Analytical solution of volatile active ingredient release and subsequent dispersion in wind tunnel

Abstract

This paper proposes a new mathematical model describing the diffusion-controlled release of an active ingredient (AI) from a cylindrical product, followed by convection-dispersion transport in a wind tunnel through which air flows. The model aims to support the development of products with targeted AI release profiles. It was motivated by the particular case of a new product formulation releasing phytochemicals with insecticide activity. The well-known analytical solution for the AI transient release from the product is coupled with the analytical solution for the convection-dispersion transport along the tunnel through a simple approximation that introduces a negligible error. An overall analytical solution is thus obtained, having obvious advantages against numerical approximations, particularly for intensive computational tasks such as model fitting to experimental data, uncertainty analysis and product composition optimization.