Effects of the reaction rate and the large size deformable aerosols on dispersion in atmospheric flow regarded as the turbulent fluid saturated porous media

Abstract

This paper describes the use of Taylor's analysis to study the dispersion of large size aerosols as the mixture of deformable agglomeration and coalescence of aerosols in the atmosphere. A proper theory is developed incorporating the resistance offered by sparsely packed aerosols following the Darcy-Brinkman model, including elastic deformation. Analytical solutions for velocity are obtained using a regular perturbation technique. Concentration distribution is determined using the advection of concentration by the atmospheric turbulent fluid in the presence of an irreversible first-order chemical reaction and a source in the boundary condition. It is shown that the aerosols are dispersed relative to a plane moving with the mean speed of atmospheric turbulent fluid as well as the mean speed of agglomeration of aerosol with a relative diffusion coefficient, D ^β, called the Taylor dispersion coefficient. This D ^β is numerically computed and the results reveal that D ^β increases with an increase in Re and Pe, but decreases with an increase in σ_ρ, β₁, and R₁, where Re is the Reynolds number, σ_ρ is the porous parameter, R₁ is the deformation parameter, and β₁, is the reaction rate parameter. This decrease in D ^β, with an increase in the porous parameter and an increase in the reaction rate parameter is favorable for the formation of clouds in the atmosphere.