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Electroconvection near an ion-selective surface with Butler–Volmer kinetics

Published online by Cambridge University Press:  11 November 2021

Gaojin Li Open the ORCID record for Gaojin Li [Opens in a new window] ,
Alex Townsend ,
Lynden A. Archer  and
Donald L. Koch Open the ORCID record for Donald L. Koch [Opens in a new window]
Gaojin Li
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
Alex Townsend
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
Lynden A. Archer
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
Donald L. Koch*
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: dlk15@cornell.edu
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Abstract

We study the effects of interfacial kinetics on the electro-hydrodynamics of ion transport near an ion-selective surface using a combination of linear stability analysis and numerical simulation. The finite kinetics of the electrolyte–electrode interface affects the ion transfer and electroconvection in many ways. On a surface of fixed topography, such as a metal surface of slow and stable ion deposition or covered by a polymer membrane, the finite kinetics reduces the current in one-dimensional ion diffusion/migration, increases the critical voltage for the onset of the electroconvective instability, changes the dynamics of the electroconvection and the overlimiting current, and enhances the lateral ion diffusion within the interfacial layer. The first three effects are indirectly caused by the reaction kinetics and can be characterized by an effective voltage difference across the liquid electrolyte. In comparison, the last effect is controlled by a direct interplay between kinetics and nonlinear electroconvection. Scaling laws for ion transport and features of electroconvection are proposed. We also analyse the linear stability of a surface which evolves under ion deposition and find that the finite kinetics decreases the growth rate of both electroconvective and morphological instabilities and therefore modifies the wavenumber of the most unstable mode.

JFM classification

MHD and Electrohydrodynamics: Electrokinetic flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 930 , 10 January 2022 , A26
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Li et al. supplementary movie 1

Da=0.1, cation concentration field

Download Li et al. supplementary movie 1(Video)
Video 8.3 MB

Li et al. supplementary movie 2

Da=0.1, v-velocity field

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Video 7.7 MB

Li et al. supplementary movie 3

Da=1, cation concentration field

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Video 8.5 MB

Li et al. supplementary movie 4

Da=1, v-velocity field

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Video 6.9 MB

Li et al. supplementary movie 5

Da=Infinity, cation concentration field
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Video 8.7 MB

Li et al. supplementary movie 6

Da=Infinity, v-velocity field. White lines represent the region of cation flux Iy+=-6.

Download Li et al. supplementary movie 6(Video)
Video 10.1 MB