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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 through plant cuticles were found to be 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.

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.