KAUST Grant NumberKUK-C1-013-04
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AbstractThe centrifugally driven viscous fingering problem arises when two immiscible fluids of different densities flow in a rotating Hele-Shaw cell. In this conventional setting an interplay between capillary and centrifugal forces makes the fluid-fluid interface unstable, leading to the formation of fingered structures that compete dynamically and reach different lengths. In this context, it is known that finger competition is very sensitive to changes in the viscosity contrast between the fluids. We study a variant of such a rotating flow problem where the fluids react and produce a gellike phase at their separating boundary. This interface is assumed to be elastic, presenting a curvature-dependent bending rigidity. A perturbative weakly nonlinear approach is used to investigate how the elastic nature of the interface affects finger competition events. Our results unveil a very different dynamic scenario, in which finger length variability is not regulated by the viscosity contrast, but rather determined by two controlling quantities: a characteristic radius and a rigidity fraction parameter. By properly tuning these quantities one can describe a whole range of finger competition behaviors even if the viscosity contrast is kept unchanged. © 2014 American Physical Society.
CitationCarvalho GD, Gadêlha H, Miranda JA (2014) Elastic fingering in rotating Hele-Shaw flows. Phys Rev E 89. Available: http://dx.doi.org/10.1103/PhysRevE.89.053019.
SponsorsJ.A.M. and G.D.C. thank CNPq for financial support through the program “Instituto Nacional de Ciência e Tecnologia de Fluidos Complexos (INCT-FCx),” and FACEPE through PRONEM project No. APQ-1415-1.05/10. H.G. acknowledges support from an Oxford University Hooke Fellowship and is supported by Award KUK-C1-013-04 from King Abdullah University of Science and Technology.
PublisherAmerican Physical Society (APS)
JournalPhysical Review E
CollectionsPublications Acknowledging KAUST Support
- Stationary patterns in centrifugally driven interfacial elastic fingering.
- Authors: Carvalho GD, Gadêlha H, Miranda JA
- Issue date: 2014 Dec
- Viscosity contrast effects on fingering formation in rotating Hele-Shaw flows.
- Authors: Miranda JA, Alvarez-Lacalle E
- Issue date: 2005 Aug
- Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study.
- Authors: Carvalho GD, Miranda JA, Gadêlha H
- Issue date: 2013 Nov
- Pattern formation and interface pinch-off in rotating Hele-Shaw flows: a phase-field approach.
- Authors: Folch R, Alvarez-Lacalle E, Ortín J, Casademunt J
- Issue date: 2009 Nov
- Elastic fingering patterns in confined lifting flows.
- Authors: Fontana JV, Miranda JA
- Issue date: 2016 Sep