A Nonlinear Dynamical Model to Study the Removal of Gaseous and Particulate Pollutants in a Rain System

Abstract. An ecological type nonlinear mathematical model is proposed to study the removal of gaseous pollutants and two distinct particulate matters by precipitation scavenging in the atmosphere. The atmosphere during precipitation consists of five interacting phases namely the raindrops phase, the gaseous pollutants phase, the smaller particulate matters phase, the larger particulate matters phase and the absorbed phase of gaseous pollutants. We assume that gaseous pollutants are removed from the atmosphere by the processes of impaction as well as by absorption while particulate matters are assumed to be removed by impaction process. The model is analyzed using stability theory of nonlinear differential equations. It is shown that, under appropriate conditions, the pollutants can be removed from the atmosphere and their removal rates would depend mainly upon the rates of emission of pollutants, rate of rain drops formation and the rate of raindrops falling on the ground. If the rate of precipitation is very high, all the pollutants (gaseous as well as particulate matters) would be removed completely from the atmosphere. A numerical study is also performed to study the dynamics of the model system. The results are found to be in line with the experimental observations published in the literature.