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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

REFERENCES

Abu-Rjal, R., Leibowitz, N., Park, S., Zaltzman, B., Rubinstein, I. & Yossifon, G. 2019 Signature of electroconvective instability in transient galvanostatic and potentiostatic modes in a microchannel-nanoslot device. Phys. Rev. Fluids 4 (8), 084203.CrossRefGoogle Scholar
Andersen, M.B., Wang, K.M., Schiffbauer, J. & Mani, A. 2017 Confinement effects on electroconvective instability. Electrophoresis 38 (5), 702–711.CrossRefGoogle ScholarPubMed
Andres, J.T.H. & Cardoso, S.S.S. 2011 Onset of convection in a porous medium in the presence of chemical reaction. Phys. Rev. E 83 (4), 046312.CrossRefGoogle Scholar
Bai, P., Li, J., Brushett, F.R. & Bazant, M.Z. 2016 Transition of lithium growth mechanisms in liquid electrolytes. Energy Environ. Sci. 9 (10), 3221–3229.CrossRefGoogle Scholar
Bard, A.J., Faulkner, L.R., Leddy, J. & Zoski, C.G. 1980 Electrochemical Methods: Fundamentals and Applications, vol. 2. Wiley.Google Scholar
Bazant, M.Z. 2013 Theory of chemical kinetics and charge transfer based on nonequilibrium thermodynamics. Acc. Chem. Res. 46 (5), 1144–1160.CrossRefGoogle ScholarPubMed
Bazant, M.Z., Chu, K.T. & Bayly, B.J. 2005 Current-voltage relations for electrochemical thin films. SIAM J. Appl. Maths 65 (5), 1463–1484.CrossRefGoogle Scholar
Bazant, M.Z., Storey, B.D. & Kornyshev, A.A. 2011 Double layer in ionic liquids: Overscreening versus crowding. Phys. Rev. Lett. 106 (4), 046102.CrossRefGoogle ScholarPubMed
Ben, Y. & Chang, H.-C. 2002 Nonlinear Smoluchowski slip velocity and micro-vortex generation. J. Fluid Mech. 461, 229–238.CrossRefGoogle Scholar
Bockris, J.O'M. & Reddy, A.K.N. 1998 Modern Electrochemistry, vol. 1. Plenum Press.Google Scholar
Brenner, H. 2005 a Kinematics of volume transport. Phys. A 349 (1–2), 11–59.CrossRefGoogle Scholar
Brenner, H. 2005 b Navier–Stokes revisited. Phys. A 349 (1–2), 60–132.CrossRefGoogle Scholar
Chazalviel, J.-N. 1990 Electrochemical aspects of the generation of ramified metallic electrodeposits. Phys. Rev. A 42 (12), 7355.CrossRefGoogle ScholarPubMed
Choudhury, S., et al. 2017 Designing solid-liquid interphases for sodium batteries. Nat. Commun. 8 (1), 898.CrossRefGoogle ScholarPubMed
Cogswell, D.A. 2015 Quantitative phase-field modeling of dendritic electrodeposition. Phys. Rev. E 92 (1), 011301.CrossRefGoogle ScholarPubMed
Davidson, S.M., Wessling, M. & Mani, A. 2016 On the dynamical regimes of pattern-accelerated electroconvection. Sci. Rep. 6, 22505.CrossRefGoogle ScholarPubMed
Demekhin, E.A., Nikitin, N.V. & Shelistov, V.S. 2013 Direct numerical simulation of electrokinetic instability and transition to chaotic motion. Phys. Fluids 25 (12), 122001.CrossRefGoogle Scholar
Demekhin, E.A., Shelistov, V.S. & Polyanskikh, S.V. 2011 Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability. Phys. Rev. E 84 (3), 036318.CrossRefGoogle ScholarPubMed
Dickinson, E.J.F. & Wain, A.J. 2020 The Butler–Volmer equation in electrochemical theory: Origins, value, and practical application. J. Electroanalyt. Chem. 114145.CrossRefGoogle Scholar
Druzgalski, C. 2016 Direct numerical simulation of electroconvective chaos near an ion-selective membrane. PhD thesis, Stanford University.Google Scholar
