_wind ≈ F_adh:

$$U_{\mathrm{c}}\approx \sqrt{\frac{2\gamma }{{\rho }_{\mathrm{air}}{R}_{\mathrm{s}}}}\sin {\theta }_{\mathrm{s}}\sqrt{\mathrm{\Delta }\theta }.$$ 3.6

Figure 7.

(a) Schematic of wind shearing a spore-laden droplet. (b) Critical wind speed required to shear spore-laden droplets from the leaf surface (equation (3.6)). The black lines correspond to θ_s ≈ 141° and hysteresis Δθ = 6.4°, as was found for our diseased wheat leaves. Red lines correspond to an idealized surface with θ_A = 180° and Δθ = 6.4°. (c) Variation of the critical wind speed with the average contact angle of the sliding droplet. (d) Phase map for the different modes of liberation and dispersal for spore-laden droplets. The black dashed line corresponds to equation (3.6), which is the minimum wind speed required to shear off a droplet from a wheat leaf (n = 1). The blue line corresponds to the minimum wind speed required to fully suspend liberated droplets, to enable long-range dispersal (equation (3.7)). The dotted black line scales to the capillary length (approx. 1 mm), beyond which droplets are too big to jump. Data points correspond to droplets jumping from healthy leaves (green circles) or diseased leaves (red), where equation (3.3) was used to solve for the wind speed U required for the experimental jumping height to correspond to the boundary layer (δ) for a leaf of x = 5 mm width. (Online version in colour.)

As expected, equation (3.6) shows that it is more difficult to dislodge a smaller droplet. From our goniometric measurements of droplets on sporulated leaves, θ_s ≈ 141° and Δθ ≈ 6.4°. Figure 7b plots U_c against the liquid-only radius of curvature, R ≈ (R_s − nr_s)^1/3, for the cases of n = 0, 1 or 10 (black curves). For large millimetric droplets, the critical wind velocity scales as U_c ∼ 1 m s⁻¹ regardless of how many spores are in the droplet. This is comparable to the critical wind speed for dry dispersal. For micrometric droplets, adding spores now serves to weakly decrease U_c, but the critical wind speed now scales as U_c ∼ 10 m s⁻¹. This means that, for all but the largest droplets, the wind velocities required to shed spore-laden droplets are high enough to transport dry spores anyway, with no droplets required. The red curves correspond to a hypothetical superhydrophobic surface that would have a perfect θ_A = 180°, but retains the same modest hysteresis as our leaves. Even for this idealized case, U_c ∼ 1 m s⁻¹ is required for wind to shed micrometric droplets, comparable to wind-induced dry dispersal. In figure 7c, we show across a wide range of non-wetting contact angles that U_c ∼ 1 m s⁻¹ for R_s = 1 mm droplets and U_c ∼ 10 m s⁻¹ for R_s = 10 μm droplets.

While large (R_s ≈ 5 mm) spore-laden droplets can be sheared off by moderate U ∼ 1 m s⁻¹ winds (or by gravity at vertical orientations), the subsequent dispersal of such droplets would be impossible. This can be seen from a simple scaling relation. For a droplet to be carried a sufficient distance by the wind, the inertia of the wind, ${\rho }_{\mathrm{a}}{U}^2{R}_{\mathrm{s}}^2$, has to be greater than the weight of the droplet, $\rho g{R}_{\mathrm{s}}^3$. This yields

$$U>\sqrt{\frac{\rho \mathrm{g}{R}_{\mathrm{s}}}{{\rho }_{\mathrm{air}}}},$$ 3.7

which for R_s ≈ 5 mm requires U_c ≈ 10 m s⁻¹ for dispersal anyway. Additionally, for the specific context of spore-laden dew droplets, it can be difficult to grow droplets this large in the first place. By contrast, for the R ≈ 30 μm size typical of jumping droplets, U_c ≈ 0.5 m s⁻¹ to be suspended in the wind.

