Diffusion of dust particles emitted from a fixed source

  • Authors

    • Khaled Al-mashrafi Section of Applied Sciences, Department of Human Resources Development, General Directorate ofEducation in Eastern Region, Ministry of Education, Sur, Oman
    2015-09-20
    https://doi.org/10.14419/ijamr.v4i4.5058
  • Air Pollution, Atmospheric Diffusion Equation, Dust Concentration, Dust Diffusion, Wind Speed.

  • 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.

  • References

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

      [2] Hassan, M.H.A. and Eltayeb, I.A., “Suspension transport of wind eroded sand particlesâ€, 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 distanceâ€, 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 atmosphereâ€, 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 transportâ€, 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 diffusivitiesâ€, 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 firesâ€, 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 Dunesâ€, Methuen, London, (1954).

      [9] Kennedy, J.F., “The formation of sediment ripples, dunes and anti-dunesâ€, 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 streamâ€, 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 Applicationsâ€, 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 dunesâ€, 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 snowâ€, Boundary-Layer Meterol. 23, (1982), pp: 233. http://dx.doi.org/10.1007/BF00123299.

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

      [15] Gillette, D. and Goodwin, P., “Microscale transport of sand-sized soil aggregates eroded by windâ€, 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 dustâ€, 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 levelâ€, 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 Equationsâ€, Mass, Academic Press, Boston, (1989).

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

  • Downloads

  • How to Cite

    Al-mashrafi, K. (2015). Diffusion of dust particles emitted from a fixed source. International Journal of Applied Mathematical Research, 4(4), 454-465. https://doi.org/10.14419/ijamr.v4i4.5058

    Received date: 2015-07-10

    Accepted date: 2015-09-14

    Published date: 2015-09-20