Application of multi-step differential transform method to the nonlinear behaviour of cloud droplets on gaseous atmospheric pollutant removal

Abstract

The determination of the concentration of gaseous atmospheric pollutants and their neutralization by rain or dew have been the subjects of research interests over the years. This paper presents close-form solutions to the transient behaviour and determination of the concentration of gaseous atmospheric pollutants using Multi-Step Differential Transform Method (MsDTM). Also, parametric studies are carried out to properly understand the chemistry of the process and the associated density of droplet required for complete neutralization. The generated analytical solution obtained by MsDTM are verified with an efficient numerical (fourth order Runge-Kutta, RK45) scheme. Results show that MsDTM is an efficient scheme for the problem. Also, the parametric study performed in this work shows that an increase in the cloud water droplet formation rate increases the atmospheric rain drop density which consequently reduces the cumulative concentration of gaseous pollutants in the atmosphere. The same effect is established for the growth rate constant of the atmospheric rain drop parameter. This work will be useful in solving to a large extent one of the challenges facing the world at large on gaseous atmospheric pollutants as well as in the determination of different pollutants neutralization period under different atmospheric conditions.