Mathematical modelling and analysis of the removal of gaseous pollutants by precipitation using general nonlinear interaction

Abstract

In this paper, we propose and analyze a simple mathematical model to study the removal of gaseous pollutants by rain using general nonlinear interaction term between raindrops density and gaseous pollutants. The atmosphere, under consideration, is assumed to consist of three phases i.e. the raindrops phase, the gaseous pollutants phase and the phase of gaseous pollutants absorbed in raindrops. The dynamics of these phases is assumed to be governed by the ordinary differential equations with source, nonlinear interaction and removal terms. The proposed model is analyzed using stability theory of differential equations. It is shown that, under appropriate conditions, the pollutants can be removed from the atmosphere significantly and the removed amount would depend upon the rates of discharge of gaseous pollutants and the intensity of rain. Further, the removal of gaseous pollutants depends upon the conditions which are conducive to precipitation/rainfall.