Diffusion of Falling Particles in Diabatic Atmospheres

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.

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“…The sedimentation of the material may be allowed by introducing a convection term in the mean steady equation that becomes [8,9]:…”

Section: Mathematical Modelmentioning

confidence: 99%

Analytic solutions of the diffusion-deposition equation for fluids heavier than atmospheric air

Barrera¹,

Brugarino²,

Piazza

et al. 2008

WIT Transactions on Ecology and the Environment

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“…The diffusion of particles is affected by their falling velocities in various ways when the sizes of particles are large enough. Yamamoto et al (1970) carried out numerical experiments of the diffusion of particles in the diabatic atmospheres, and they showed that the rate of deposition of particles on the ground depends on the falling velocity of particles. From those facts, it is expected that when the rain falls, the diffusion-sedimentation and washout processes occur simultaneously and therefore the size distri-bution of aerosols is changed by this combined process.…”

Section: Introductionmentioning

confidence: 99%

Effect of Diffusion-Sedimentation and Washout Processes on Aerosol Size Distributions

Sato¹

1979

Journal of the Meteorological Society of Japan

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It is studied how the size distribution of the so-called giant aerosols is changed by the diffusion-sedimentation and washout in the atmospheric boundary layer. An instantaneous and a continuous sources of infinite horizontal extent are assumed for ejection of aerosols into the atmosphere.The size distribution are calculated numerically as a function of time and height above ground for various combinations cf the eddy diffusivity profile and the rainfall intensity. The computational results are as follows. (1) The size distribution changes with time or height in such a way that the concentration of particles decreases with increase of particle size. (2) The effect of the diffusion-sedimentation simply reflects on the deformation of the size distribution of larger particles. (3) The degree of deformation of the size distribution by the washout increases with increase of particle size in the case of instantaneous source, and it is most pronounced for intermediate particle size range when the time duration of particle emission is sufficiently long.

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A Generalized Analytical Model for Crosswind-Integrated Concentrations with Ground-Level Deposition in the Atmospheric Boundary Layer

Kumar

Sharan

2014

Environ Model Assess

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Diffusion of Falling Particles in Diabatic Atmospheres

Cited by 4 publications

References 7 publications

Analytic solutions of the diffusion-deposition equation for fluids heavier than atmospheric air

Analytic solutions of the diffusion-deposition equation for fluids heavier than atmospheric air

Effect of Diffusion-Sedimentation and Washout Processes on Aerosol Size Distributions

A Generalized Analytical Model for Crosswind-Integrated Concentrations with Ground-Level Deposition in the Atmospheric Boundary Layer

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