Druzgalski, C.L., Andersen, M.B. & Mani, A. 2013 Direct numerical simulation of electroconvective instability and hydrodynamic chaos near an ion-selective surface. Phys. Fluids 25 (11), 110804.CrossRefGoogle Scholar
Druzgalski, C. & Mani, A. 2016 Statistical analysis of electroconvection near an ion-selective membrane in the highly chaotic regime. Phys. Fluids 1 (7), 073601.CrossRefGoogle Scholar
Fleury, V., Chazalviel, J.N. & Rosso, M. 1993 Coupling of drift, diffusion, and electroconvection, in the vicinity of growing electrodeposits. Phys. Rev. E 48 (2), 1279.CrossRefGoogle ScholarPubMed
Gibou, F., Fedkiw, R., Caflisch, R. & Osher, S. 2003 A level set approach for the numerical simulation of dendritic growth. J. Sci. Comput. 19 (1), 183–199.CrossRefGoogle Scholar
Griebel, M., Merz, W. & Neunhoeffer, T. 1999 Mathematical modeling and numerical simulation of freezing processes of a supercooled melt under consideration of density changes. Comput. Vis. Sci. 1 (4), 201–219.CrossRefGoogle Scholar
Guerra, E., Kelsall, G.H., Bestetti, M., Dreisinger, D., Wong, K., Mitchell, K.A.R. & Bizzotto, D. 2004 Use of underpotential deposition for evaluation of overpotential deposition kinetics of reactive metals. J. Electrochem. Soc. 151 (1), E1–E6.CrossRefGoogle Scholar
Holze, R. 2007 Electrochemical Thermodynamics and Kinetics, vol. 9. Springer Science & Business Media.Google Scholar
Huth, J.M., Swinney, H.L., McCormick, W.D., Kuhn, A. & Argoul, F. 1995 Role of convection in thin-layer electrodeposition. Phys. Rev. E 51 (4), 3444.CrossRefGoogle ScholarPubMed
Karatay, E., Andersen, M.B., Wessling, M. & Mani, A. 2016 Coupling between buoyancy forces and electroconvective instability near ion-selective surfaces. Phys. Rev. Lett. 116 (19), 194501.CrossRefGoogle ScholarPubMed
Karatay, E., Druzgalski, C.L. & Mani, A. 2015 Simulation of chaotic electrokinetic transport: performance of commercial software versus custom-built direct numerical simulation codes. J. Colloid Interface Sci. 446, 67–76.CrossRefGoogle ScholarPubMed
Kim, S.J., Ko, S.H., Kang, K.H. & Han, J. 2010 Direct seawater desalination by ion concentration polarization. Nat. Nanotechnol. 5 (4), 297.CrossRefGoogle ScholarPubMed
Kim, S.J., Wang, Y.-C., Lee, J.H., Jang, H. & Han, J. 2007 Concentration polarization and nonlinear electrokinetic flow near a nanofluidic channel. Phys. Rev. Lett. 99 (4), 044501.CrossRefGoogle Scholar
Kwak, R., Pham, V.S., Lim, K.M. & Han, J. 2013 Shear flow of an electrically charged fluid by ion concentration polarization: scaling laws for electroconvective vortices. Phys. Rev. Lett. 110 (11), 114501.CrossRefGoogle ScholarPubMed
Lacroix, J.C., Atten, P. & Hopfinger, E.J. 1975 Electro-convection in a dielectric liquid layer subjected to unipolar injection. J. Fluid Mech. 69 (3), 539–563.CrossRefGoogle Scholar
Leal, L.G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes, vol. 7. Cambridge University Press.CrossRefGoogle Scholar
Lerman, I., Rubinstein, I. & Zaltzman, B. 2005 Absence of bulk electroconvective instability in concentration polarization. Phys. Rev. E 71 (1), 011506.CrossRefGoogle ScholarPubMed
Li, G., Archer, L.A. & Koch, D.L. 2019 Electroconvection in a viscoelastic electrolyte. Phys. Rev. Lett. 122 (12), 124501.CrossRefGoogle Scholar
