Modeling Electrochemical Migration and Growth of Isolated Metal Particles

Abstract

Electrokinetic phenomena within complex structures are relevant in microfluidics. For example, ion concentration polarization is used for electrokinetic trapping for enhanced biosensing using molecular probes 1 . Concentration polarization near ion-selective membranes also plays an important role in separation systems for desalination 2 . Aside from microfluidics, electrochemical growth-dissolution phenomenon has been reported in lithium ion battery systems where lithium plating and subsequent growth of dendrites can exacerbate the loss of cyclable lithium through the formation of isolated Lithium (i-Li) islands 3 . Initially thought to be “dead”, these islands were shown to migrate from one electrode to the other through a deposition-dissolution mechanism 3 . We present a mathematical solution for the growth and migration of an electrochemically active metal particle in a background current. A broad range of phenomena such as viscous fingering 4 , diffusion-limited aggregation 4 and electrochemical deposition 5 follow Laplacian growth and have been traditionally described using conformal map-dynamics in two dimensions. Some non-Laplacian phenomena like electrochemical transport 6,7 and advection-diffusion-limited aggregation 6 fall into the conformally invariant category 8 and can still be simplified using conformal-mapping techniques. Our solution applies conformal mapping to the non-Laplacian growth of the metal particle to evaluate the role of particle morphology in the evolution of the phase boundary. In addition to migration, dissolution-deposition was found to lead to formation of cusps on the phase boundary under certain conditions. The solution is applicable for a general class of problems with a reactive post or particle in an applied background flux. Analytical solutions such as the one presented here are expected to augment numerical simulations and lead to expressions that capture conditions for the onset of morphological instabilities. References S. Park, B. Sabbagh, R. Abu-Rjal, and G. Yossifon, Lab Chip , 22 , 814–825 (2022) https://pubs.rsc.org/en/content/articlehtml/2022/lc/d1lc00864a. D. Deng et al., Desalination , 357 , 77–83 (2015). F. Liu et al., Nature 2021 600:7890 , 600 , 659–663 (2021) https://www.nature.com/articles/s41586-021-04168-w. J. Mathiesen, I. Procaccia, H. L. Swinney, and M. Thrasher, Europhys Lett , 76 , 257 (2006) https://iopscience.iop.org/article/10.1209/epl/i2006-10246-x. D. A. Kessler, J. Koplik, and H. Levine, http://dx.doi.org/10.1080/00018738800101379 , 37 , 255–339 (2006) https://www.tandfonline.com/doi/abs/10.1080/00018738800101379. M. Z. Bazant, J. Choi, and B. Davidovitch, Phys Rev Lett , 91 , 045503 (2003) https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.91.045503. Z. Gu et al., Phys Rev Fluids , 7 , 033701 (2022) https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.033701. M. Z. Bazant, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences , 460 , 1433–1452 (2004) https://royalsocietypublishing.org/doi/10.1098/rspa.2003.1218.