Green's Function and Eigenvalue Representation of Time Lag for Absorptive Permeation Across a Heterogeneous Membrane
| Autor: | Jenn-Shing Chen, Kwei-Tin Yeh, Wen-Yih Chang |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Diffusion equation
Chemistry Mathematical analysis 02 engineering and technology General Chemistry Penetration (firestop) Permeation 010402 general chemistry 021001 nanoscience & nanotechnology Thermal diffusivity 01 natural sciences 0104 chemical sciences Partition coefficient Membrane Boundary value problem 0210 nano-technology Eigenvalues and eigenvectors |
| Zdroj: | Journal of the Chinese Chemical Society. 64:1048-1057 |
| ISSN: | 0009-4536 |
| DOI: | 10.1002/jccs.201700118 |
| Popis: | The time-lag problem is treated for absorptive penetration across a heterogeneous membrane, where both the diffusivity D(x) and the partition coefficient K(x) depend on the coordinate x (0 ≦ x ≦ h), with 0 and h being the coordinates of the upstream and downstream faces, respectively. A new concept of time-lag distribution is introduced, and the first (time) moment tL1 and the second (time) moment tL2 over this distribution are also difined and treated in the Lapalce domain in conjuction with the Green's function G(x,y), and eigenvalues associated with the time-independent diffusion equation subject to the absorbing boundary condition at both ends of the membrane. Our central results include tL1=∫0hGxxdx=∑i1λi and tL2=∫0h∫0hGxyGyxdxdy=∑i1λi2+∑i1λi2, where λi is the ith eigenvalue of the aforementioned diffusion equation. The merits of these new resprentations and comparison with the treatments of Frisch or Eyring are also discussed. |
| Databáze: | OpenAIRE |
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