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Hydrodynamic Entrance Length for Laminar Flow in Microchannels with Rectangular Cross Section

dc.contributor.authorGermán Ferreira
dc.contributor.authorArtur Sucena
dc.contributor.authorLuís L. Ferrás
dc.contributor.authorFernando T. Pinho
dc.contributor.authorAlexandre M. Afonso
dc.contributor.otherAIMEN—Northwest Association of Metallurgical Research, C/. Polígono Industrial de Cataboi SUR-PPI-2 (Sector 2) Parcela 3, O Porriño, 36418 Pontevedra, Spain
dc.contributor.otherCentro de Estudos de Fenómenos de Transporte, Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal
dc.contributor.otherCentro de Matemática, Departamento de Matemática da Universidade do Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
dc.contributor.otherCentro de Estudos de Fenómenos de Transporte, Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal
dc.contributor.otherCentro de Estudos de Fenómenos de Transporte, Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal
dc.date.accessioned2021-07-23T14:40:01Z
dc.date.available2025-10-02T04:56:03Z
dc.date.issued01-07-2021
dc.identifier.issn-
dc.identifier.urihttps://www.mdpi.com/2311-5521/6/7/240
dc.description.abstractThis work presents a detailed numerical investigation on the required development length (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">L</mi><mo>=</mo><mi>L</mi><mo>/</mo><mi>B</mi></mrow></semantics></math></inline-formula>) in laminar Newtonian fluid flow in microchannels with rectangular cross section and different aspect ratios (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>R</mi></mrow></semantics></math></inline-formula>). The advent of new microfluidic technologies shifted the practical Reynolds numbers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula>) to the range of unitary (and even lower) orders of magnitude, i.e., creeping flow conditions. Therefore, accurate estimations of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">L</mi></semantics></math></inline-formula> at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo>≤</mo><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> are important for microsystem design. At such low Reynolds numbers, in which inertial forces are less dominant than viscous forces, flow characteristics become necessarily different from those at the macroscale where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> is typically much larger. A judicious choice of mesh refinement and adequate numerical methods allowed obtaining accurate results and a general correlation for estimating <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">L</mi></semantics></math></inline-formula>, valid in the ranges <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>R</mi><mi>e</mi><mo>≤</mo><mn>2000</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.1</mn><mo>≤</mo><mi>A</mi><mi>R</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>, thus covering applications in both macro and microfluidics.
dc.format-
dc.language.isoEN
dc.publisherMDPI AG
dc.relation.uri['https://lipidworld.biomedcentral.com/submission-guidelines', 'https://lipidworld.biomedcentral.com/', 'https://lipidworld.biomedcentral.com/about', 'https://www.springernature.com/gp/open-research/policies/journal-policies/apc-waiver-countries']
dc.rights['CC BY', 'CC BY-NC-ND']
dc.subject['lipid biochemistry', 'lipid synthesis', 'pharmacology', 'toxicology', 'lipid metabolism', 'Nutritional diseases. Deficiency diseases', 'RC620-627']
dc.subject.lccThermodynamics
dc.titleHydrodynamic Entrance Length for Laminar Flow in Microchannels with Rectangular Cross Section
dc.typeArticle
dc.description.keywordsdevelopment length
dc.description.keywords3D microchannels
dc.description.keywordsnewtonian fluid
dc.description.keywordseffects of Reynolds number and aspect ratio
dc.description.keywordsnumerical methods
dc.description.keywordsfinite volume method
dc.description.pages-
dc.description.doi10.3390/fluids6070240
dc.title.journalFluids
dc.identifier.e-issn2311-5521
dc.identifier.oaioai:doaj.org/journal:546bcb42d9d34966bcb35d8062a2e4a5
dc.journal.infoVolume 6, Issue 7


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