Time dependent mathematical model of secondary air pollutant with instantaneous and delayed removal

Abstract

A comprehensive time dependent atmospheric diffusion model of secondary pollutants (e.g. SO42-) produced from primary gaseous pollutants by means of chemical reaction is presented. The primary pollutants are emitted from various types of time dependent sources like (i) instantaneous (ii) continuous (constant flux) (iii) step function type. The mathematical model has been solved analytically and explicit analytic expressions for primary and secondary pollutants are obtained in the forms of Dirac delta and Heaviside functions. Analyses have been carried out for the role of instantaneous (dry deposition) and delayed removal (chemical reaction, wet deposition and settling) phenomena on the secondary pollutants ground level concentration. One of the important findings is that all these natural removal phenomena reduce ground level concentration of secondary pollutant significantly when primary pollutants are emitted from continuous sources. There will be an increase of ground level concentration near sources at any time for small values of pure settling velocity.