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Front. Plant Sci. | doi: 10.3389/fpls.2018.01888

Mathematical Modeling of Diffusion of a Hydrophilic Ionic Fertilizer in Plant Cuticles: Surfactant and Hygroscopic Effects

 Eloise C. Tredenick1*, Troy W. Farrell1, 2 and  W. Alison Forster3
  • 1School of Mathematical Sciences, Queensland University of Technology, Australia
  • 2ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematical Sciences, Faculty of Science and Engineering, Queensland University of Technology, Australia
  • 3Plant Protection Chemistry New Zealand (PPCNZ) Ltd., New Zealand

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds to reduce their environmental impact and increase financial returns. One way to improve efficacy is by enhancing foliar penetration. The plant leaf cuticle is the most significant barrier to agrochemical diffusion within the leaf. The importance of a mechanistic mathematical model has been noted previously in the literature, as each penetration experiment is dictated by its specific parameters, namely plant species, environmental conditions such as relative humidity and spray formulation including adjuvant addition. A mechanistic mathematical model has been previously developed by the authors, focusing on plant cuticle diffusion of calcium chloride through tomato fruit cuticles including pore swelling, ion binding and evaporation, along with the ability to vary the active ingredient concentration and type, relative humidity and plant species. Here we further develop this model to include adjuvant effects as well as the hygroscopic nature of deliquescent ionic solutions with evaporation on the cuticle surface. These modifications to a penetration and evaporation model provide a novel addition to the literature and allow the model to be applied to many types of evaporating ionic hygroscopic solutions on many types of substrates, not just plant cuticles. We validate our theoretical model results against appropriate experimental data, discuss key sensitivities and relate theoretical predictions to physical mechanisms. The important governing mechanisms influencing surfactant enhanced penetration of ionic active ingredients through plant cuticles was found to be cuticle structure including tortuosity, maximum aqueous pore radius, pore density, cuticle thickness and initial contact angle of the applied droplet; ion binding, relative humidity and evaporation including hygroscopic water absorption parameters for point of deliquescence. The sensitivity analysis indicated surfactants increase penetration by changing the point of deliquescence of a solution, which alters the water absorption and the initial contact angle, which alters the number of pores under the droplet. The results of the validation and sensitivity analysis imply that this model accounts for many of the mechanisms governing penetration in plant cuticles.

Keywords: plant cuticle, ionic active ingredient, Porous diffusion, Adsorption, mathematical model, aqueous pores, Penetration, surfactant

Received: 04 May 2018; Accepted: 06 Dec 2018.

Edited by:

Sanna Sevanto, Los Alamos National Laboratory (DOE), United States

Reviewed by:

John A. Morgan, Purdue University, United States
Mauricio Hunsche, Universität Bonn, Germany
Antonio Heredia, Universidad de Málaga, Spain  

Copyright: © 2018 Tredenick, Farrell and Forster. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Ms. Eloise C. Tredenick, Queensland University of Technology, School of Mathematical Sciences, Brisbane, Australia,