Mathematical modelling of adjuvant-enhanced active ingredient leaf uptake of pesticides

The global importance of effective and affordable pesticides to optimise crop yield and to support health of our growing population cannot be understated. But to develop new products or refine existing ones in response to climate and environmental changes is both time-intensive and expensive which is why the agrochemical industry is increasingly interested in using mechanistic models as part of their formulation development toolbox. In this work, we develop such a model to describe uptake of pesticide spray droplets across the leaf surface. We simplify the leaf structure by identifying the outer cuticle as the main barrier to uptake; the result is a novel, hybrid model in which two well-mixed compartments are separated by a membrane in which we describe the spatio-temporal distribution of the pesticide. This leads to a boundary value partial differential equation problem coupled to a pair of ordinary differential equation systems which we solve numerically. We also simplify the pesticide formulation into two key components: the Active Ingredient which produces the desired effect of the pesticide and an Adjuvant which is present in the formulation to facilitate effective absorption of the Active Ingredient into the leaf. This approach gives rise to concentration-dependent diffusion. We take an intuitive approach to parameter estimation using a small experimental data set and subsequently demonstrate the importance of the concentration-dependent diffusion in replicating the data. Finally, we demonstrate the need for further work to identify how the physicochemical properties of pesticides affect flow into and across the leaf surface.