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

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.