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Intercomparison of diffusion coefficient derived from the through-diffusion experiment using different numerical methods.

Chen CL, Wang TH, Lee CH, Teng SP - J Radioanal Nucl Chem (2014)

Bottom Line: More importantly, the best advantage of proposed method over others is that one can derive three diffusion coefficients based on one run of experiment.Furthermore, we proposed a formula to determine the conceptual critical time (Tc), which is particularly beneficial for the selection of using CC-VC or VC-VC method.Based on our proposed method, it becomes possible to calculate diffusion coefficient from a through-diffusion experiment in a shorter period of time.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan ; Division of Chemical Engineering, Institute of Nuclear Energy Research, Taoyuan, Taiwan.

ABSTRACT

Diffusion is a dominant mechanism regulating the transport of released nuclides. The through-diffusion method is typically applied to determine the diffusion coefficients (D). Depending on the design of the experiment, the concentrations in the source term [i.e., inlet reservoir (IR)] or the end term [i.e., outlet reservoir (OR)] can be fixed or vary. The combinations involve four distinct models (i.e., the CC-CC model, CC-VC model, VC-CC model, and the VC-VC model). Studies discussing the VC-CC model are scant. An analytical method considering the decay effect is required to accurately interpret the radioactive nuclide diffusion experiment results. Therefore, we developed a CC-CC model and a CC-VC model with a decay effect and the simplified formulas of these two models to determine the diffusion coefficient (i.e., the CC-CC method and CC-VC method). We also proposed two simplified methods using the VC-VC model to determine the diffusion coefficient straightforwardly based upon the concentration variation in IR and OR. More importantly, the best advantage of proposed method over others is that one can derive three diffusion coefficients based on one run of experiment. In addition, applying our CC-VC method to those data reported from Radiochemica Acta 96:111-117, 2008; and J Contam Hydrol 35:55-65, 1998, derived comparable diffusion coefficient lying in the identical order of magnitude. Furthermore, we proposed a formula to determine the conceptual critical time (Tc), which is particularly beneficial for the selection of using CC-VC or VC-VC method. Based on our proposed method, it becomes possible to calculate diffusion coefficient from a through-diffusion experiment in a shorter period of time.

No MeSH data available.


Related in: MedlinePlus

Schematic diagram of three various through-diffusion models. a CC–CC Model, b CC–VC Model, c VC–VC Model
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Fig1: Schematic diagram of three various through-diffusion models. a CC–CC Model, b CC–VC Model, c VC–VC Model

Mentions: The experimental concept of the CC–CC model is demonstrated in Fig. 1a. The solute concentration in the IR (left-hand side) is assumed constant while the solute concentration in the OR (right-hand side) should always be zero all the time. However, when conducting a diffusion experiment, the solute concentration in the IR would actually decrease because the radioactive nuclides will decay and diffuse into the media. The solute concentration in the right-hand side (OR) would change as well because certain amount of solute have diffused through the media. In order to keep the experimental conditions meet the boundary condition of CC–CC model, one must periodically add additional solute into IR and periodically replace the solution in the OR. From this point of view, a practical alternative is to greatly increase the volume of both IR and OR so that the varying solute concentration may be reasonably assumed negligible.Fig. 1


Intercomparison of diffusion coefficient derived from the through-diffusion experiment using different numerical methods.

Chen CL, Wang TH, Lee CH, Teng SP - J Radioanal Nucl Chem (2014)

Schematic diagram of three various through-diffusion models. a CC–CC Model, b CC–VC Model, c VC–VC Model
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4514585&req=5

Fig1: Schematic diagram of three various through-diffusion models. a CC–CC Model, b CC–VC Model, c VC–VC Model
Mentions: The experimental concept of the CC–CC model is demonstrated in Fig. 1a. The solute concentration in the IR (left-hand side) is assumed constant while the solute concentration in the OR (right-hand side) should always be zero all the time. However, when conducting a diffusion experiment, the solute concentration in the IR would actually decrease because the radioactive nuclides will decay and diffuse into the media. The solute concentration in the right-hand side (OR) would change as well because certain amount of solute have diffused through the media. In order to keep the experimental conditions meet the boundary condition of CC–CC model, one must periodically add additional solute into IR and periodically replace the solution in the OR. From this point of view, a practical alternative is to greatly increase the volume of both IR and OR so that the varying solute concentration may be reasonably assumed negligible.Fig. 1

Bottom Line: More importantly, the best advantage of proposed method over others is that one can derive three diffusion coefficients based on one run of experiment.Furthermore, we proposed a formula to determine the conceptual critical time (Tc), which is particularly beneficial for the selection of using CC-VC or VC-VC method.Based on our proposed method, it becomes possible to calculate diffusion coefficient from a through-diffusion experiment in a shorter period of time.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan ; Division of Chemical Engineering, Institute of Nuclear Energy Research, Taoyuan, Taiwan.

ABSTRACT

Diffusion is a dominant mechanism regulating the transport of released nuclides. The through-diffusion method is typically applied to determine the diffusion coefficients (D). Depending on the design of the experiment, the concentrations in the source term [i.e., inlet reservoir (IR)] or the end term [i.e., outlet reservoir (OR)] can be fixed or vary. The combinations involve four distinct models (i.e., the CC-CC model, CC-VC model, VC-CC model, and the VC-VC model). Studies discussing the VC-CC model are scant. An analytical method considering the decay effect is required to accurately interpret the radioactive nuclide diffusion experiment results. Therefore, we developed a CC-CC model and a CC-VC model with a decay effect and the simplified formulas of these two models to determine the diffusion coefficient (i.e., the CC-CC method and CC-VC method). We also proposed two simplified methods using the VC-VC model to determine the diffusion coefficient straightforwardly based upon the concentration variation in IR and OR. More importantly, the best advantage of proposed method over others is that one can derive three diffusion coefficients based on one run of experiment. In addition, applying our CC-VC method to those data reported from Radiochemica Acta 96:111-117, 2008; and J Contam Hydrol 35:55-65, 1998, derived comparable diffusion coefficient lying in the identical order of magnitude. Furthermore, we proposed a formula to determine the conceptual critical time (Tc), which is particularly beneficial for the selection of using CC-VC or VC-VC method. Based on our proposed method, it becomes possible to calculate diffusion coefficient from a through-diffusion experiment in a shorter period of time.

No MeSH data available.


Related in: MedlinePlus