Diffusion of dust particles emitted from a fixed source

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    In this paper, we investigate the mathematical model for the diffusion of dust particles emitted from a fixed source. Mathematically, the time-dependent diffusion equation in the presence of a point source whose strength is dependent on time is solved. The solution in closed form for a source of general time dependence is obtained. A number of special cases, in which the source function of time is explicitly given and special values of the diffusion parameters are taken are examined in detail. The numerical calculations show the strong dependence of the concentration of dust on the speed of the wind, the source, and its position in the vertical direction. It is also found that the diffusion parameters play an important role in the spread of the dust particles in the atmosphere. When diffusion is present only in the vertical direction, it is found that for small times the dust spreads with a front that travels with the speed of the wind.


  • Keywords


    Air Pollution; Atmospheric Diffusion Equation; Dust Concentration; Dust Diffusion; Wind Speed.

  • References


      [1] El-Baz, F., Eltayeb, I.A. and Hassan, M.H.A., “Sand Transport and Desertification in Arid and Semi-Arid Lands”, World Scientific Publishing Co., Singapore (1990).

      [2] Hassan, M.H.A. and Eltayeb, I.A., “Suspension transport of wind eroded sand particles”, Geophys. J. Internet. , 104, (1991b), pp: 147-152. http://dx.doi.org/10.1111/j.1365-246X.1991.tb02500.x.

      [3] Sharan M., Singh M.P., and Yadav, A.K., “Mathematical model for atmospheric dispersion in low winds with eddy diffusivities as linear functions of downwind distance”, Atmospheric Environment, 30, (1996), pp: 1137-1145. http://dx.doi.org/10.1016/1352-2310(95)00368-1.

      [4] Roberts, O.F.T., “The theoretical scattering of smoke in a turbulent atmosphere”, Proc. Roy. Soc. London Ser. A, 104, (1923), pp: 640-654. http://dx.doi.org/10.1098/rspa.1923.0132.

      [5] Takeuchi, M., “Vertical Profiles and horizontal increase of drift-snow transport”, J. Glaciol, 26, (1980), pp: 481.

      [6] Koch, W., “A solution of the two-dimensional atmospheric diffusion equation with height-dependent diffusion coefficient and height-dependent wind speed and eddy diffusivities”, Atmospheric Environment, 23, (1989), pp: 1729-1732. http://dx.doi.org/10.1016/0004-6981(89)90057-7.

      [7] Kevin B.M., Howard R.B. and Ronald G.R., “Numerical simulation of smoke plumes from large oil fires”, Atmospheric Environment, 30, (1996), pp: 4125-4136. http://dx.doi.org/10.1016/1352-2310(96)00151-3.

      [8] Bagnold, R.A., “The physics of Blown sand and Desert Dunes”, Methuen, London, (1954).

      [9] Kennedy, J.F., “The formation of sediment ripples, dunes and anti-dunes”, Ann. Rev. Fluid Mech., 1, (1969), pp: 147-168. http://dx.doi.org/10.1146/annurev.fl.01.010169.001051.

      [10] Abbott, J.E. and Francis, J.R.D., “Saltation and suspension trajectories of solid grains in a water stream”, Phil. Trans. R. Soc. London, A284, (1977), pp: 225-253. http://dx.doi.org/10.1098/rsta.1977.0009.

      [11] Noubissié, S. and Woafo, P., “Statistical Mechanics and its Applications”, Physica A, 345, (2005), pp: 9-16. http://dx.doi.org/10.1016/j.physa.2004.06.157.

      [12] Eltayeb, I.A. and Hassan, M.H.A., “On the non-linear evolution of sand dunes”, Geophys. J. R. astr. Soc., 65, (1981), pp: 31-45.

      [13] Schmidt, R.A., “Vertical profiles of wind speed, snow concentration, and humidity in blowing snow”, Boundary-Layer Meterol. 23, (1982), pp: 233. http://dx.doi.org/10.1007/BF00123299.

      [14] Pasquill, F., “Atmospheric Diffusion”, D. Van Nostrand, Princeton, (1962).

      [15] Gillette, D. and Goodwin, P., “Microscale transport of sand-sized soil aggregates eroded by wind”, J. Geophys. Res., 79, (1974), pp:4080-4084. http://dx.doi.org/10.1029/JC079i027p04080.

      [16] Hassan M.H.A and Eltayeb, I.A., “Time-dependent transport of dust”, J. Geophys. Res., 96, (1991a), pp: 9337-9339. http://dx.doi.org/10.1029/91JD00229.

      [17] Eltayeb, I.A. and Hassan, M.H.A., “Diffusion of dust particles from a point source above ground level and a line source at ground level”, Geophys. J. Int. 142, (2000), pp: 426-438. http://dx.doi.org/10.1046/j.1365-246x.2000.00172.x.

      [18] Zwillinger, D., “Handbook of Differential Equations”, Mass, Academic Press, Boston, (1989).

      [19] Abramowitz, M. and Stegun, I., “Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables”, Dover, New York, (1965).


 

View

Download

Article ID: 5058
 
DOI: 10.14419/ijamr.v4i4.5058




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.