International Journal of Thermophysics

, Volume 34, Issue 7, pp 1239–1254 | Cite as

Dielectric Response of a Charged Prolate Spheroid in an Electrolyte Solution

  • C. Chassagne


We derived the so-called standard set of electrokinetic equations in prolate spheroidal coordinates for all ionic strengths, zeta potentials, and applied electric field frequencies, with the assumption, however, that the particle’s electrophoretic mobility is small. We subsequently solved these equations using finite differences methods. We show that the dipolar coefficient of a prolate spheroid reduces to that of a sphere in the corresponding limit, but deviates strongly from it when the eccentricity of the spheroid is large, for the same particle volume. We also verified that a previously published analytical theory (Chassagne and Bedeaux, J. Colloid Interface Sci., 326:240, 2008) is in good agreement with the numerical results for a large range of zeta potentials, ionic strengths, and frequencies.


Dielectric spectroscopy Electrokinetics Spheroids Zeta potential 


  1. 1.
    H.R. Kruyt, Colloid Science, vol. 1, Irreversible Systems (Elsevier Publishing Company, Amsterdam, 1952)Google Scholar
  2. 2.
    W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions (Cambridge University Press, Cambridge, 1989)CrossRefGoogle Scholar
  3. 3.
    H. Ohshima, K. Furusawa (eds.), Electrical Phenomena at Interfaces, Fundamentals, Measurements and Applications (Dekker, New York, 2002)Google Scholar
  4. 4.
    E.H.B. DeLacey, L.R. White, J. Chem. Soc. Faraday Trans. 2 77, 2007 (1981)CrossRefGoogle Scholar
  5. 5.
    C.S. Mangelsdorf, L.R. White, J. Chem. Soc. Faraday Trans. 94(16), 2441; 94(17), 2583 (1998)Google Scholar
  6. 6.
    C.S. Mangelsdorf, L.R. White, J. Chem. Soc. Faraday Trans. 93(17), 3145 (1997)CrossRefGoogle Scholar
  7. 7.
    M. Fixman, J. Chem. Phys. 72, 5177 (1980)ADSCrossRefGoogle Scholar
  8. 8.
    M. Fixman, J. Chem. Phys. 78, 1483 (1983)ADSCrossRefGoogle Scholar
  9. 9.
    E.J. Hinch, J. Sherwood, W.C. Chen, P.N. Sen, J. Chem. Soc. Faraday Trans. 2 80, 535 (1984)CrossRefGoogle Scholar
  10. 10.
    R.W. O’Brien, J. Colloid Interface Sci. 92, 204 (1983)CrossRefGoogle Scholar
  11. 11.
    R.W. O’Brien, J. Colloid Interface Sci. 113, 81 (1986)CrossRefGoogle Scholar
  12. 12.
    J.D. Sherwood, H.A. Stone, Phys. Fluids 7, 697 (1995)ADSMATHCrossRefGoogle Scholar
  13. 13.
    R.W. O’Brien, D.N. Ward, J. Colloid Interface Sci. 121, 402 (1988)CrossRefGoogle Scholar
  14. 14.
    C. Chassagne, D. Bedeaux, G.J.M. Koper, J. Colloid Interface Sci. 255(1), 129 (2002)Google Scholar
  15. 15.
    C. Chassagne, D. Bedeaux, G.J.M. Koper, Langmuir 19(9), 3619 (2003)Google Scholar
  16. 16.
    C. Chassagne, D. Bedeaux, J. Colloid Interface Sci. 326, 240 (2008)CrossRefGoogle Scholar
  17. 17.
    A. Jeffrey, Handbook of Mathematical Formulas and Integrals, 3rd edn. (Elsevier Academic Press, Amsterdam, 2004)MATHGoogle Scholar
  18. 18.
    A.J. Poza, J.J. Lopez-Garcia, A. Hayas, J. Horno, J. Colloid Interface Sci. 219, 241 (1999)CrossRefGoogle Scholar
  19. 19.
    J. Bladel, Electromagnetic Fields, 2nd edn., IEEE Press Series on Electromagnetic Wave Theory (John Wiley & Sons, Inc. Hoboken, NJ, 2007)Google Scholar
  20. 20.
    B.J. Yoon, S. Kim, J. Colloid Interface Sci. 128, 275 (1989)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Environmental Fluid Mechanics, Faculty of Civil Engineering and GeosciencesDelft University of Technology DelftThe Netherlands

Personalised recommendations