Atmospheric Diffusion and Deposition of Particulate Matter

Abstract

The physical situation considered is described by a nonhomogeneous, gravity-modified, dimensional, time-varying, convective-diffusive transport equation. This partial differential equation, subject to a nonhomogeneous boundary condition and source term, was solved analytically by integral transforms for a third type (Monin) boundary condition which describes the total flux of particles at the earth boundary. By applying the transform kernels provided, the analytical solutions to the cases of first (Dirichlet) or second (Neumann) type boundary conditions may be obtained directly from the general, modular solution presented. The inclusion of the particle flux boundary condition is a significant improvement over previous three-dimensional studies which either assumed infinite geometry in all three dimensions thus avoiding complicating boundary conditions or used “tilting plume” techniques (corrections applied to gaseous no-deposit solutions) which do not properly represent the concurrent processes of diffusive spread and settling.