Mathematical modeling of controlled-release systems of herbicides using lignins as matrices - A review

The herbicides applied in soils can be easily lost, owing to leaching, vola tilization, and bio- and photodegradation. Controlled-release systems using polymeric matrices claim to solve these problems. The movement of the herb icides in the soil is also an important phenomenon to be studied in order t o evaluate the loss processes. The development of mathematical models is a relevant requirement for simulation and optimization of such systems. This study reviews mathematical models as an initial step for modeling data obta ined for controlled-release systems of herbicides (diuron, 2,4-dichlorophen oxyacetic acid, and ametryn) using sugarcane bagasse lignin as a polymeric matrix. The release kinetic studies were carried out using several acceptor systems including a water loath, soil, and soil-packed columns. Generally, these models take into account phenomena such as unsteady-state mass trans fer by diffusion (Fick's law) and convection, consumption by several proces ses, and partitioning processes, resulting in partial differential equation s with respect to time and space variables.