Li, G., Townsend, A., Archer, L.A. & Koch, D.L. 2021 Suppression of electroconvective and morphological instabilities by an imposed cross flow of the electrolyte. Phys. Rev. Fluids 6 (3), 033701.CrossRefGoogle Scholar
Lin, H., Storey, B.D., Oddy, M.H., Chen, C.-H. & Santiago, J.G. 2004 Instability of electrokinetic microchannel flows with conductivity gradients. Phys. Fluids 16 (6), 1922–1935.CrossRefGoogle Scholar
Lopez, J., Pei, A., Oh, J.Y., Wang, G.-J.N., Cui, Y. & Bao, Z. 2018 Effects of polymer coatings on electrodeposited lithium metal. J. Am. Chem. Soc. 140 (37), 11735–11744.CrossRefGoogle ScholarPubMed
Mani, A. & Wang, K.M. 2020 Electroconvection near electrochemical interfaces: experiments, modeling, and computation. Annu. Rev. Fluid Mech. 52, 509–529.CrossRefGoogle Scholar
Marcus, R.A. 1956 On the theory of oxidation-reduction reactions involving electron transfer. I. J. Chem. Phys. 24 (5), 966–978.CrossRefGoogle Scholar
Marcus, Y. & Hefter, G. 2004 Standard partial molar volumes of electrolytes and ions in nonaqueous solvents. Chem. Rev. 104 (7), 3405–3452.CrossRefGoogle ScholarPubMed
Milora, C.J., Henrickson, J.F. & Hahn, W.C. 1973 Diffusion coefficients and kinetic parameters in copper sulfate electrolytes and in copper fluoborate electrolytes containing organic addition agents. J. Electrochem. Soc. 120 (4), 488.CrossRefGoogle Scholar
Munichandraiah, N., Scanlon, L.G., Marsh, R.A., Kumar, B. & Sircar, A.K. 1994 Determination of the exchange current density of the ${\rm Li}^++{\rm e}^-\leftrightarrows {\rm Li}$ reaction in polymer electrolytes by galvanostatic linear polarization of symmetrical cells. J. Electroanalyt. Chem. 379 (1-2), 495–499.CrossRefGoogle Scholar
Nielsen, C.P. & Bruus, H. 2015 a Morphological instability during steady electrodeposition at overlimiting currents. Phys. Rev. E 92 (5), 052310.CrossRefGoogle ScholarPubMed
Nielsen, C.P. & Bruus, H. 2015 b Sharp-interface model of electrodeposition and ramified growth. Phys. Rev. E 92 (4), 042302.CrossRefGoogle ScholarPubMed
Oddy, M.H. & Santiago, J.G. 2005 Multiple-species model for electrokinetic instability. Phys. Fluids 17 (6), 064108.CrossRefGoogle Scholar
Olver, S. & Townsend, A. 2013 A fast and well-conditioned spectral method. SIAM Rev. 55 (3), 462–489.CrossRefGoogle Scholar
Pham, S.V., Kwon, H., Kim, B., White, J.K., Lim, G. & Han, J. 2016 Helical vortex formation in three-dimensional electrochemical systems with ion-selective membranes. Phys. Rev. E 93 (3), 033114.CrossRefGoogle ScholarPubMed
Pham, V.S., Li, Z., Lim, K.M., White, J.K. & Han, J. 2012 Direct numerical simulation of electroconvective instability and hysteretic current-voltage response of a permselective membrane. Phys. Rev. E 86 (4), 046310.CrossRefGoogle ScholarPubMed
Pimenta, F. & Alves, M.A. 2018 Numerical simulation of electrically-driven flows using openfoam. arXiv:1802.02843.CrossRefGoogle Scholar
Rubi, J.M. & Kjelstrup, S. 2003 Mesoscopic nonequilibrium thermodynamics gives the same thermodynamic basis to Butler–Volmer and Nernst equations. J. Phys. Chem. B 107 (48), 13471–13477.CrossRefGoogle Scholar
Rubinstein, S.M., Manukyan, G., Staicu, A., Rubinstein, I., Zaltzman, B., Lammertink, R.G.H., Mugele, F. & Wessling, M. 2008 Direct observation of a nonequilibrium electro-osmotic instability. Phys. Rev. Lett. 101 (23), 236101.CrossRefGoogle ScholarPubMed
