Analytical solution for coupled diffusion of three-components liquid in porous pellet
(1. School of Resource and Civil Engineering, Northeastern University,
Shenyang 110004, China;
2. School of Materials and Metallurgy, Northeastern University,
Shenyang 110004, China)
Shenyang 110004, China;
2. School of Materials and Metallurgy, Northeastern University,
Shenyang 110004, China)
Abstract: The coupled three-components liquid diffusion within a porous pellet was investigated. The coupled diffusion model was given according to irreversible thermodynamics, and the rigorous solutions of the model subject to the homogeneous boundary conditions of the first kind are derived by employing Hankel transform technique and the standard technique resolving ordinary differential system. The method can also be used to solve the other coupled diffusion problems within a pellet with different kinds of boundary conditions. Then the case computations were conducted. The calculation results show that the effect of interdiffussion on the concentration of components depends upon the diffusion time strongly, after a long diffusion period, a very small cross diffusion coefficient will induce the observable change of concentration profile, and that, when the cross coefficients are close to 5%-7% of the main coefficients, the significant effect of coupled diffusion on the concentration profiles of components is observed. The case computations also show that interdiffussion can induce non-monotonous concentration profiles. So, for the diffusion taking place within ternary system, the concentration profiles obtained by the analysis of interdiffussion can be very different from that obtained by the equivalent binary system analysis method.
Key words: ternary system; coupled diffusion; analytical solution; irreversible thermodynamics