Skip to main content
Log in

Analytical solutions for anomalous transport of volatile pollutants in nonaqueous-phase liquid contaminated soil

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, we study a fractal model for the transport of a volatile component from a nonaqueous-phase liquids (NAPL) trapped in homogeneous soil. By introducing a kind of new integral transform in fractal space, analytical solutions of fractal model are given. Numerical results are presented graphically for various values of fractal dimension.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Sahimi, M.: Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata, and simulated annealing. Rev. Mod. Phys. 65(4), 1393–1536 (1993)

    Article  Google Scholar 

  2. Roberts, A.P., Knackstedt, M.A.: Transport and elastic properties of fractal media. Physica A 233(3–4), 848–858 (1996)

    Article  Google Scholar 

  3. Perrier, E., Bird, N., Rieu, M.: Generalizing the fractal model of soil structure: the pore-solid fractal approach. Geoderma 88(3–4), 137–164 (1999)

    Article  Google Scholar 

  4. Giona, M., Cerbellia, S., Adrovera, A.: Symmetric product measures: Binomial processes and invariant manifold intersections in dynamical systems. Physica A 356(2–4), 447–467 (2005)

    Article  MathSciNet  Google Scholar 

  5. Ma, J.H., Cui, Y.Q., Liulixia: A study on the complexity of a business cycle model with great excitements in non-resonant condition. Chaos Solitons Fractals 39, 2258–2267 (2009)

    Article  Google Scholar 

  6. Giona, M.: First-order reaction–diffusion kinetics in complex fractal media. Chem. Eng. Sci. 47, 1503–1515 (1992)

    Article  Google Scholar 

  7. Lehmann, P., Stähli, M., Papritz, A., Gygi, A., Flühler, H.: A fractal approach to model soil structure and to calculate thermal conductivity of soils. Transp. Porous Media 52, 313–332 (2003)

    Article  Google Scholar 

  8. Yu, B.M.: Analysis of flow in fractal porous media. Appl. Mech. Rev. 61, 050801 (2008), 19 pp.

    Article  Google Scholar 

  9. Mukhopadhyay, S., Cushman, J.H.: Diffusive transport of volatile pollutants in nonaqueous-phase liquid contaminated soil: a fractal model. Transp. Porous Media 30, 125–154 (1998)

    Article  Google Scholar 

  10. Jiang, X.Y., Xu, M.Y.: The fractional finite Hankel transform and its applications in fractal space. J. Phys. A, Math. Theor. 42, 385201 (2009), 11 pp.

    Article  MathSciNet  Google Scholar 

  11. Debnath, L., Bhatta, D.: Integral Transforms and Their Applications. Chapman & Hall/CRC, Boca Raton (2007)

    Google Scholar 

  12. Tan, W.C., Takashi, M.: Stokes’ first problem for a second grade fluid in a porous half-space with heated boundary. Int. J. Non-Linear Mech. 40, 515–522 (2005)

    Article  MATH  Google Scholar 

  13. Povstenko, Y.Z.: Time-fractional radial diffusion in a sphere. Nonlinear Dyn. 53, 55–65 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Povstenko, Y.Z.: Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation. Int. J. Solids Struct. 44, 2324–2348 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  15. Agrawal, O.P.: Fractional diffusion-wave equation defined in a bounded domain. Nonlinear Dyn. 29, 145–155 (2002)

    Article  MATH  Google Scholar 

  16. Wang, C.Y.: The recirculating flow due to a moving lid on a cavity containing a Darcy–Brinkman medium. Appl. Math. Model. 33, 2054–2061 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Fetecau, C., Hayat, T., Fetecau, C., Ali, N.: Unsteady flow of a second grade fluid between two side walls perpendicular to plate. Nonlinear Anal. Real World Appl. 9, 1236–1252 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  18. Fetecau, C., Fetecau, Corina, Zierep, J.: Decay of a potential vortex and propagation of a heat wave in a second grade fluid. Int. J. Non-Linear Mech. 37, 1051–1056 (2002)

    Article  MATH  Google Scholar 

  19. Wang, S.W., Xu, M.Y.: Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus. Nonlinear Anal. Real World Appl. 10, 1087–1096 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  20. Watson, G.N.: A Treatise on the Theory of Bessel Functions, 2nd edn. Cambridge University Press, New York (1944)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaoyun Jiang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jiang, X., Qi, H. Analytical solutions for anomalous transport of volatile pollutants in nonaqueous-phase liquid contaminated soil. Nonlinear Dyn 62, 895–904 (2010). https://doi.org/10.1007/s11071-010-9772-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-010-9772-9

Keywords

Navigation