{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:47:22Z","timestamp":1760150842249,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T00:00:00Z","timestamp":1643328000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009117","name":"Chemnitz University of Technology","doi-asserted-by":"publisher","award":["ID 88-2021"],"award-info":[{"award-number":["ID 88-2021"]}],"id":[{"id":"10.13039\/100009117","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The limiting current density is one of to the most important indicators in electroplating for the maximal current density from which a metal can be deposited effectively from an electrolyte. Hence, it is an indicator of the maximal deposition speed and the homogeneity of the thickness of the deposited metal layer. For these reasons, a major interest in the limiting current density is given in practical applications. Usually, the limiting current density is determined via measurements. In this article, a simple model to compute the limiting current density is presented, basing on a system of diffusion\u2013reaction equations in one spatial dimension. Although the model formulations need many assumptions, it is of special interest for screenings, as well as for comparative work, and could easily be adjusted to measurements.<\/jats:p>","DOI":"10.3390\/axioms11020053","type":"journal-article","created":{"date-parts":[[2022,1,29]],"date-time":"2022-01-29T01:41:59Z","timestamp":1643420519000},"page":"53","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Mathematical Modeling of the Limiting Current Density from Diffusion-Reaction Systems"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9229-8793","authenticated-orcid":false,"given":"Stephan Daniel","family":"Schwoebel","sequence":"first","affiliation":[{"name":"Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany"}]},{"given":"Markus","family":"Mueller","sequence":"additional","affiliation":[{"name":"Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1554-170X","authenticated-orcid":false,"given":"Thomas","family":"Mehner","sequence":"additional","affiliation":[{"name":"Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2390-9159","authenticated-orcid":false,"given":"Thomas","family":"Lampke","sequence":"additional","affiliation":[{"name":"Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,28]]},"reference":[{"key":"ref_1","unstructured":"Bard, A.J., and Faulkner, L.R. 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