Evaporating droplets on inclined plant leaves and synthetic surfaces: Experiments and mathematical models.

HYPOTHESIS: Evaporation of surfactant droplets on leaves is complicated due to the complex physical and chemical properties of the leaf surfaces. However, for certain leaf surfaces for which the evaporation process appears to follow the standard constant-contact-radius or constant-contact-angle modes, it should be possible to mimic the droplet evaporation with both a well-chosen synthetic surface and a relatively simple mathematical model. EXPERIMENTS: Surfactant droplet evaporation experiments were performed on two commercial crop species, wheat and capsicum, along with two synthetic surfaces, up to a 90° incline. The time-dependence of the droplets' contact angles, height, volume and contact radius was measured throughout the evaporation experiments. Mathematical models were developed to simulate the experiments. FINDINGS: With one clear exception, for all combinations of surfaces, surfactant concentrations and angles, the experiments appear to follow the standard evaporation modes and are well described by the mathematical models (modified Popov and Young-Laplace-Popov). The exception is wheat with a high surfactant concentration, for which droplet evaporation appears nonstandard and deviates from the diffusion limited models, perhaps due to additional mechanisms such as the adsorption of surfactant, stomatal density or an elongated shape in the direction of the grooves in the wheat surface.

A note on the Stokes phenomenon in flow under an elastic sheet.

The Stokes phenomenon is a class of asymptotic behaviour that was first discovered by Stokes in his study of the Airy function. It has since been shown that the Stokes phenomenon plays a significant role in the behaviour of surface waves on flows past submerged obstacles. A detailed review of recent research in this area is presented, which outlines the role that the Stokes phenomenon plays in a wide range of free surface flow geometries. The problem of inviscid, irrotational, incompressible flow past a submerged step under a thin elastic sheet is then considered. It is shown that the method for computing this wave behaviour is extremely similar to previous work on computing the behaviour of capillary waves. Exponential asymptotics are used to show that free-surface waves appear on the surface of the flow, caused by singular fluid behaviour in the neighbourhood of the base and top of the step. The amplitude of these waves is computed and compared to numerical simulations, showing excellent agreements between the asymptotic theory and computational solutions. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Image analysis of shatter and pinning events on hard-to-wet leaf surfaces by drops containing surfactant.

BACKGROUND: A key challenge for developing computer models of spray retention by plants is to accurately predict how spray drops behave when impacting leaf surfaces. One poorly understood outcome occurs when drops bounce or shatter on impact but leave behind a proportion of the liquid on the surface (designated as pinning). This process is studied via impaction experiments with two hard-to-wet leaf surfaces (fat-hen: Chenopodium album and barnyard grass: Echinochloa crus-galli L. P. Beauv) and one hydrophobic artificial surface (Teflon) using three liquid formulations. RESULTS: Drops that impact upon Teflon underwent pinning shatter events via a well-known mechanism referred to as receding breakup. Drops impacting on leaf surfaces did not undergo receding breakup because the liquid rim was not in direct contact with the leaf surface when it broke into secondary droplets. However, pinning did occur on plant surfaces via a different mechanism, especially when using formulations containing a surfactant. CONCLUSION: Newly developed image analysis and methodology has allowed quantification of the volume fraction pinned to surfaces when drops shatter. The addition of surfactant can increase both the probability of pinning and the pinned volume when drops shatter on fat-hen or Teflon. However, the surfactants studied did not substantially improve the probability of pinning on barnyard grass. The difference in behaviour between the two leaf surfaces and the underlying mechanism is worth further study. © 2020 Society of Chemical Industry.

Simulating spray droplet impaction outcomes: comparison with experimental data.

BACKGROUND: A suite of plant retention spray models has been developed to simulate spray retention using virtual surfaces (either single leaves or whole plants) and their outputs compared with experimental data for the equivalent spray scenarios. RESULTS: The results for a single formulation (0.1% v/v lecithin mixture in water) and difficult to wet plant species Chenopodium album L (common lambsquarters) are presented. They include experimental observations with single leaves, as well as simulations of virtual impaction events, conducted to provide for the first time estimates of f (the proportion of theoretical impact drop diameter at shatter). With this factor prescribed, multi-plant simulations using a range of nozzle types and droplet sizes (volume mean diameter (VMD) range 241 to 530 µm) are compared with equivalent experimentally determined spray retention by real plants. The simulations demonstrated that impaction resulted predominantly in shatter with the production of daughter droplets, and that retention is mainly due to re-capture of these droplets. Overall the simulations show the same trends as experimental retention results from different nozzle applications, but at best predicted retention results were 68% to 79% of experimental percentage retention, depending on plant spacing. CONCLUSIONS: Retention is the result of some primary drop capture but predominantly by recapture of shatter droplets as the modelling illustrates. The value of f affects the droplet shatter outcome and can result in fewer, more energetic daughter droplets, or more droplets but with lower energies. However, this effect alone cannot explain the discrepancy between actual and simulated results. Possible operational influences are discussed. © 2020 Society of Chemical Industry.