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Effective diffusivities of radioactive nuclides in compacted bentonite were calculated theoretically by using an electric double layer theory. Comparison between calculated diffusivities and measured ones show good agreements.The effective diffusivity is dominated by pore structure and pore diffusivity Dp. The pore structure can be characterized by effective porosity ε eff, constrictivity δ, and tortuosity Γ. The δ was assumed to be unity. The ε eff and the Γ were determined experimentally. The Dp was estimated by means of the electric double layer theory. In the estimation, smectite interlayer was assumed the space between parallel plane sheets of smectite crystal lattice.Diffusion experiments were carried out by using Cs+ for monovalent cation, C1- and Tc04- for monovalent anion, and tritiated water for neutral molecule. The measured and calculated effective diffusivities in different densities showed the same tendency of cation > neutral > anion. The dry density of bentonite became higher, the discrepancy between the estimated and the measured diffusivities became larger. The calculation was limited by the applicability of the electric double layer theory in the near surface region of smectite.

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In this study, the balance equation for local entropy density defined on each partition is obtained by the decomposition of the time-evolution operator for local entropy density, on the level of the master equation, by using symmetric and antisymmetric properties for the inversion of partition, density pairs and a given drift velocity. The resultant equation includes the following terms: convection, diffusion, entropy flow due to a thermostat and entropy production. The averaging of the four terms recover the corresponding terms in a balance equation for the macroscopic entropy density of irreversible thermodynamics for a thermostated system. Moreover, an empirical law of order estimation is introduced to explain the limiting behavior of the averaged quantities in the macroscopic limit for the bulk system. The law makes it possible to separate some minor contributions from the major four terms and, for example, to explain the positive entropy production rate in a nonequilibrium state for volume-preserving systems, even if the state is far from steady state. They are numerically confirmed on an invertible, dissipative multibaker chain system, named a circuit model. These properties are independent of partitioning.Keywords: symmetry-based decomposition; local entropy density; coarse graining; dissipative system; positive entropy production; law of order estimation; multibaker map