Mathematical modelling of droplet evaporation and surfactant effects on pesticide leaf uptake

Many plant pesticides are administered as spray, landing as droplets on the leaf surface after when the chemical components of the pesticide may successfully penetrate into the leaf tissue. Environmental factors such as sun exposure typically cause droplets to evaporate over time, reducing the volume of the droplet. This is an important process to understand because the volume and shape of a droplet can significantly impact the likelihood of successful pesticide uptake into the leaf. Chemical compounds known as surfactants are often added to pesticides to increase the contact surface area of droplets with the leaf. In this study, we investigate the effects of droplet evaporation, and change in droplet shape by developing a novel model in which evaporation creates a temporally changing domain which we couple to a boundary value partial differential equation model for flow across the cuticle and source and sink compartments governed by ordinary differential equations. We approximate parameters from limited experimental data and model simplifications. We explore the interplay between evaporation rate, contact surface area, and the amount of pesticide which penetrates the leaf system. Results show that evaporation rate is crucial in determining how much of the pesticide is wasted and how the rate of uptake into the leaf is affected by the evaporation, but that surfactants can ameliorate some of this effect.