Modelling water droplet movement on a leaf surface

The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.

Modelling water droplet movement on a leaf surface

Modelling droplet movement on leaf surfaces is an important component in understanding how water, pesticide or nutrient is absorbed through the leaf surface. A simple mathematical model is proposed in this paper for generating a realistic, or natural looking trajectory of a water droplet traversing a virtual leaf surface. The virtual surface is comprised of a triangular mesh structure over which a hybrid Clough-Tocher seamed element interpolant is constructed from real-life scattered data captured by a laser scanner. The motion of the droplet is assumed to be affected by gravitational, frictional and surface resistance forces and the innovation of our approach is the use of thin-film theory to develop a stopping criterion for the droplet as it moves on the surface. The droplet model is verified and calibrated using experimental measurement; the results are promising and appear to capture reality quite well.

The development of virtual leaf surface models for interactive agrichemical spray applications

This project constructed virtual plant leaf surfaces from digitised data sets for use in droplet spray models. Digitisation techniques for obtaining data sets for cotton, chenopodium and wheat leaves are discussed and novel algorithms for the reconstruction of the leaves from these three plant species are developed. The reconstructed leaf surfaces are included into agricultural droplet spray models to investigate the effect of the nozzle and spray formulation combination on the proportion of spray retained by the plant. A numerical study of the post-impaction motion of large droplets that have formed on the leaf surface is also considered.

Mapping leaf surface landscapes.

Leaf surfaces provide the ecologically relevant landscapes to those organisms that encounter or colonize the leaf surface. Leaf surface topography directly affects microhabitat availability for colonizing microbes, microhabitat quality and acceptability for insects, and the efficacy of agricultural spray applications. Prior detailed mechanistic studies that examined particular fungi-plant and pollinator-plant interactions have demonstrated the importance of plant surface topography or roughness in determining the outcome of the interactions. Until now, however, it has not been possible to measure accurately the topography--i.e., the three-dimensional structure--of such leaf surfaces or to record precise changes in patterns of leaf surface elevation over time. Using contact mode atomic force microscopy, we measured three-dimensional coordinates of upper leaf surfaces of Vaccinium macrocarpon (cranberry), a perennial plant, on leaves of two age classes. We then produced topographic maps of these leaf surfaces, which revealed striking differences between age classes of leaves: old leaves have much rougher surfaces than those of young leaves. Atomic force microscope measurements were analyzed by lag (1) autocorrelation estimates of leaf surfaces by age class. We suggest that the changes in topography result from removal of epicuticular lipids and that the changes in leaf surface topography influence phylloplane ecology. Visualizing and mapping leaf surfaces permit detailed investigations into leaf surface-mediated phenomena, improving our understanding of phylloplane interactions.

A comparison of techniques for the reconstruction of leaf surfaces from scanned data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

Simulating droplet motion on virtual leaf surfaces

A curvilinear thin film model is used to simulate the motion of droplets on a virtual leaf surface, with a view to better understand the retention of agricultural sprays on plants. The governing model, adapted from Roy et al. (2002 J. Fluid Mech. 454, 235–261) with the addition of a disjoining pressure term, describes the gravity- and curvature driven flow of a small droplet on a complex substrate: a cotton leaf reconstructed from digitized scan data. Coalescence is the key mechanism behind spray coating of foliage, and our simulations demonstrate that various experimentally observed coalescence behaviours can be reproduced qualitatively. By varying the contact angle over the domain, we also demonstrate that the presence of a chemical defect can act as an obstacle to the droplet’s path, causing break-up. In simulations on the virtual leaf, it is found that the movement of a typical spray size droplet is driven almost exclusively by substrate curvature gradients. It is not until droplet mass is sufficiently increased via coalescence that gravity becomes the dominating force.

