Transient response of an electrolyte to a thermal quench
- We study the transient response of an electrolytic cell subject to a small, suddenly applied temperature increase at one of its two bounding electrode surfaces. An inhomogeneous temperature profile then develops, causing, via the Soret effect, ionic rearrangements towards a state of polarized ionic charge density q and local salt density c. For the case of equal cationic and anionic diffusivities, we derive analytical approximations to q,c, and the thermovoltage VT for early (t≪τT) and late (t≫τT) times as compared to the relaxation time τT of the temperature. We challenge the conventional wisdom that the typically large Lewis number, the ratio a/D of thermal to ionic diffusivities, of most liquids implies a quickly reached steady-state temperature profile onto which ions relax slowly. Though true for the evolution of c, it turns out that q (and VT) can respond much faster. Particularly when the cell is much bigger than the Debye length, a significant portion of the transient response of the cell falls in the t≪τT regime, for which our approximated q (corroborated by numerics) exhibits a density wave that has not been discussed before in this context. For electrolytes with unequal ionic diffusivities, VT exhibits a two-step relaxation process, in agreement with experimental data of Bonetti et al. [J. Chem. Phys. 142, 244708 (2015)].
Author: | Mathijs Janssen, Markus Bier |
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Persistent identifier: | https://doi.org/10.1103/PhysRevE.99.042136 |
Parent Title (English): | Physical Review E |
Document Type: | Article |
Language: | English |
Year of publication: | 2019 |
Publishing Institution: | Hochschule für Angewandte Wissenschaften Würzburg-Schweinfurt |
Release Date: | 2023/06/19 |
Tag: | Electrochemistry, Electrokinetic flows, Ionic transport, Nonequilibrium & irreversible thermodynamics, Thermoelectrics, Thermophoresis, Ionic fluids, Condensed Matter, Materials & Applied Physics, Statistical Physics, General Physics |
Volume: | 99 |
Issue: | 4 |
First Page: | 042136 |
Institutes and faculty: | Fakultäten / Fakultät für angewandte Natur- und Geisteswissenschaften |