Appendix B: Solving Diffusion Equations and Advection–Dispersion Equations for Radioactive Materials

  • Shinichi Nakayama
Part of the An Advanced Course in Nuclear Engineering book series (ACNE)


Chapter 7 explained that the transport of radionuclides affecting the performance assessment of radioactive waste disposal can be described with diffusion equations or advection–dispersion equations. This chapter shows some basic mass transfer problems incorporating diffusion, advection/dispersion, radioactive decay, and sorption retardation along with methods of solving them.


Diffusion Equation Decay Chain Retardation Effect Retardation Factor Infinite Medium 


  1. 1.
    J. Crank, The mathematics of diffusion, 2nd edn. (Oxford University Press, Oxford, 1975)Google Scholar
  2. 2.
    H.S. Carslaw, J.C. Jaeger, Conduction of heat in solids (Oxford University Press, Oxford, 1959)Google Scholar
  3. 3.
    H. Bateman, The solution of a system of differential equations occurring in the theory of radioactive transformations. Proc. Cambridge Philos. Soc 15(pt V), 423–427 (1910)MATHGoogle Scholar
  4. 4.
    T.H. Pigford, P.L. Chambré, M. Albert, M. Harada, F. Iwamoto, T. Kanki, D. Leung, S. Masuda, S. Muraoka, D. Ting, Migration of radionuclides through sorbing media: analytical solutions – II, LBL-11616 (Lawrence Berkeley Laboratory, Berkeley, 1980)Google Scholar
  5. 5.
    K. Higashi, T.H. Pigford, Analytical models for migration of radionuclides in geologic sorbing media. J. Nucl. Sci. Technol. 17, 700–709 (1980)CrossRefGoogle Scholar

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© Authors 2015

Authors and Affiliations

  • Shinichi Nakayama
    • 1
  1. 1.Japan Atomic Energy AgencyTokaiJapan

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