Modeling the removal of gaseous pollutants and particulate matters from the atmosphere of a city

In this paper, a nonlinear mathematical model is proposed and analyzed to study the removal of gaseous pollutants and particulate matters from the atmosphere of a city by precipitation. The atmosphere consists of four interacting phases i.e. the raindrops phase, the gaseous pollutants phase, the phase of gaseous pollutants absorbed (dissolved) in rain drops and the phase of particulate matters. The dynamics of these phases is assumed to be governed by ordinary differential equations with source, interaction, removal and recycle terms. The proposed model is analyzed by using stability theory of differential equations. It is shown that the pollutants can be removed from the atmosphere and their removal rates depend mainly upon the rates of emission of the pollutants, rate of rain drops formation and the rate of falling rain drops on the ground. If the rate of precipitation is very high, the pollutants may be removed completely from the atmosphere.