Modelling the Effect of Washout of Hot Pollutants for Increasing Rain in an Industrial Area

Abstract

In areas where hot gases and nanoparticulate materials are released uncontrollably from pollutants generating sources which are human population density dependent, the rainfall is significantly affected. When these hot gases and nanoparticulate materials mix with clouds, the cloud droplets evaporate, causing no rain or less intense rain. For increasing rain, the abatement of these pollutants is necessary and the washout of these pollutants by water drops is one of the effective removal mechanisms. Taking this into account, in this paper, a nonlinear mathematical model is proposed to analyse the effect of hot pollutants on rainfall and its control by washout of hot pollutants at sources of emission using spraying water droplets. To model the phenomenon, five nonlinearly interacting variables are considered namely densities of water vapours, clouds droplets, raindrops, the cumulative concentration of hot pollutants and the density of water drops introduced in the atmosphere to washout the hot pollutants. On analysing the model, using the stability theory of differential equations, it is found that the rain fall decreases as the cumulative concentration of hot pollutants increases. The spraying of water drops at the sources of emissions in the industrial area reduces the cumulative concentration of hot pollutants, which ultimately stimulates an increase in the density of raindrops in the atmosphere. Numerical simulation is also done to validate analytical results. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.