Virginia TechAfkhami, ShahriarRenardy, Yuriko Y.2013-12-042013-12-042013-08Shahriar 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/10.1063/1.48173741070-6631http://hdl.handle.net/10919/24386We 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-USIn CopyrightSurface-tensionStabilitySimulationsGenerationsEmulsionsTrackingArticle - Refereedhttp://scitation.aip.org/content/aip/journal/pof2/25/8/10.1063/1.4817374https://doi.org/10.1063/1.4817374