Rubinstein, I. & Zaltzman, B. 2000 Electro-osmotically induced convection at a permselective membrane. Phys. Rev. E 62 (2), 2238.CrossRefGoogle Scholar
Rubinstein, I. & Zaltzman, B. 2001 Electro-osmotic slip of the second kind and instability in concentration polarization at electrodialysis membranes. Math. Models Meth. Appl. Sci. 11 (02), 263–300.CrossRefGoogle Scholar
Rubinstein, I., Zaltzman, B. & Kedem, O. 1997 Electric fields in and around ion-exchange membranes. J. Membr. Sci. 125 (1), 17–21.CrossRefGoogle Scholar
Rubinstein, I., Zaltzman, B. & Lerman, I. 2005 Electroconvective instability in concentration polarization and nonequilibrium electro-osmotic slip. Phys. Rev. E 72 (1), 011505.CrossRefGoogle ScholarPubMed
Sundström, L. & Bark, F.H. 1995 On morphological instability during electrodeposition with a stagnant binary electrolyte. Electrochim. Acta 40 (5), 599–614.CrossRefGoogle Scholar
Takaki, T. 2014 Phase-field modeling and simulations of dendrite growth. ISIJ Intl 54 (2), 437–444.CrossRefGoogle Scholar
Taylor, G.I. 1966 Studies in electrohydrodynamics. I. The circulation produced in a drop by an electric field. Proc. R. Soc. Lond. 291 (1425), 159–166.Google Scholar
Trau, M., Saville, D.A. & Aksay, I.A. 1997 Assembly of colloidal crystals at electrode interfaces. Langmuir 13 (24), 6375–6381.CrossRefGoogle Scholar
Tu, Y., Chao, X., Sang, J., Huang, S. & Zou, X. 2008 Thin-layer electrodeposition of Zn in the agar gel medium. Phys. A 387 (16-17), 4007–4014.CrossRefGoogle Scholar
de Valença, J.C., Wagterveld, R.M., Lammertink, R.G.H. & Tsai, P.A. 2015 Dynamics of microvortices induced by ion concentration polarization. Phys. Rev. E 92 (3), 031003.CrossRefGoogle ScholarPubMed
Wang, C., Bao, J., Pan, W. & Sun, X. 2017 Modeling electrokinetics in ionic liquids. Electrophoresis 38 (13-14), 1693–1705.CrossRefGoogle ScholarPubMed
Wei, S., Cheng, Z., Nath, P., Tikekar, M.D., Li, G. & Archer, L.A. 2018 Stabilizing electrochemical interfaces in viscoelastic liquid electrolytes. Sci. Adv. 4 (3), eaao6243.CrossRefGoogle ScholarPubMed
Williams, F.A. 1971 Theory of combustion in laminar flows. Annu. Rev. Fluid Mech. 3 (1), 171–188.CrossRefGoogle Scholar
Yariv, E. 2009 Asymptotic current-voltage relations for currents exceeding the diffusion limit. Phys. Rev. E 80 (5), 051201.CrossRefGoogle ScholarPubMed
Yossifon, G. & Chang, H.-C. 2008 Selection of nonequilibrium overlimiting currents: universal depletion layer formation dynamics and vortex instability. Phys. Rev. Lett. 101 (25), 254501.CrossRefGoogle ScholarPubMed
Zaltzman, B. & Rubinstein, I. 2007 Electro-osmotic slip and electroconvective instability. J. Fluid Mech. 579, 173–226.CrossRefGoogle Scholar
Zhang, D., Warren, A.J., Li, G., Cheng, Z., Han, X., Zhao, Q., Liu, X., Deng, Y. & Archer, L.A. 2020 Electrodeposition of zinc in aqueous electrolytes containing high molecular weight polymers. Macromolecules 53 (7), 2694–2701.CrossRefGoogle Scholar
Zholkovskij, E.K., Vorotyntsev, M.A. & Staude, E. 1996 Electrokinetic instability of solution in a plane-parallel electrochemical cell. J. Colloid Interface Sci. 181 (1), 28–33.CrossRefGoogle Scholar

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
Download Li et al. supplementary movie 5(Video)
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