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

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    Type
    Article
    Authors
    Carvalho, Gabriel D.
    Miranda, José A.
    Gadêlha, Hermes
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2013-11-11
    Permanent link to this record
    http://hdl.handle.net/10754/598654
    
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    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.
    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.
    Publisher
    American Physical Society (APS)
    Journal
    Physical Review E
    DOI
    10.1103/PhysRevE.88.053006
    PubMed ID
    24329350
    ae974a485f413a2113503eed53cd6c53
    10.1103/PhysRevE.88.053006
    Scopus Count
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