Impaction of spray droplets on leaves: Influence of formulation and leaf character on shatter, bounce and adhesion

This paper combines experimental data with simple mathematical models to investigate the influence of spray formulation type and leaf character (wettability) on shatter, bounce and adhesion of droplets impacting with cotton, rice and wheat leaves. Impaction criteria that allow for different angles of the leaf surface and the droplet impact trajectory are presented; their predictions are based on whether combinations of droplet size and velocity lie above or below bounce and shatter boundaries. In the experimental component, real leaves are used, with all their inherent natural variability. Further, commercial agricultural spray nozzles are employed, resulting in a range of droplet characteristics. Given this natural variability, there is broad agreement between the data and predictions. As predicted, the shatter of droplets was found to increase as droplet size and velocity increased, and the surface became harder to wet. Bouncing of droplets occurred most frequently on hard to wet surfaces with high surface tension mixtures. On the other hand, a number of small droplets with low impact velocity were observed to bounce when predicted to lie well within the adhering regime. We believe this discrepancy between the predictions and experimental data could be due to air layer effects that were not taken into account in the current bounce equations. Other discrepancies between experiment and theory are thought to be due to the current assumption of a dry impact surface, whereas, in practice, the leaf surfaces became increasingly covered with fluid throughout the spray test runs.

The tarani mutation alters surface curvature in Arabidopsis leaves by perturbing the patterns of surface expansion and cell division

The leaf surface usually stays flat, maintained by coordinated growth. Growth perturbation can introduce overall surface curvature, which can be negative, giving a saddle-shaped leaf, or positive, giving a cup-like leaf. Little is known about the molecular mechanisms that underlie leaf flatness, primarily because only a few mutants with altered surface curvature have been isolated and studied. Characterization of mutants of the CINCINNATA-like TCP genes in Antirrhinum and Arabidopsis have revealed that their products help maintain flatness by balancing the pattern of cell proliferation and surface expansion between the margin and the central zone during leaf morphogenesis. On the other hand, deletion of two homologous PEAPOD genes causes cup-shaped leaves in Arabidopsis due to excess division of dispersed meristemoid cells. Here, we report the isolation and characterization of an Arabidopsis mutant, tarani (tni), with enlarged, cup-shaped leaves. Morphometric analyses showed that the positive curvature of the tni leaf is linked to excess growth at the centre compared to the margin. By monitoring the dynamic pattern of CYCLIN D3;2 expression, we show that the shape of the primary arrest front is strongly convex in growing tni leaves, leading to excess mitotic expansion synchronized with excess cell proliferation at the centre. Reduction of cell proliferation and of endogenous gibberellic acid levels rescued the tni phenotype. Genetic interactions demonstrated that TNI maintains leaf flatness independent of TCPs and PEAPODs.

Alternatives to Sedum on green roofs: Can broad leaf perennial plants offer better ‘cooling service’?

Green roof plants alter the microclimate of building roofs and may improve roof insulation. They act by providing cooling by shading, but also through transpiration of water through their stomata. However, leaf surfaces can become warmer when plants close the stomata and decrease water loss in response to drying substrate (typically associated with green roofs during summers), also reducing transpirational cooling. By using a range of contrasting plant types (Sedum mix – an industry green roof ‘standard’, Stachys byzantina, Bergenia cordifolia and Hedera hibernica) we tested the hypothesis that plants differ in their ‘cooling potential’. We firstly examined how leaf morphology influenced leaf temperature and how drying substrate altered that response. Secondly, we investigated the relationship between leaf surface temperatures and the air temperatures immediately above the canopies (i.e. potential to provide aerial cooling). Finally we measured how the plant type influenced the substrate temperature below the canopy (i.e. potential for building cooling). In our experiments Stachys outperformed the other species in terms of leaf surface cooling (even in drying substrate, e.g. 5 oC cooler compared with Sedum), substrate cooling beneath its canopy (up to 12 oC) and even - during short intervals over hottest still periods - the air above the canopy (up to 1 oC, when soil moisture was not limited). We suggest that the choice of plant species on green roofs should not be entirely dictated by what survives on the shallow substrates of extensive systems, but consideration should be given to supporting those species providing the greatest eco-system service potential.

