Quantitative Evaluation of Possible Errors Induced by Using Simplified Analytical Solutions to the Laboratory In-Diffusion Test

Laboratory diffusion test has been widely used for characterizing the diffusive and adsorptive properties of synthetic, geological and geotechnical materials in many scientific fields and engineering practices. Although many types of laboratory diffusion test are currently available, different methods have different advantages and disadvantages. An overview of conventional test methods has recently been performed by Zhang and Takeda et al. (WM06) and rigorous solutions to the laboratory through-diffusion tests were developed and discussions on how to select an appropriate test method, design optimum test conditions and determine data sampling for the through-diffusion tests were performed by Takeda and Zhang et al. (WM06). In addition, theoretical evaluation of possible errors which may be caused by using simplified boundary conditions for developing solutions to the laboratory through-diffusion tests were quantitatively examined by Zhang and Takeda (WM05). As a new part of the systematic study, rigorous solutions to the laboratory in-diffusion test, with emphasis on the decreasing source concentration in-diffusion test, are further derived and illustrated in this paper. The new solutions are then used to exam possible errors which may be induced by using simplified solution in interpreting the in-diffusion test data, or data analyses. The theoretical examinations in this study found that the errors in determining the transport properties for a test specimen depend on both test condition and test duration. The conditions and/or applicability of using the simplified solutions are then clarified and illustrated through a series of theoretical simulations. The theories and approaches presented in this paper may offer practical considerations for effective implementations of an in-diffusion test and for proper interpretation of the test results. They can also be used to assess the quality of, or analyze the potential errors in existing data when citing them from previous scientific articles. (authors)