Handle URI:
http://hdl.handle.net/10754/598124
Title:
Elastic fingering in rotating Hele-Shaw flows
Authors:
Carvalho, Gabriel D.; Gadêlha, Hermes; Miranda, José A.
Abstract:
The 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.
Citation:
Carvalho 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.
Publisher:
American Physical Society (APS)
Journal:
Physical Review E
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
21-May-2014
DOI:
10.1103/PhysRevE.89.053019
PubMed ID:
25353892
Type:
Article
ISSN:
1539-3755; 1550-2376
Sponsors:
J.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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorCarvalho, Gabriel D.en
dc.contributor.authorGadêlha, Hermesen
dc.contributor.authorMiranda, José A.en
dc.date.accessioned2016-02-25T13:13:07Zen
dc.date.available2016-02-25T13:13:07Zen
dc.date.issued2014-05-21en
dc.identifier.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.en
dc.identifier.issn1539-3755en
dc.identifier.issn1550-2376en
dc.identifier.pmid25353892en
dc.identifier.doi10.1103/PhysRevE.89.053019en
dc.identifier.urihttp://hdl.handle.net/10754/598124en
dc.description.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.en
dc.description.sponsorshipJ.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.en
dc.publisherAmerican Physical Society (APS)en
dc.titleElastic fingering in rotating Hele-Shaw flowsen
dc.typeArticleen
dc.identifier.journalPhysical Review Een
dc.contributor.institutionUniversidade Federal de Pernambuco, Recife, Brazilen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en

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