Confocal laser scanning microscopy elucidation of the micromorphology of the leaf cuticle and analysis of its chemical composition

Electron microscopy techniques such as transmission electron microscopy (TEM) and scanning electron microscopy (SEM) have been invaluable tools for the study of the micromorphology of plant cuticles. However, for electron microscopy, the preparation techniques required may invariably introduce artefacts in cuticle preservation. Further, there are a limited number of methods available for quantifying the image data obtained through electron microscopy. Therefore, in this study, optical microscopy techniques were coupled with staining procedures and, along with SEM were used to qualitatively and quantitatively assess the ultrastructure of plant leaf cuticles. Leaf cryosections of Triticum aestivum (wheat), Zea mays (maize), and Lupinus angustifolius (lupin) were stained with either fat-soluble azo stain Sudan IV or fluorescent, diarylmethane Auramine O and were observed under confocal laser scanning microscope (CLSM). For all the plant species tested, the cuticle on the leaf surfaces could be clearly resolved in many cases into cuticular proper (CP), external cuticular layer (ECL), and internal cuticular layer (ICL). Novel image data analysis procedures for quantifying the epicuticular wax micromorphology were developed, and epicuticular waxes of L. angustifolius were described here for the first time. Together, application of a multifaceted approach involving the use of a range of techniques to study the plant cuticle has led to a better understanding of cuticular structure and provides new insights into leaf surface architecture.

Leaf paraheliotropism in Styrax camporum confers increased light use efficiency and advantageous photosynthetic responses rather than photoprotection

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Leaf structure of the cerrado (Brazilian savanna) woody plants

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Changes in leaf physiology caused by Calacarus heveae (Acari, Eriophyidae) on rubber tree

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Droplet deposition during spray and leaf pH in aquatic weed control

A diversidade morfológica da superfície foliar existente entre as espécies de plantas e a presença de estruturas foliares como tricomas, estômatos, cutícula e ceras podem exercer grande influência na aderência e deposição das gotas de pulverização, assim como na absorção do herbicida. Desta forma, o objetivo do presente trabalho foi estudar, em quatro espécies de plantas daninhas aquáticas (Enhydra anagallis, Eichhornia crassipes, Heteranthera reniformis e Typha subulata), a área de molhamento de gotas de pulverização nas superfícies foliares adaxial e abaxial, bem como o pH foliar. O experimento foi realizado em Botucatu-SP. As plantas foram cultivadas em caixas d'água sob condições de campo, e quando atingiram seu pleno desenvolvimento (antes do florescimento), foram realizadas as avaliações de pH foliar e da área de molhamento de gotas de pulverização. As tensões superficiais das gotas aplicadas (0,5 mL), apresentadas pelas soluções de glyphosate aplicado isolado a 5,0% v v-1 (Rodeo 480 g L-1 e.a. produto comercial), glyphosate + Aterbane BR (5,0% + 0,5% v v-1), glyphosate + Silwet L-77 (5,0% + 0,05% v v-1), além das soluções com os adjuvantes isolados, Aterbane BR (0,5% v v-1) e Silwet L-77 (0,05% v v-1) foram respectivamente 72,1; 28,7; 23,3; 37,3 e 22,1 mN m-1. As médias obtidas de pH foliar variaram entre 5,50 e 7,50, destacando-se a espécie E. anagallis com valores de 6,68 e 7,02 para as faces adaxial e abaxial, respectivamente. Dentre as plantas daninhas aquáticas avaliadas T. subulata foi a espécie que apresentou as maiores médias de área de molhamento nas faces adaxial e abaxial da folha, proporcionada pelas as soluções de glyphosate + Aterbane BR, glyphosate + Silwet L-77 e Silwet L-77, com valores de 12,99-7,03; 20,04-17,95 e 31,81-25,91 mm², respectivamente.