A mathematical model for the removal of pollutants from the atmosphere through artificial rain

Abstract

To reduce the pollution from the atmosphere or polluted cities like the capital city Delhi of India, use of artificial rain is a solution. In this paper, we have proposed and analyzed a nonlinear mathematical model to reduce the pollution level by rain making. In the proposed model five variables are considered, namely; (i) number density of water vapor, (ii) number density of cloud drops, (iii) number density of raindrops, (iv) cumulative concentration of aerosols, and (v) concentration of pollutant particles suspended in the region of consideration. The effect of environmental fluctuations has been studied with the help of Lyapunov functionals. The model is analyzed in the presence of white noise and proved that if rain persists, the pollutants can be totally washed out. It has been observed that the environmental disturbances are not much favorable in such experiments as the presence of environmental disturbance may destabilize the system. It is found that to remove pollutants completely, it is necessary to prevent the formation of pollutants. The simulation is performed to support the analytical findings.