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Model. and Simul. in Eng. Sci."],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Electroplated coatings, i.e. coatings formed by electrodepositons, play an important role in tribological and corrosion protection. Within the theory diffusion boundary layer models play an important part in investigations on electrodeposition. For direct current approaches, the model is applied and investigated directly in depth with great success. For pulse plating, uses exact solutions to Fick\u2019s second law for certain pulse-forms or is more indirect and relies on identification with a direct-current model the modeling approach. The identification is then used to deduce from direct current to pulse plating, or uses relations from exact solutions to compute the limiting current density for pulse plating from the limiting current density for direct current. The article investigates if the used identification scheme, by averaging, holds true in general and finds that it does not hold true for high current distributions due to the identification of a physical model for direct current with an unphysical model for pulse plating. Motivated by this situation in the article models and their numerical treatment are derived, which grant physicality of the models and the limiting current distribution, independent from the pulse-form. Additionally, in the article a methodology to compute the maximal applicable current density for pulse plating is derived, in form of approximately solving an optimal control problem, without relying on the identification with direct current and exact solutions for the given pulse-form. Besides theoretical results, the article develops an easy to implement numerical methodology to simulate the models alongside the theoretical results.<\/jats:p>","DOI":"10.1186\/s40323-025-00309-2","type":"journal-article","created":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T15:03:30Z","timestamp":1757343810000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Theoretical investigations and methodology for modeling and direct simulation of electrochemical pulse plating in the diffusion boundary layer"],"prefix":"10.1186","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9229-8793","authenticated-orcid":false,"given":"Stephan D.","family":"Schw\u00f6bel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Mehner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Lampke","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,9,8]]},"reference":[{"key":"309_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-3115-2","volume-title":"Galvanotechnik","author":"J Billiter","year":"1957","unstructured":"Billiter J. 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