A volume-of-fluid formulation for the study of co-flowing fluids governed by the Hele-Shaw equations

Simple item page
dc.contributorVirginia Techen
dc.contributor.authorAfkhami, Shahriaren
dc.contributor.authorRenardy, Yuriko Y.en
dc.contributor.departmentMathematicsen
dc.date.accessed2013-11-20en
dc.date.accessioned2013-12-04T14:59:20Zen
dc.date.available2013-12-04T14:59:20Zen
dc.date.issued2013-08en
dc.description.abstractWe present a computational framework to address the flow of two immiscible viscous liquids which co-flow into a shallow rectangular container at one side, and flow out into a holding container at the opposite side. Assumptions based on the shallow depth of the domain are used to reduce the governing equations to one of Hele-Shaw type. The distinctive feature of the numerical method is the accurate modeling of the capillary effects. A continuum approach coupled with a volume-of-fluid formulation for computing the interface motion and for modeling the interfacial tension in Hele-Shaw flows is formulated and implemented. The interface is reconstructed with a height-function algorithm. The combination of these algorithms is a novel development for the investigation of Hele-Shaw flows. The order of accuracy and convergence properties of the method are discussed with benchmark simulations. A microfluidic flow of a ribbon of fluid which co-flows with a second liquid is simulated. We show that for small capillary numbers of O(0.01), there is an abrupt change in interface curvature and focusing occurs close to the exit.en
dc.description.sponsorshipNSF-DMS 0907788en
dc.description.sponsorshipNSF-DMS-1311707en
dc.identifier.citationShahriar Afkhami and Yuriko Renardy., “A volume-of-fluid formulation for the study of co-flowing fluids governed by the Hele-Shaw equations,” Phys. Fluids (1994-present), 25, 082001 (2013); DOI:http//dx.doi.org/10.1063/1.4817374en
dc.identifier.doihttps://doi.org/10.1063/1.4817374en
dc.identifier.issn1070-6631en
dc.identifier.urihttp://hdl.handle.net/10919/24386en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/pof2/25/8/10.1063/1.4817374en
dc.language.isoen_USen
dc.publisherAmerican Institute of Physicsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectSurface-tensionen
dc.subjectStabilityen
dc.subjectSimulationsen
dc.subjectGenerationsen
dc.subjectEmulsionsen
dc.subjectTrackingen
dc.titleA volume-of-fluid formulation for the study of co-flowing fluids governed by the Hele-Shaw equationsen
dc.title.serialPhysics of Fluidsen
dc.typeArticle - Refereeden

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
1.4817374.pdf
Size:
1.78 MB
Format:
Adobe Portable Document Format
Description:
Main article
Download

Collections

Scholarly Works, Mathematics