Journal article
Laplace transform methods for transient diffusion; or, some good questions from Ralph White
- Abstract:
- Motivated by years of correspondence with Prof. Ralph White, I discuss two unconventional ways to solve diffusion problems with Laplace transforms. A method to derive error-function series, alternatives to Fourier series that converge rapidly and avoid the Gibbs phenomenon at short times, is illustrated by example. It is shown how Mittag-Leffler partial-fractions expansions can facilitate derivations of Fourier-series solutions from the same starting point. Several basic problems pertinent to electrochemical transport are analyzed, culminating in the development of a modified Cottrell equation applicable to thin films of unsupported electrolytic solutions sandwiched between planar electrodes.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.5MB, Terms of use)
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- Publisher copy:
- 10.1149/1945-7111/acf6e2
Authors
- Publisher:
- IOP Publishing
- Journal:
- Journal of The Electrochemical Society More from this journal
- Volume:
- 170
- Issue:
- 9
- Article number:
- 093509
- Publication date:
- 2023-09-20
- Acceptance date:
- 2023-09-05
- DOI:
- EISSN:
-
1945-7111
- ISSN:
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0013-4651
- Language:
-
English
- Keywords:
- Pubs id:
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1526274
- Local pid:
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pubs:1526274
- Deposit date:
-
2023-09-19
Terms of use
- Copyright holder:
- Charles W. Monroe
- Copyright date:
- 2023
- Rights statement:
- Copyright © 2023 The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited.
- Licence:
- CC Attribution (CC BY)
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