Dr. Leonid V. Matveev
Doctor of Sciences Leonid Matveev now is director of Nuclear Safety Institute of Russian Academy of Sciences. He also gives the lectures on anomalous transport in heterogeneous media and kinetics of processes in condensed matter at Moscow Institute of Physics and Technology. He got PhD in physics and mathematics from Moscow Institute of Physics and Technology, Doctor of Sciences in Physics and Mathematics from Nuclear Safety Institute of RAS. The main results he has achieved are in the theory of condensed matter, statistical physics, radiation material science and non-classical transport processes in highly heterogeneous media.
Non-classical transport and the problems of ecological safety in nuclear power engineering
One of the serious problems of the safe development of nuclear power engineering is the management of radioactive waste (RW), in particular, the isolation of RW in deep underground (or near-surface) storage facilities. To justify the ecological safety of burials, knowledge of the laws governing the transport of radionuclides in geological media, is required. We provide overview of the results of studies performed at the Laboratory of Theoretical Physics of the Nuclear Safety Institute, which are devoted to impurity transport in geological structures. Our studies are based on the analysis of physical models that take into account the real properties of geological environments. We have taken into account the fact that geological structures are highly heterogeneous, which can be characterized by fractal geometry and a sharp contrast in the spatial distribution of transport characteristics. The transport is considered to be due to classical physical mechanisms which are diffusion, advection, and sorption. It is shown that, depending on the structure of the medium, non-classical transport modes, such as sub- and super-diffusion, quasi-diffusion, can be realized. Of particular importance for justifying the safety of radionuclide burials is the structure of the concentration distribution at asymptotically far distances. It is established that in all physical models the decrease of concentration in asymptotics is exponential. This conclusion sharply distinguishes our theory from the abstract mathematical constructions, such as models with fractional derivatives, CTRW, where the asymptotic decrease of concentration is power-law. We found that in a stationary medium transport modes can change with time. A consequence of this property is the multistage spatial structure of the concentration asymptotic behavior. The rule is realized: a more distant asymptotic step is formed by an earlier transport regime. Special attention should be paid to the model of impurity transport that we developed in the statistically homogeneous sharply contrasting medium, which is most often encountered in nature. Here, at earlier times, the classical regime of fast advection-diffusion is realized, which over time is replaced by quasi-diffusion or sub-diffusion, which, in turn, end with slow advection-diffusion. One of our models is devoted to the transport of impurities in a statistically homogeneous sharply contrasting medium in the presence of colloids. Sorption on colloids makes the list of realized transport modes more diverse and leads to a significant acceleration of impurity transport itself. We also analyzed the transport regimes and asymptotic concentration profiles under conditions when the impurity source is surrounded by a low-permeable diffusion barrier. At relatively early times, the presence of a barrier leads to both renormalization of the source power and a slowdown in the growth of the main region of impurity localization, as well as a modification of asymptotic concentration profiles. At later times, only a modification of asymptotic behavior is observed. The results of our study of the kinetics of the impurity leaching from contaminated areas are presented for the case when the medium has pronounced double-porous properties. The possibility of significant acceleration of the remediation process by introducing colloidal particles into the fluid is demonstrated.
Radioactive waste, Non-classical transport, Super-diffusion, Sub-diffusion