Skip to main content
SpringerLink
Log in

An approximate analytical solution for the deposition of heavy particles released from an elevated line source

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

This work re-examines and further develops an analytical solution for the deposition swath of heavy particles released in the atmosphere from an elevated source over uniform terrain, correcting the particle diffusivity for the crossing trajectory effect. The revised (approximate) analytical solution proves to be accurate within 20% over a wide range of micrometeorological conditions and particle size, despite its neglect of the turbulence component of the deposition flux. It compares very satisfactorily with experimental data and with the simulations of a Lagrangian stochastic model, provided the variable U(H)/w g ≤7 (ratio of the mean horizontal wind speed at source height to the particle settling velocity). In this domain of validity, simple formulae relating the statistics of the deposition swath to U(H)/w g are derived.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barad, M. L. (1958). ‘Project Prairie Grass, A Field Program in Diffusion’. Geophysi. Res. Papers 59, I–III

  • Brooke J.W., Hanratty T.J. (1994). ‘Free-Flight Mixing and Deposition of Aerosols’. Phys. Fluids. 6(10): 3404–3415

    Article  Google Scholar 

  • Csanady G.T. (1963). ‘Turbulent Diffusion of Heavy Particles in the Atmosphere’. J. Atmos. Sci. 20, 201–208

    Article  Google Scholar 

  • Deacon E.L. (1949). ‘Vertical Diffusion in the Lowest Layers of the Atmosphere’. Quart. J. Roy. Meteorol. Soc. 75, 89–103

    Article  Google Scholar 

  • Deardorff J.W. (1978). ‘Closure of Second- and Third-Moment Rate Equations for Diffusion in Homogeneous Turbulence’. Phys. Fluids 21, 525–530

    Article  Google Scholar 

  • Farmer, R. A. (1969). Liquid Droplets Trajectories in Two-Phase Flow, PhD thesis, Massachussets Institute of Technology

  • Forney L.J., Spielman L.A. (1974). ‘Deposition of Coarse Aerosols from Turbulent Flow’. J. Aerosol Sci. 5, 257–271

    Article  Google Scholar 

  • Friedlander S.K., Johnstone H.F. (1957). ‘Deposition of Suspended Particles from Turbulent Gas Streams’. Ind. Eng. Chem. 49, 1151–1156

    Article  Google Scholar 

  • Godson W.L. (1958). ‘The Diffusion of Particulate Matter from an Elevated Source’. Arch. F. Met. Geophys. und Biokl. A 10, 305–327

    Article  Google Scholar 

  • Hage K.D. (1961). ‘On the Dispersion of Large Particles from a 15-m Source in the Atmosphere’. J. Meteorol. 18, 534–539

    Google Scholar 

  • Liu Y.H., Agarwal J.K. (1974). ‘Experimental Observation of Aerosol Deposition in Turbulent Flow’. J. Aerosol Sci. 5, 145–155

    Article  Google Scholar 

  • McCoy D.D., Hanratty T.J. (1977). ‘Rate of Deposition of Droplets in Annular Two-Phase Flow’. Int. J. Multiphase Flow 3, 319–331

    Article  Google Scholar 

  • Patankar, S. V. (1980). Numerical Heat Transfer and Fluid Flow, Hemisphere Publ

  • Raupach, M. R. (2002). ‘Diffusion of Heavy Particles in a Turbulent Flow’. Geophys. Monograph., Environmental Mechanics: Water, Mass and Energy Tranfer in the Biosphere 129, American Geophysical Union, Washington, pp. 301–316

  • Rounds W. (1955). ‘Solutions of the Two-Dimensional Diffusion Equations’. Trans. Amer. Geophys. Union 36, 395–405

    Google Scholar 

  • Sawford B L. (1991). ‘Lagrangian Stochastic Simulations of the Turbulent Motion of Heavy Particles’. Boundary-Layer Meteorol. 54, 147–166

    Article  Google Scholar 

  • Schmel G.A. (1971). ‘Particle Diffusivities and Deposition Velocities over a Horizontal Smooth Surface’. J. Colloid. Interface Sci. 37, 891–906

    Article  Google Scholar 

  • Schwediman L.C., Postma A.K. (1961). ‘Turbulent Deposition in Sampling Lines’. USAEC Report No. HW-65309

  • Slinn W.G.N. (1982). ‘Predictions for Particle Deposition to Vegetative Canopies’. Atmos. Environ. 16, 1785–1794

    Article  Google Scholar 

  • Taylor G.I. (1921). ‘Diffusion by Continuous Movements’. Proc. London Math. Soc. Ser. 2. 20: 196–212

    Google Scholar 

  • Walker E.R. (1965). ‘A Particulate Diffusion Experiment’. J. Appl. Meteorol. 4, 614–621

    Article  Google Scholar 

  • Wells A.C., Chamberlin A.C. (1967). ‘Transport of Small Particles to Vertical Surfaces’. Br. J. Appl. Phys. 18, 1793–1799

    Article  Google Scholar 

  • Wilson J.D. (2000). ‘Trajectory Models for Heavy Particles in Atmospheric Turbulence: Comparison with Observations’. J. Appl. Meteorol. 39, 1894–1912

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Earth & Atmospheric Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2E3

    T. Bouvet & J. D. Wilson

Authors
  1. T. Bouvet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. D. Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Bouvet.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bouvet, T., Wilson, J.D. An approximate analytical solution for the deposition of heavy particles released from an elevated line source. Boundary-Layer Meteorol 119, 1–18 (2006). https://doi.org/10.1007/s10546-005-9016-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10546-005-9016-6

Keywords

Search

Navigation