Effect of rain on removal of a gaseous pollutant and two different particulate matters from the atmosphere of a city

A nonlinear five-dimensional mathematical model is proposed and analyzed to study the removal of a gaseous pollutant and two different particulate matters by rain from the atmosphere of a city. The atmosphere, during rain, is assumed to consist of five interacting phases namely, the raindrops phase, the gaseous pollutant phase, its absorbed phase and the phases of two different particulate matters, one being formed by the gaseous pollutant. We assume that the gaseous pollutant is removed from the atmosphere by the processes of absorption while the two particulate matters are removed only by the process of impaction with different removal rates. By analyzing the model, it is shown that under appropriate conditions, these pollutants can be removed from the atmosphere and their equilibrium levels, remaining in the atmosphere, would depend mainly upon the rates of emission of pollutants, growth rate of raindrops, the rate of raindrops falling on the ground, etc. It is found that if the rates of conversion of gaseous pollutant into the particulate matter and rainfall are very large, then the gaseous pollutants would be removed completely from the atmosphere.