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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

Estimation of D for Case_S, Case_S*, Case_D+, Case_D−, and Case_D* by Eqs. (34, 37, 38). a VC–VC method by Eq. (34), b VC–VC IR method by Eq. (37), c VC–VC OR method by Eq. (38). White circle:Case_S, plus sign:Case_S*, white square:Case_D+, white triangle:Case_D−, whitediamond:Case_D*
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Fig2: Estimation of D for Case_S, Case_S*, Case_D+, Case_D−, and Case_D* by Eqs. (34, 37, 38). a VC–VC method by Eq. (34), b VC–VC IR method by Eq. (37), c VC–VC OR method by Eq. (38). White circle:Case_S, plus sign:Case_S*, white square:Case_D+, white triangle:Case_D−, whitediamond:Case_D*

Mentions: In this section, we first validated the proposed simple formulas Eq. (37), called VC–VC IR method, and Eq. (38), called VC–VC OR method, to estimate D in the VC–VC model by calculating the default values of five cases (Case_S*, Case_S, Case_D+, Case_D*, and Case_D−), as shown in Table 1 and Fig. 2, and compared them with the results of Eq. (34). After plotting the linear relationship against time (t), we acquired an approximate slope by using a linear regression. The experimental diffusion coefficients were obtained by inputting the approximate slope into Eqs. (34), 37, and 38). By comparing the obtained diffusion coefficients with the theoretical coefficients (Table 2), we could assess the validity of the proposed models.Table 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)

Estimation of D for Case_S, Case_S*, Case_D+, Case_D−, and Case_D* by Eqs. (34, 37, 38). a VC–VC method by Eq. (34), b VC–VC IR method by Eq. (37), c VC–VC OR method by Eq. (38). White circle:Case_S, plus sign:Case_S*, white square:Case_D+, white triangle:Case_D−, whitediamond:Case_D*
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Related In: Results  -  Collection

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Fig2: Estimation of D for Case_S, Case_S*, Case_D+, Case_D−, and Case_D* by Eqs. (34, 37, 38). a VC–VC method by Eq. (34), b VC–VC IR method by Eq. (37), c VC–VC OR method by Eq. (38). White circle:Case_S, plus sign:Case_S*, white square:Case_D+, white triangle:Case_D−, whitediamond:Case_D*
Mentions: In this section, we first validated the proposed simple formulas Eq. (37), called VC–VC IR method, and Eq. (38), called VC–VC OR method, to estimate D in the VC–VC model by calculating the default values of five cases (Case_S*, Case_S, Case_D+, Case_D*, and Case_D−), as shown in Table 1 and Fig. 2, and compared them with the results of Eq. (34). After plotting the linear relationship against time (t), we acquired an approximate slope by using a linear regression. The experimental diffusion coefficients were obtained by inputting the approximate slope into Eqs. (34), 37, and 38). By comparing the obtained diffusion coefficients with the theoretical coefficients (Table 2), we could assess the validity of the proposed models.Table 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