Abstract
To overcome the water crisis for irrigation and other purposes, in this paper, we propose a non-linear mathematical model for artificial rain making by considering five dependent variables namely, water vapor density, densities of cloud droplets of small and large sizes, density of rain drops and cumulative concentration of mixture of aerosols of different sizes. It is assumed that these aerosols are conducive to the process of rain making, i.e. (a) the formation of small size cloud droplets from water vapors through the processes of nucleation and condensation, (b) changing them into large size cloud droplets through the processes of condensation, agglomeration, etc., and (c) changing these large cloud droplets into rain drops. The proposed model is analyzed using stability theory of differential equations. It is found that only one equilibrium is feasible and sufficient conditions for stability of such equilibrium are obtained. It is shown that the intensity of rainfall increases as the cumulative concentration of externally introduced aerosols in the atmosphere increases. Analysis reveals that for the continuous rainfall, it is necessary that water vapors must be continuously formed in the atmosphere. The numerical simulation of the model supports the analytical results.
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