Definition Of Diffusion Coefficient Research Articles

Modeling of all-solid-state thin-film Li-ion batteries: Accuracy improvement

Thin-film Solid-State Batteries (TFSSB) is one of most promising and quickly developing fields in modern electrochemical energy storage. Modeling these devices is interesting from theoretical and practical point of view. This paper represents a simulation approach for TFSSB which overcome a major drawback of available mathematical models, i.e. decline in accuracy of the models at high current rates. A one-dimensional electrochemical model, including charge transfer kinetics on the electrolyte-electrode interface, diffusion and migration in electrolyte as well as diffusion in intercalation electrode has been developed and the simulation results are compared to experimental voltage-capacity measurements. A new definition of diffusion coefficient as a function of concentration, based on the experimental measurements, is used to improve the performance of the model. The simulation results fit the available experimental data at low and high discharge currents up to 5 mA cm−2. The models show that the cathode diffusion constant is a prime factor limiting the rate capability for TFSSB in particular for ultrafast charging applications.

On the Diffusion Coefficients for Reactor Physics Applications

The definition of the multigroup diffusion coefficient for reactor physics problems is not unique; rather, it is based on limiting approximations made to the Boltzmann transport equation. In this paper, we present several new diffusion closures in an attempt to gain increased accuracy over the standard P1-based diffusion theory. First, the Levermore-Pomraning flux-limited diffusion theory is applied to reactor physics problems both in its original form and in a new modified form that makes the methodology more robust with respect to the energy variable. Additionally, two novel definitions of the diffusion coefficient are introduced that permit a neutron flux that is greater than first order in angle. These various diffusion theories are completed by developing consistent boundary conditions for each case. Diffusion theory solutions are computed for each unique closure and are compared against transport theory analytically for a simple half-space problem and numerically for a suite of simplified one-dimensional reactor problems. Conclusions and observations are made for each diffusion method in terms of its underlying assumptions and accuracy of the benchmark solutions.

Comparison of Definitions of Ordinary Diffusion Coefficients in Multi-component Mixture

Concentrating our attentions on the definitions of diffusion coefficients in multi-component mixture, we have compared two theories given by Hirschfelder et al. and by Chapman-Cowling. Differences between the two definitions of diffusion coefficients are clarified with respect to (i) treatment for removing a degree of indeterminancy of the coefficients, (ii) condition for mass balances and (iii) symmetric relation.Moreover, an expression of Chapman-Cowling coefficients was obtained in terms of those by Hirschfelder et al. The relation and the inverse, derived before by Ern et al., enable us to exchange mutually the two coefficients.

Comparison of Definitions of Ordinary Diffusion Coefficients in Multi-component Mixture.

Concentrating our attentions on the definitions of diffusion coefficients in multi-component mixture, we have compared two theories given by Hirschfelder et al. and by Chapman-Cowling. Differences between the two definitions of diffusion coefficients are clarified with respect to (i) treatment for removing a degree of indeterminancy of the coefficients, (ii) condition for mass balances and (iii) symmetric relation. Moreover, an expression of Chapman-Cowling coefficients was obtained in terms of those by Hirschfelder et al. The relation and the inverse, derived before by Ern et al., enable us to exchange mutually the two coefficients.

Relation between Koebke’s Equivalence Theory and Benoist’s Cell Homogenization Procedure

In this article, the authors apply Koebke's equivalence theory to a uniform slab lattice of symmetric cells on which a macroscopic buckling is superimposed. It is shown that Koebke's procedure, up to second-order accuracy in buckling, leads to Benoist's (corrected) definition of diffusion coefficient, and the discontinuity factors are found to be independent of the position of the cell in the lattice. Some comments regarding the use of equivalence theory in typical reactor core calculations are also made.