Kinetics of Lipophilic Pesticide Uptake by Living Maize

We report the uptake of a lipophilic fungicide into the cuticle of living leaves of young maize from droplets of a suspension concentrate. The action of a “coffee-ring” effect is demonstrated during fungicide formulation drying, and the fungicide particle distribution is quantified. We develop a simple, two-dimensional model of uptake leading to a “reservoir” of cuticular fungicide. This model allows inferences of physicochemical properties for fungicides inside the cuticular medium. The diffusion coefficient closely agrees with literature penetration experiments (Dcut ≈ 10–18 m2 s–1). The logarithm of the inferred cuticle–water partition coefficient log10 Kcw = 6.03 ± 0.04 is consistent with ethyl acetate as a model solvent for the maize cuticle. Two limiting kinetic uptake regimes are inferred from the model for short and long times, with the transition resulting from longitudinal saturation of the cuticle beneath the droplet. We discuss the strengths, limitations, and generalizability of our model within the “cuticle reservoir” approximation.

These segmented images were then quantitatively analysed. Average values and standard errors 25 for properties of the total deposit were extracted from RLM images and presented in Table 1. 26 Average values and standard errors for properties of the leaf surface and deposited particles 27 were extracted from cryo-SEM images and presented in Table 2 and Table 3, respectively.    Table 3 contains values that were calculated rather than directly measured from the images.

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The volumes of particles in the interior region were calculated by approximating the particles 39 as ellipsoids on a flat surface and using the measured values for the particles' projected area,

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, and minor axis length, , in the following equation: The inferred particle density in the interior region, , was calculated from the calculated Γ interior particle 43 particle volume, the density of solid fungicide , and the number of particles ( = 1.5 g/cm 3 ) 44 observed in a representative area, , of size, : rep rep 45 Γ interior particle (μg cm -2 ) = × rep × rep From this, the total mass of particles in the interior (measured area of ) was calculated: interior 47 interior = Γ interior particle × interior

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The particle density in the coffee ring, was then calculated by comparison to the total Γ ring particle 49 mass measured on the surface from the uptake studies, , and the average area of the

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Ring thickness measurement 64 We tested several methods for measuring the coffee ring thickness from RLM images of the 65 deposits of droplets of fungicide after 1 hour of drying and manual 0.2μL 375ppm 66 segmentation into coffee ring, deposit interior and deposit exterior. The radial thickness was 67 measured relative to the centroid of the deposit to give a radial thickness distribution across the 68 range . The histogram of the local thickness heatmap of the mask of the coffee ring 0 ≤ < 2 69 segment gives the distribution of the local thickness across the whole coffee ring area.

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However, it over-represents the large local thickness regions (greater local thickness results in 71 more pixels within that area) and so the number of pixels in each bin was normalised against 72 the local thickness value of that bin to measure the distribution of the local thickness around 73 the coffee ring perimeter. The distance-to-nearest-edge heatmap was generated for the mask of the coffee ring segment. A midline around the coffee ring was generated along the maximum 75 cusp of the distance-to-nearest-edge heatmap. The distribution along this midline of local 76 thickness and double-distance-to-nearest-edge (which equals the edge-to-edge distance at the 77 maximum)provides alternative measures of the coffee ring thickness around the coffee ring   value as it avoids the generation of the midline, which is an additional source of error and 103 increases the characterisation time.

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Preliminary uptake study raw data and additional analysis 105 As described in the main text, we performed a preliminary uptake study to assess the uptake   If we include two diffusion zones, then one must include an additional separation at 1.5μm 160 least to avoid the diffusion zones significantly overlapping. However, to ensure no interference, 161 a minimum centre-to-centre separation of was used. This ensures that over the course of 3mm 162 24 hours, a diffusing particle would not expect to interfere with the uptake at an adjacent droplet 163 if its diffusion coefficient is or less. Given the measured and expected values 2 × 10 -12 m 2 s -1 164 of the diffusion coefficient (see main text) we conclude that uptake from a single droplet is 165 independent of the other droplets.

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Additional description of the model 167 The model developed is based on Fick's 2 nd Law of diffusion 6 in two-dimensional cylindrical 168 coordinates, , perpendicular distance from axis of symmetry, and , distance from reference 169 plane perpendicular to symmetry axis: where is the concentration and is the diffusion coefficient. 172 We implement a complete set of boundary conditions, presented in Supplementary Figure 6. 173 We apply zero-flux boundaries at the flat cuticle's longitudinal interfaces, which we justify in 174 the main text as applying the "wax reservoir" limit such that no material is lost from the cuticle 175 into the air or sub-cuticle. We define a value as the simulation's radial limit at which we  190 In order to simplify the mathematics and generalise the results of a simulation, we convert these 191 parameters to dimensionless values using the following conversions presented in Table 5.
192 where is the total dimensional mass in the cuticle, is the dimensional flux at a given position An exponentially expanding grid 7-10 was used since the concentration gradients decrease with 210 distance from the source disc and so the density of the grid required to achieve accurate 211 simulation also decreases with distance. The distribution of points in such a grid for a generic 212 coordinate is given as: (to give a symmetric distribution about ), before expanding to . This = 1 = 0.5 = Max 217 is done to ensure high density of points around the disc edge where concentration gradients are 218 largest. A backward implicit discretisation 11-13 is used to resolve the steps in time.

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This discretised, finite difference system is then solved fully implicitly and iteratively using 220 the Biconjugate Gradient Stabilised method (BICGSTAB), with a relative convergence 221 tolerance of , with a semi-coarsening multigrid (SMG) preconditioner. The numerical 1 × 10 -6 222 simulation was performed on a Linux(Centos) machine with an Intel Core i7-6800K CPU 223 (3.40GHz, 6 cores), 32GB of RAM, and an Nvidia Quadro GP100. The simulation program 224 was written in C++, utilising the HYPRE software package (version 2.18.2) 14, 15 executed with