Analysis on fractal-like behaviour expected for migration of radionuclides in geologic sorbing media

In earlier work. we shelved that within nonhomogeneous sorbing media the desorption process becomes fractal-like. In migration of radionuclides in geologic media, the adsorption is an essential factor retardating the migration. Moreover, geologic media is inherently nonhomogeneous. It is therefore probable that the migration is significantly influenced by the fractal-like feature. Based on this idea, we have analyzed migration behaviours by employing a new model and compared the results with those obtained using conventional models. The nuclides migrate in the media with the flow of ground water being continually trapped on adsorption sites and released (desorbed) to the flow. The concept of the overall residence-time distribution function for nuclides on the adsorption sites is introduced in the new model. This function obeys the power form, similar to t(-1-alpha) (alpha > 0) for sufficiently large t (t denotes time). The migration behaviours predicted by our theory are qualitatively different from those by conventional theories, and the details of the differences are greatly dependent on the exponent alpha. In particular: the migration behaviour in cases of 0<alpha<1 is characterized by far larger retardation effects.