Skip to main content
SpringerLink
Log in

Analytical solution to Poisson-Boltzmann equation for two interacting parallel identical plates with constant surface potential

  • Published:
Colloid Journal Aims and scope Submit manuscript

Abstract

In this paper, we suggest an analytical solution to Poisson-Boltzmann equation for the calculation of potential distributions between two identical plates with high constant surface potential. Our expression fits well to the exact values of the potential between two parallel plates. Numerical results indicate that this analytical solution provides accurate description for the dimensionless distance ≤ 2. The suggested solution can be successfully applied in calculating the potential for identical plates with high or moderate surface potentials. A simple analytical expression for the energy of interactions between two identical plates with constantly high surface potential is also given. The solutions in analytical, exact and numerical forms become indistinguishable when y 0 ≥ 3, κx ≤ 4 and y 0 = 2.0, κx ≤ 3, respectively. When y 0 = 2.0, κx ≤ 1.2, the approximate solution is in close agreement with the exact solution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. McCormack, D., Carnie, S.L., and Chan, D.Y.C., J. Colloid Interface Sci., 1995, vol. 169, p. 177.

    Article  CAS  Google Scholar 

  2. Verwey, E.J.W. and Overbeek, J.Th.G., Theory of the stability of lyophobic colloids, Amsterdam: Elsevier, 1948.

    Google Scholar 

  3. Langmuir, I., J. Chem. Phys., 1938, vol. 6, p. 893.

    Article  Google Scholar 

  4. Luo, G.X., Wang, H.P., and Jin, J., Langmuir, 2001, vol. 17, p. 2167.

    Article  CAS  Google Scholar 

  5. Luo, G.X., Feng, R., Jin, J., and Wang, H.P., J. Colloid Interface Sci., 2001, vol. 241, p. 81.

    Article  CAS  Google Scholar 

  6. Zhang, Y., Jin, J., Luo, G., and Wang, H., Colloid. Polym. Sci., 2003, vol. 281, p. 401.

    Article  CAS  Google Scholar 

  7. Wang, H., Hou, C., and Jin, J., J. Colloid Interface Sci., 2003, vol. 263, p. 684.

    Article  CAS  Google Scholar 

  8. Wang, Q., Luo, G., Wang, H., Hou, C., and Jin, J., J. Colloid Interface Sci., 2006, vol. 297, p. 845.

    Article  CAS  Google Scholar 

  9. Honig, E.P. and Mul, P.M., J. Colloid Interface Sci., 1971, vol. 36, p. 258.

    Article  CAS  Google Scholar 

  10. Ohshima, H., Healy, Th.W., and White, L.R., J. Colloid Interface Sci., 1982, vol. 90, p. 17.

    Article  CAS  Google Scholar 

  11. Ohshima, H., Colloids Surf., A, 1999, vol. 146, p. 213.

    Article  CAS  Google Scholar 

  12. Nguyen, A.V., Evans, G.M., and Jameson, G.J., J. Colloid Interface Sci., 2000, vol. 230, p. 205.

    Article  CAS  Google Scholar 

  13. Zhang, S., J. Colloid Interface Sci., 2006, vol. 297, p. 644.

    Article  CAS  Google Scholar 

  14. Ohshima, H., J. Colloid Interface Sci., 2010, vol. 350, p. 249.

    Article  CAS  Google Scholar 

  15. Wang, C.Y., Kuo, C.-Y., and Chang, C.C., J. Eng. Math., 2011, vol. 70, p. 33.

    Article  Google Scholar 

  16. Kumar, S. and Sloan, L.H., Math. Comput., 1987, vol. 178, p. 585.

    Google Scholar 

  17. Yato, A. and Papadopoulos, K.D., Colloid Polym. Sci., 1985, vol. 263, p. 913.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, Liaoning Shihua University, 113001, Dalian, People’s Republic of China

    Guozhi Liu

  2. Department of Chemistry, School of Chemistry and Materials Science, Liaoning Shihua University, Dalian, 113001, People’s Republic of China

    Genxiang Luo

Authors
  1. Guozhi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Genxiang Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Genxiang Luo.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, G., Luo, G. Analytical solution to Poisson-Boltzmann equation for two interacting parallel identical plates with constant surface potential. Colloid J 75, 565–570 (2013). https://doi.org/10.1134/S1061933X13050074

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061933X13050074

Keywords

Search

Navigation