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A new prediction of wavelength selection in radial viscous fingering involving normal and tangential stresses
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10.1063/1.4849495
/content/aip/journal/pof2/25/12/10.1063/1.4849495
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/12/10.1063/1.4849495
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch of a Hele-Shaw cell with an inviscid liquid, injected amid a viscous liquid. A close-up shows schematically the isocontours of the pressure field.

Image of FIG. 2.
FIG. 2.

Flowfields for perturbation of wavenumber = 8 and amplitude 0.05 for the Brinkman model and viscous potential flow, at , η = 1/2, and = 1. Tangential velocities vary continuously only for the Brinkman solution. The interface is represented as a grey line.

Image of FIG. 3.
FIG. 3.

Dispersion relations using different models: ( − · − ) potential flow, (- - -) viscous potential flow, and (—) Brinkman model. The aspect ratio is fixed to = 200, while the capillary number changes between , and 1.

Image of FIG. 4.
FIG. 4.

Most unstable modified wavenumber plotted against logarithm of capillary number. Plotted results are: (− · −) potential flow, (- - -) VPF, and (—) Brinkman model with aspect ratio = 200. Maxworthy's experimental results are also shown, indicated by ○ symbols. The grey shaded region includes all wavenumbers of the Brinkman model, where the growth rate is within 1% of the maximal growth rate.

Image of FIG. 5.
FIG. 5.

Most unstable finger number as a function of capillary number: (− · −) potential flow, (- - -) viscous potential flow, and (—) Brinkman model. Dotted lines show the experimental result of Maxworthy 7 for low surface tension and the theoretical result of Logvinov 16 who used the Brinkman model for zero surface tension fingering of a flat interface with aspect ratio = 200. For higher capillary number the number of fingers becomes inversely proportional to the gap width.

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/content/aip/journal/pof2/25/12/10.1063/1.4849495
2013-12-20
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A new prediction of wavelength selection in radial viscous fingering involving normal and tangential stresses
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/12/10.1063/1.4849495
10.1063/1.4849495
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