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From the same journal

Development of tip-splitting and side-branching patterns in elastic fingering

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Development of tip-splitting and side-branching patterns in elastic fingering. / Fontana, João V.; Gadelha, Hermes; Miranda, José A.

In: Physical Review E, Vol. 93, No. 3, 033126, 28.03.2016.

Research output: Contribution to journalArticlepeer-review

Harvard

Fontana, JV, Gadelha, H & Miranda, JA 2016, 'Development of tip-splitting and side-branching patterns in elastic fingering', Physical Review E, vol. 93, no. 3, 033126. https://doi.org/10.1103/PhysRevE.93.033126

APA

Fontana, J. V., Gadelha, H., & Miranda, J. A. (2016). Development of tip-splitting and side-branching patterns in elastic fingering. Physical Review E, 93(3), [033126]. https://doi.org/10.1103/PhysRevE.93.033126

Vancouver

Fontana JV, Gadelha H, Miranda JA. Development of tip-splitting and side-branching patterns in elastic fingering. Physical Review E. 2016 Mar 28;93(3). 033126. https://doi.org/10.1103/PhysRevE.93.033126

Author

Fontana, João V. ; Gadelha, Hermes ; Miranda, José A. / Development of tip-splitting and side-branching patterns in elastic fingering. In: Physical Review E. 2016 ; Vol. 93, No. 3.

Bibtex - Download

@article{1d7cf593836e4a08962825facc5640c5,
title = "Development of tip-splitting and side-branching patterns in elastic fingering",
abstract = "Elastic fingering supplements the already interesting features of the traditional viscous fingering phenomena in Hele-Shaw cells with the consideration that the two-fluid separating boundary behaves like an elastic membrane. Sophisticated numerical simulations have shown that under maximum viscosity contrast the resulting patterned shapes can exhibit either finger tip-splitting or side-branching events. In this work, we employ a perturbative mode-coupling scheme to get important insights into the onset of these pattern formation processes. This is done at lowest nonlinear order and by considering the interplay of just three specific Fourier modes: a fundamental mode n and its harmonics 2n and 3n. Our approach further allows the construction of a morphology diagram for the system in a wide range of the parameter space without requiring expensive numerical simulations. The emerging interfacial patterns are conveniently described in terms of only two dimensionless controlling quantities: the rigidity fraction C and a parameter Γ that measures the relative strength between elastic and viscous effects. Visualization of the rigidity field for the various pattern-forming structures supports the idea of an elastic weakening mechanism that facilitates finger growth in regions of reduced interfacial bending rigidity.",
author = "Fontana, {Jo{\~a}o V.} and Hermes Gadelha and Miranda, {Jos{\'e} A.}",
note = "{\textcopyright}2016 American Physical Society. This is an author-produced version of the published paper. Uploaded in accordance with the publisher{\textquoteright}s self-archiving policy. Further copying may not be permitted; contact the publisher for details",
year = "2016",
month = mar,
day = "28",
doi = "10.1103/PhysRevE.93.033126",
language = "English",
volume = "93",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "3",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Development of tip-splitting and side-branching patterns in elastic fingering

AU - Fontana, João V.

AU - Gadelha, Hermes

AU - Miranda, José A.

N1 - ©2016 American Physical Society. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

PY - 2016/3/28

Y1 - 2016/3/28

N2 - Elastic fingering supplements the already interesting features of the traditional viscous fingering phenomena in Hele-Shaw cells with the consideration that the two-fluid separating boundary behaves like an elastic membrane. Sophisticated numerical simulations have shown that under maximum viscosity contrast the resulting patterned shapes can exhibit either finger tip-splitting or side-branching events. In this work, we employ a perturbative mode-coupling scheme to get important insights into the onset of these pattern formation processes. This is done at lowest nonlinear order and by considering the interplay of just three specific Fourier modes: a fundamental mode n and its harmonics 2n and 3n. Our approach further allows the construction of a morphology diagram for the system in a wide range of the parameter space without requiring expensive numerical simulations. The emerging interfacial patterns are conveniently described in terms of only two dimensionless controlling quantities: the rigidity fraction C and a parameter Γ that measures the relative strength between elastic and viscous effects. Visualization of the rigidity field for the various pattern-forming structures supports the idea of an elastic weakening mechanism that facilitates finger growth in regions of reduced interfacial bending rigidity.

AB - Elastic fingering supplements the already interesting features of the traditional viscous fingering phenomena in Hele-Shaw cells with the consideration that the two-fluid separating boundary behaves like an elastic membrane. Sophisticated numerical simulations have shown that under maximum viscosity contrast the resulting patterned shapes can exhibit either finger tip-splitting or side-branching events. In this work, we employ a perturbative mode-coupling scheme to get important insights into the onset of these pattern formation processes. This is done at lowest nonlinear order and by considering the interplay of just three specific Fourier modes: a fundamental mode n and its harmonics 2n and 3n. Our approach further allows the construction of a morphology diagram for the system in a wide range of the parameter space without requiring expensive numerical simulations. The emerging interfacial patterns are conveniently described in terms of only two dimensionless controlling quantities: the rigidity fraction C and a parameter Γ that measures the relative strength between elastic and viscous effects. Visualization of the rigidity field for the various pattern-forming structures supports the idea of an elastic weakening mechanism that facilitates finger growth in regions of reduced interfacial bending rigidity.

UR - http://www.scopus.com/inward/record.url?scp=84963542729&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.93.033126

DO - 10.1103/PhysRevE.93.033126

M3 - Article

AN - SCOPUS:84963542729

VL - 93

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 3

M1 - 033126

ER -