The classical models for electric double layer can be improved by using molecular dynamics and including different physical effects such as Brownian motion, dipole-dipole interaction, ion-dipole interaction. In this paper the Brownian motion is included in the classical model. It changes the ion concentration near charged metal (Titani-um) surface which leads to change in local net charge in the electrolyte, relative permittivity and potential.
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Syed, A. Z., Rienen, U. van, & Elter, P. (2013). Effects of Brownian Motion on Electrical Double Layer. Biomedical Engineering / Biomedizinische Technik. https://doi.org/10.1515/bmt-2013-4348