Nonlinear Porous Diffusion Modeling of Hydrophilic Ionic Agrochemicals in Astomatous Plant Cuticle Aqueous Pores: A Mechanistic Approach

Abstract

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds in order to reduce their environmental impact and deliver improved financial returns. Enhanced foliar uptake is one means of improving efficacy. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The usefulness of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted previously in the literature, as the results of each uptake experiment are specific to each formulation of active ingredient, plant species and environmental conditions. In this work we develop a mathematical model and numerical simulation for the uptake of hydrophilic ionic agrochemicals through aqueous pores in plant cuticles. We propose a novel, nonlinear, porous diffusion model for ionic agrochemicals in isolated cuticles, which extends simple diffusion through the incorporation of parameters capable of simulating: plant species variations, evaporation of surface droplet solutions, ion binding effects on the cuticle surface and swelling of the aqueous pores with water. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms. Major influencing factors have been found to be cuticle structure, including tortuosity and density of the aqueous pores, and to a lesser extent humidity and cuticle surface ion binding effects.

Surface Properties and Permeability to Calcium Chloride of Fagus sylvatica and Quercus petraea Leaves of Different Canopy Heights

“…The process of foliar absorption may take place via the cuticle, stomata, irregularities in the cuticle, trichomes or other epidermal structures ( Fernández et al, 2017 ). In light of cuticular permeability trials, it has been hypothesized that lipophilic molecules should diffuse through the more lipophilic domain of the hydrophobic cuticle ( Niederl et al, 1998 ; Buchholz, 2006 ), while small, polar molecules such as water may follow a different diffusion pathway which is currently not well characterized and has been associated with a “dynamic aqueous continuum” forming due to hydration ( Fernández et al, 2017 ), and to “polar” or “aqueous” pores ( Franke, 1967 ; Schönherr, 2006 ; Tredenick et al, 2017 ) in the cuticle, whose occurrence has never been directly demonstrated so far ( Fernández et al, 2016 , 2017 ).…”

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

“…The model takes the form of a nonlinear, quasi-one-dimensional, diffusion model. We will briefly describe the modeling formulation, however we note that a full description can be found in the authors previous work (Tredenick et al, 2017). A schematic diagram of the model domain based on the experimental setup (Kraemer et al, 2009) is shown in Figure 3.…”

“…Current mathematical models of penetration of ionic AIs have been created as alternatives to time consuming and expensive field/laboratory studies and fall into two categories: the first employ empirical expressions that require a rate constant to be measured specific to each different plant species, hydrophilic AI, adjuvant and environmental conditions (Forster et al, 2006; Schreiber and Schönherr, 2009, p. 132) and the second incorporate diffusion (Hsu, 1983; Satchivi et al, 2000; Veraverbeke et al, 2003; Mercer, 2007; Pecha et al, 2012). Comprehensive reviews can be found elsewhere (Forster et al, 2004; Trapp, 2004; Tredenick et al, 2017). These models, however, do not include important governing mechanisms such as ion binding, sessile droplet evaporation with water absorption including POD and relative humidity.…”

“…These models, however, do not include important governing mechanisms such as ion binding, sessile droplet evaporation with water absorption including POD and relative humidity. The authors previously introduced a mechanistic mathematical model in Tredenick et al (2017) to simulate ionic agrochemical penetration through plant cuticles with sessile droplet evaporation, the ability to vary plant species, type and initial concentration of active ingredient, relative humidity and ion binding. Adjuvants were not included and only a simplistic evaporation formulation was used, which did not consider the POD or water absorption of ionic AI solutions.…”

Measuring the passive cuticular membrane permeability of potassium with a parallel artificial membrane permeability assay and the implications for foliar nutrient formulations

“…Interestingly, the major factor influencing uptake in the model was found to be cuticle structure, including tortuosity and density of the aqueous pores. Relative humidity and binding of ions to the surface of cuticles, although still rated high after sensitivity analysis, were less influential [8]. An ion-pairing mechanism has also been proposed as a method to increase the permeability of very polar positively charged cationic drugs through membranes.…”