In this paper, a six dimensional nonlinear mathematical model is proposed to study the effect of the density of cloud droplets (formed due to the presence of vapors in the atmosphere) on the removal of pollutants, both gaseous and particulate, from the atmosphere. We assume that there exist six nonlinearly interacting phases in the atmosphere i.e. the vapor phase, the phase of cloud droplets, the phase of raindrops, the phase of gaseous pollutants, the phase of particulate matters and the phase of gaseous pollutants absorbed in raindrops. It is further assumed that the dynamics of the system undergo ecological type growth and nonlinear interactions. The model is analyzed qualitatively using the stability theory of ordinary differential equations and computer simulations. By analyzing the model, it is shown that under appropriate conditions, gaseous pollutants and particulate matters would be removed from the atmosphere and their respective equilibrium levels would depend upon the intensity of rain caused by cloud droplets, emission rate of pollutants, the rate of raindrops falling on the ground, etc. It is pointed out that, if due to unfavorable atmospheric conditions cloud droplets are not formed, rain may not occur and pollutants would not be removed.
Sundar, Shyam; Sharma, Rajan K.; and Naresh, Ram
Modelling the Role of Cloud Density on the Removal of Gaseous Pollutants and Particulate Matters from the Atmosphere,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 8,
2, Article 6.
Available at: https://digitalcommons.pvamu.edu/aam/vol8/iss2/6