{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T17:56:31Z","timestamp":1760550991498,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,11,20]],"date-time":"2019-11-20T00:00:00Z","timestamp":1574208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2013\/07375-0"],"award-info":[{"award-number":["2013\/07375-0"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["307483\/2017-7"],"award-info":[{"award-number":["307483\/2017-7"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/EMS\/00532\/2019","PTDC\/EMS-ENE\/3362\/2014"],"award-info":[{"award-number":["UID\/EMS\/00532\/2019","PTDC\/EMS-ENE\/3362\/2014"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Universidade Federal da Grande Dourados","award":["EDITAL PROPP No 14"],"award-info":[{"award-number":["EDITAL PROPP No 14"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>The phenomenon of electro-osmosis was studied by performing numerical simulations on the flow between parallel walls and at the nozzle microchannels. In this work, we propose a numerical approximation to perform simulations of vortex formation which occur after the passage of the fluid through an abrupt contraction at the microchannel. The motion of the charges in the solution is described by the Poisson\u2013Nernst\u2013Planck equations and used the generalized finite differences to solve the numerical problem. First, solutions for electro-osmotic flow were obtained for the Phan\u2013Thien\/Thanner model in a parallel walls channel. Later simulations for electro-osmotic flow were performed in a nozzle. The formation of vortices near the contraction within the nozzle was verified by taking into account a flow perturbation model.<\/jats:p>","DOI":"10.3390\/mi10120796","type":"journal-article","created":{"date-parts":[[2019,11,20]],"date-time":"2019-11-20T11:06:03Z","timestamp":1574247963000},"page":"796","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Numerical Study of Electro-Osmotic Fluid Flow and Vortex Formation"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2801-5437","authenticated-orcid":false,"given":"Wesley De Souza","family":"Bezerra","sequence":"first","affiliation":[{"name":"Faculdade de Ci\u00eancias Exatas e Tecnologia, FACET, Universidade Federal da Grande Dourados, Cidade Universitaria-Rodovia Dourados-Itahum, Km 12, Dourados 79804-970, Brasil"}]},{"given":"Antonio","family":"Castelo","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada e Estat\u00edstica, ICMC, Universidade de S\u00e3o Paulo, Av. Trabalhador S\u00e3o-carlense, 400, S\u00e3o Carlos 13566-590, Brasil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2825-0709","authenticated-orcid":false,"given":"Alexandre M.","family":"Afonso","sequence":"additional","affiliation":[{"name":"Faculdade de Engenharia da Universidade do Porto, Departamento de Engenharia Mec\u00e2nica, Centro de Estudos de Fen\u00f3menos de Transporte (CEFT), 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1002\/elps.200390029","article-title":"Microchannel wall coatings for protein separations by capillary and chip electrophoresis","volume":"24","author":"Doherty","year":"2003","journal-title":"Electrophoresis"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4491","DOI":"10.1021\/ac010423z","article-title":"An integrated fluorescence detection system in poly (dimethylsiloxane) for microfluidic applications","volume":"73","author":"Chabinyc","year":"2001","journal-title":"Anal. 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