  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.
