Similarity solution of the telford coagulation equation

  • S. A. El-Wakil
  • M. A. Madkour
  • A. Abu El-Ela
  • A. M. El-Grayhy
Original Papers
  • 32 Downloads

Abstract

A direct operational method is used to transform the collision integral in the Telford coagulation equation for aerosols to a polynomial in derivatives with respect to volume. This polynomial is approximated by the Padé approximation technique. This procedure reduces the integro-differential form to a partial differential equation which is solved by the similarity method. Exact as well as approximate expressions for the particle size distribution are obtained.

Keywords

Particle Size Differential Equation Partial Differential Equation Particle Size Distribution Mathematical Method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Drake, R. L.,Topics in Current Aerosol Research, vol. 2, Ed. M. Hidy and R. Brock, Pergamon, Oxford 1972.Google Scholar
  2. 2.
    Friedlander, S. K.,Smoke, Dust and Hasz, Wiley, New York 1977.Google Scholar
  3. 3.
    Simons, S., J. Phys. A.19, 1413 (1986).Google Scholar
  4. 4.
    Brown, P. S., J. Atmospheric Sci.44, 242 (1987).Google Scholar
  5. 5.
    Shock, J. D. R., Danbar, I. H., Ramsdale, S. A., Simons, S. and Williams, M. M. R., Ann. Nucl. Eng.14, 1 (1987).Google Scholar
  6. 6.
    Futcher, E., Hoare, M. R., Hendriks, E. M. and Ernst, M. H., Physica101A, 185 (1980).Google Scholar
  7. 7.
    Hendriks, E. M., Ernst, M. H., Futcher, E. and Hoare, M. R., Physica101A, 375 (1980).Google Scholar
  8. 8.
    Futcher, F. J. and Hoare, M. R., Phys. Lett.75A, 443 (1980).Google Scholar
  9. 9.
    Williams, M. M. R., J. Phys. A. Math. Gen.14, 2073 (1981).Google Scholar
  10. 10.
    Williams, M. M. R., Ann. Nucl. Energy9, 499 (1982).Google Scholar
  11. 11.
    Liverman, T. P. G.,Generalized Function and Direct Operational Methods. Prentice Hall, Englewood Cliffs 1964.Google Scholar
  12. 12.
    Baker, G. and Gammel, J.,The Padé Approximant in Theoretical Physics. Academic Press, New York 1970.Google Scholar
  13. 13.
    Hill, J. M.,Solution of Differential Equations by Means of One-Parameter Groups. Pitman Adv. Publ. Progr., Boston 1982.Google Scholar
  14. 14.
    Scott, W. T., J. Atmospheric Sci.25, 871 (1968).Google Scholar

Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • S. A. El-Wakil
    • 1
  • M. A. Madkour
    • 1
  • A. Abu El-Ela
    • 1
  • A. M. El-Grayhy
    • 1
  1. 1.Physics Department, Faculty of ScienceMansoura UniversityMansouraEgypt

Personalised recommendations