Modelling the Removal of Gaseous Pollutants and Particulate Matters from the Atmosphere of a City by Rain: Effect of Cloud Density

In this paper, an original nonlinear mathematical model for the removal of gaseous pollutants and particulate matters from the atmosphere of an industrial city by rain is proposed and analyzed. It is assumed that five interacting phases in the atmosphere of the city exist, i.e., cloud droplets phase, raindrops phase, gaseous pollutants phase, particulate matters phase, and the phase of absorbed gaseous pollutants in raindrops. It is assumed further that these phases undergo nonlinear interactions in the atmosphere, while gaseous pollutant interacts with cloud droplets as well as with raindrops but particulate matters interact only with raindrops. The gravitational settling and reversible reaction processes have also been considered appropriately in the model. By analyzing the model, it is shown that both the gaseous pollutants and particulate matters may be removed from the atmosphere under certain conditions, provided the rates of formation of cloud droplets and raindrops are sufficiently large. It is noted that under unfavorable atmospheric conditions, rain does not occur and pollutants are not removed from the atmosphere.