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, volatilization, and bio- and photodegradation. Controlled-release systems using polymeric matrices claim to solve these problems. The movement of the herbicides in the soil is also an important phenomenon to be studied in order to 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 obtained for controlled-release systems of herbicides (diuron, 2,4-dichlorophenoxyacetic 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 bath, soil, and soil-packed columns. Generally, these models take into account phenomena such as unsteady-state mass transfer by diffusion (Fick's law) and convection, consumption by several processes, and partitioning processes, resulting in partial differential equations with respect to time and space variables.