Figure 7d summarizes the four primary regimes of liberating spore-laden droplets. For low wind speeds (blue region), jumping droplets can clear the boundary layer but their dispersal is only short-range, as the wind cannot fully support the weight of the droplets. For moderate wind speeds (pink), jumping droplets can fully suspend in the wind for long-range dispersal. For high wind speeds and large droplets, wind shear can shed droplets for short-range dispersal (green). Finally, for very high wind speeds, the wind can both shear the droplets from the surface and fully support their weight for long-range dispersal (red). In short, spore liberation and dispersal via some combination of vibration, wind and/or gravity requires conditions of U ∼ 1–10 m s⁻¹ and only tends to be effective for removing some of the larger spore agglomerates. Microscopic jumping droplets, on the other hand, enable even isolated spores to clear the boundary layer, can be suspended in winds as slow as U ∼ 0.1 m s⁻¹ for long-range dispersal, and even in the near absence of wind can vault spores beyond the leaf’s edges.

4. Discussion

This coalescence-induced catapulting of spores from a surface is reminiscent of ballistospores being launched from thousands of fungal species [33]. However, there are two important mechanistic differences. First, a ballistospore must be delicately hinged to an outgrowth known as a sterigma, such that the shift in centre-of-mass induced by coalescence can detach the spore from this weak attachment [34]. Second, this elevation of the spore above the actual surface of the uredinium requires creative surface chemistry to trigger coalescence: hygroscopic substances are secreted from the proximal end of the spore to generate a Buller’s drop, which coalesces with a hydrophilic film located on the spore itself [35]. For these reasons, ballistospore ejection is exclusively tailored to liberate native fungal spores from their outgrowths and is incapable of removing foreign pathogens. Indeed, this combination of three-dimensional architecture and localized surface chemistry is so complex that even a primitive effort at ejecting a synthetic ballistospore was only recently achieved [36]. By contrast, jumping-droplet condensation should be able to liberate a wide variety of non-native pathogens from any location on a non-wetting surface and does not require sterigma or chemicals.

In conclusion, naturally forming dew is sufficient to liberate pathogenic material from non-wetting organisms. The mechanism is the jumping-droplet mode of condensation that occurs on superhydrophobic surfaces. Specifically, we found that jumping-droplet condensation on diseased wheat leaves was capable of liberating leaf rust spores at rates of $\mathcal{O}(10)$ cm⁻² h⁻¹, which corresponds to about 100 spores per leaf for an hour-long dew cycle. The 2–5 mm jumping heights of the spore-containing droplets is sufficient to clear the boundary layer even in calm conditions (approx. 0.01 m s⁻¹), enabling subsequent dispersal to nearby plants via wind and/or gravity regardless of leaf orientation. By contrast, we showed that the wind-induced liberation of dry spores required much stronger winds (approx. 1–10 m s⁻¹) and only tends to be effective for large spore agglomerates. For non-wetting plants, we therefore propose that jumping-droplet condensation can be considered as a new key mechanism for plant pathogen dispersal, in addition to strong winds and rainsplash. This explosive ejection of pathogenic material from the condensing surface could be a positive attribute for the organism in question, but could also be responsible for spreading the disease to its neighbours. Thus it turns out that plants, like tetrapods, are capable of ‘sneezing’.

Data accessibility

The data supporting the findings of this study are available within the article and the associated electronic supplementary material. Any other data are available from the corresponding author upon request.

Authors' contributions

D.S., J.B.B. and S.J. conceived the research. H.G. grew the wheat plants and innoculated the samples. S.N. and C.E.B. discovered the jumping-droplet phenomenon on wheat leaves. S.F.A. and C.E.B. characterized the wettability of wheat leaves. S.N. and S.F.A. captured and modelled the jumping-droplet dynamics. S.N. and S.B. performed the out-of-plane spore capturing experiments. S.F.A. performed wind tunnel and vibration experiments. S.N., S.F.A., H.G., S.J., D.S. and J.B.B. discussed and interpreted the results. S.N., S.F.A. and J.B.B. prepared the manuscript. All authors proofread the paper, made comments and approved the manuscript.

Competing interests

We declare we have no competing interests.

Funding

This work was supported by the USDA National Institute of Food and Agriculture, Award No. 2018-67013-28063.