Modeling approach to assess clustering impact on release rates of pesticides from microencapsulated products

The pesticide release rate from polymer-encapsulated microcapsules is controlled by diffusion across the polymer membrane, membrane thickness, and pesticide loading. However, conditions for microcapsule clustering following conventional application practices and the impact of clustering on the overall release rate are often ignored. Microcapsules are delivered to target surfaces using water droplets as a carrier, and capillary-driven velocities arise within the deposited sessile drop as the water evaporates. This work describes experimental observations and a quasi-static mathematical approach used to elucidate microcapsule clusters that remain following the drop-drying process, along with the anticipated patterns for pesticide release as a function of cluster geometries. The dynamic behavior of a drying sessile drop was modeled as a trajectory of constrained quasi-static equilibrium shapes having a fixed contact line. Observed monolayer clustering of microcapsules was a function of the initial contact angle and size of the sessile drop, evaporation rate, and the microcapsule number density within the drop. The net pesticide release rate from microcapsule clusters was calculated from superposition of smaller decomposed cluster geometries for which release rates were determined by numerical solution to the mass balance governing equation, thereby coupling the self-assembly of microcapsule and microcapsule clustering with environmental release rate predictions.