The influence of longitudinal diffusion on the transport 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
    2016-01-09
    https://doi.org/10.14419/ijamr.v5i1.5367
  • Dust Diffusion, Atmospheric Diffusion Equation, Longitudinal Diffusion, Wind Speed, Unsteady State.

  • Abstract

    The mathematical model for the diffusion of dust particles emitted from a fixed source in the presence of the longitudinal diffusion and absence of latitudinal and vertical diffusions, is investigated. The diffusion of dust particles in the atmosphere is governed by the atmospheric diffusion equation. In the previous paper [1], the general case of the time-dependent diffusion equation in the presence of a point source whose strength is dependent on time, was solved. The calculations showed that the diffusion parameters play an important role in the spread of the dust particles in the atmosphere. In the previous paper, we examined the model in the presence of vertical diffusion and absence of other diffusions to show that for small times, the dust spreads with a front that travels with the speed of the wind. In the current paper, the vertical and latitudinal diffusions are absent while the longitudinal diffusion is present. It is found that the solution depends on the source of time dependence. To study the nature of the solution, two special cases of the source are specified. In the both cases, it is found that there is no discontinuity front, and the dust particles spread slowly into the direction of the wind.

  • References

    1. [1] Al-Mashrafi, K.S., “Diffusion of dust particles emitted from a fixed sourceâ€, International Journal of Applied Mathematical Research, 4 (4), (2015), pp: 454-465. http://dx.doi.org/10.14419/ijamr.v4i4.5058.

      [2] 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.

      [3] Llewelyn, R.P., “An analytical model for transport, dispersion and elimination of air pollutants emitted from a point sourceâ€, Atmospheric Environment, 17, (1983), pp: 249-256. http://dx.doi.org/10.1016/0004-6981(83)90040-9.

      [4] Skidmore, E.L., “Soil erosion by wind: an overview, in physics of desertification†(F. EL-Baz and M. H. Hassan, eds.), Martinus Nijhoff Publishers, Dordrecht, (1986), pp: 261-273.

      [5] 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.

      [6] Bagnold, R.A., “The physics of Blown sand and Desert Dunesâ€, Methuen, London, (1954).

      [7] 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.

      [8] Eltayeb, I.A. and Hassan, M.H.A., “Two-dimensional transport of dust from an infinite line source at ground levelâ€, Geophys. J. Int., .110, (1992), pp: 571-576. http://dx.doi.org/10.1111/j.1365-246X.1992.tb02092.x.

      [9] Eltayeb, I.A. and Hassan, M.H.A., “The Evolution of dust emitted by a uniform source above ground levelâ€, International Journal of Mathematics and Mathematical Sciences, (2003), pp: 3327-3343. http://dx.doi.org/10.1155/S0161171203106163.

      [10] Gillette, D.A., “Threshold Friction Velocities for Dust production for Agricultural Soilsâ€. J. Geophys. Res., 93, (1988), pp: 12645 – 12662. http://dx.doi.org/10.1029/JD093iD10p12645.

      [11] 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.

      [12] 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.

      [13] Sharan M., and Gupta S., “Two-dimensional analytical model for estimating crosswind-integrated concentration in a capping inversion: eddy diffusivity as a function of downwind distance from the sourceâ€, Atmospheric Environment, 36, (2002), pp: 97-105. http://dx.doi.org/10.1016/S1352-2310(01)00449-6.

      [14] 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.

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

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

      [17] Taylor G.I., “Diffusion by continuous movementsâ€. Proc. London Math. Soc., 20, (1921), pp: 196–212.

      [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).

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  • How to Cite

    Al-Mashrafi, K. (2016). The influence of longitudinal diffusion on the transport of dust particles emitted from a fixed source. International Journal of Applied Mathematical Research, 5(1), 11-17. https://doi.org/10.14419/ijamr.v5i1.5367

    Received date: 2015-09-27

    Accepted date: 2015-12-21

    Published date: 2016-01-09