Interdiffusion in r-component (r ≥ 2) one dimensional mixture showing constant concentration
Marek Danielewski1
, Konstanty Holly2, Wojciech Krzyżański3
1University of Mining and Metallurgy, Faculty of Materials Science and Ceramics, ul. Mickiewicza 30, 30-059 Cracow, Poland. 2Jagiellonian University, Institute of Mathematics, ul. Reymonta 4, 30-059 Cracow, Poland. 3SUNY at Buffalo, 547 Cooke Hall, Buffalo, NY 14260-1200, USA.
DOI:
https://doi.org/10.7494/cmms.2008.1.0187
Abstract:
It is shown that multicomponent nonequilibrium system relaxing by a diffusion process exhibit unique behavior during evolution toward stationary state. The Darken’s postulate that the total mass flow is a sum of diffusion flux and translation are applied for the general case of diffusional transport in r-component solution (process defined as interdiffusion in unidimensional mixture). The equations of local mass conservation (continuity equations), the Darken’s flux formulas, the postulate of constant molar volume of the mixture (valid e.g. in solid solutions) and the initial and boundary conditions form a self-consistent interdiffusion problem. The variational form of the interdiffusion problem is derived. It has been proved that: i) there exists a weak solution of variational formulation of interdiffusion problem in open as well as in closed systems, ii) a weak solution of variational formulation of interdiffusion problem is the unique solution, iii) the standard deviation of molar ratio of mixture components in the closed system is monotonically decreasing to 0 when time t → ∞ (i.e. mixture becomes homogeneous) and iv) in closed system the gradients of density of every mixture component vanish at the mixture boundaries.
Cite as:
Danielewski, M., Holly, K., Krzyżański, W., (2008). Interdiffusion in r-component (r ≥ 2) one dimensional mixture showing constant concentration. Computer Methods in Materials Science, 8(1), 31 – 46. https://doi.org/10.7494/cmms.2008.1.0187
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