Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study

Handle URI:
http://hdl.handle.net/10754/598654
Title:
Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study
Authors:
Carvalho, Gabriel D.; Miranda, José A.; Gadêlha, Hermes
Abstract:
We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. © 2013 American Physical Society.
Citation:
Carvalho GD, Miranda JA, Gadêlha H (2013) Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study. Phys Rev E 88. Available: http://dx.doi.org/10.1103/PhysRevE.88.053006.
Publisher:
American Physical Society (APS)
Journal:
Physical Review E
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
11-Nov-2013
DOI:
10.1103/PhysRevE.88.053006
PubMed ID:
24329350
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 through 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.authorMiranda, José A.en
dc.contributor.authorGadêlha, Hermesen
dc.date.accessioned2016-02-25T13:33:52Zen
dc.date.available2016-02-25T13:33:52Zen
dc.date.issued2013-11-11en
dc.identifier.citationCarvalho GD, Miranda JA, Gadêlha H (2013) Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study. Phys Rev E 88. Available: http://dx.doi.org/10.1103/PhysRevE.88.053006.en
dc.identifier.issn1539-3755en
dc.identifier.issn1550-2376en
dc.identifier.pmid24329350en
dc.identifier.doi10.1103/PhysRevE.88.053006en
dc.identifier.urihttp://hdl.handle.net/10754/598654en
dc.description.abstractWe study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. © 2013 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 through 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.titleInterfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear studyen
dc.typeArticleen
dc.identifier.journalPhysical Review Een
dc.contributor.institutionUniversidade Federal de Pernambuco, Recife, Brazilen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
kaust.grant.numberKUK-C1-013-04en

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