Analytic Solutions Of The Diffusion-deposition
Equation For Fluids Heavier Than Atmospheric Air
Author(s)
F. P. Barrera, T. Brugarino, V. Piazza & L. Pignato
Abstract
A steady-state bi-dimensional turbulent diffusion equation was studied to find the
concentration distribution of a pollutant near the ground. We have considered the
air pollutant emitted from an elevated point source in the lower atmosphere in adiabatic
conditions. The wind velocity and diffusion coefficient are given by power
laws. We have found analytical solutions using or the Lie Group Analysis or the
Method of Separation of Variables. The classical diffusion equation has been modified
introducing the falling term with non-zero deposition velocity.
Analytical solutions are essential to test numerical models for the great difficulty
in validating with experiments.
Keywords: atmospheric pollution, diffusion equation, exact solutions.
1 Introduction
The classical form of the mean steady diffusion equation is valid for elementary
particles of the fluid or when the foreign particles are of the same density as
the fluid. If the density and dimensions are high enough to have terminal velocities
vs not negligible, the distribution of the particles will be affected in various
ways [1–4].
A simple approximation is to consider that the particle sinks at a rate vs and the
ground acts as a permeable surface and retains all material passing through it.
Using a very simple model it is possible to examine various cases. It is possible
to have exact solutions of the mean steady diffusion when the turbulent diffusivity
kz and the terminal velocity vd depend somehow on the height [5–7].
Keywords
atmospheric pollution, diffusion equation, exact solutions.
Related Book
Other papers in this volume
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