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Mathematical Modelling of Hydrophilic Ionic Fertiliser Diffusion in Plant Cuticles: Lipophilic Surfactant Effects

1
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia
2
ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), Queensland University of Technology, Brisbane, QLD 4001, Australia
3
Plant Protection Chemistry NZ Ltd., PO Box 6282, Rotorua, Bay of Plenty 3043, New Zealand
*
Authors to whom correspondence should be addressed.
Plants 2019, 8(7), 202; https://doi.org/10.3390/plants8070202
Received: 18 April 2019 / Revised: 24 June 2019 / Accepted: 28 June 2019 / Published: 2 July 2019
(This article belongs to the Section Plant Physiology and Metabolism)
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Abstract

The global agricultural industry requires improved efficacy of sprays being applied to weeds and crops to increase financial returns and reduce environmental impact. Enhancing foliar penetration is one way to improve efficacy. Within the plant leaf, the cuticle is the most significant barrier to agrochemical diffusion. It has been noted that a comprehensive set of mechanisms for ionic active ingredient (AI) penetration through plant leaves with surfactants is not well defined, and oils that enhance penetration have been given little attention. The importance of a mechanistic mathematical model has been noted previously in the literature. Two mechanistic mathematical models have been previously developed by the authors, focusing on plant cuticle penetration of calcium chloride through tomato fruit cuticles. The models included ion binding and evaporation with hygroscopic water absorption, along with the ability to vary the AI concentration and type, relative humidity, and plant species. Here, we further develop these models to include lipophilic adjuvant effects, as well as the adsorption and desorption, of compounds on the cuticle surface with a novel Adaptive Competitive Langmuir model. These modifications to a penetration model provide a novel addition to the literature. We validate our theoretical model results against appropriate experimental data, discuss key sensitivities, and relate theoretical predictions to physical mechanisms. The results indicate the addition of the desorption mechanism may be one way to predict increased penetration at late times, and the sensitivity of model parameters compares well to those present in the literature. View Full-Text
Keywords: plant cuticle; hydrophilic ionic active ingredient; porous diffusion; adsorption; desorption; lipophilic; mathematical model; aqueous pores; surfactant; competitive Langmuir; ion transport plant cuticle; hydrophilic ionic active ingredient; porous diffusion; adsorption; desorption; lipophilic; mathematical model; aqueous pores; surfactant; competitive Langmuir; ion transport
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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MDPI and ACS Style

Tredenick, E.C.; Farrell, T.W.; Forster, W.A. Mathematical Modelling of Hydrophilic Ionic Fertiliser Diffusion in Plant Cuticles: Lipophilic Surfactant Effects. Plants 2019, 8, 202.

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