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Application of Floquet theory to the stability of liquid films on structured surfaces
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10.1063/1.4834376
/content/aip/journal/pof2/25/12/10.1063/1.4834376
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/12/10.1063/1.4834376
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch of a liquid film in contact with a surface structured by periodic array of gas-filled grooves. Dimensional Cartesian coordinates * and * are shown. The plot below the sketch illustrates the periodic function β*(*) used to model slip length variation due to the presence of the grooves.

Image of FIG. 2.
FIG. 2.

Perturbation growth rate plotted versus the wavenumber based on Floquet theory for , β = 0.3 (solid line). The solution for the substrate without grooves (β = 0) is also shown by the dashed line for comparison.

Image of FIG. 3.
FIG. 3.

The maximum perturbation growth rate as a function of β for different geometric parameters of the structuring: δ = 0.5 (solid line), δ = 0.4 (dashed line), and δ = 0.3 (dotted-dashed line); for all three cases.

Image of FIG. 4.
FIG. 4.

A dispersion curve with a discontinuity obtained for β = 0.3, δ = 0.5, (top); the maximum growth rate as a function of the scaled slip length for δ = 0.5, (bottom).

Image of FIG. 5.
FIG. 5.

Comparison of the dispersion curves obtained from Floquet theory (solid line) and the discretized eigenvalue problem approach (filled squares) for β = 0.3, δ = 0.5, .

Image of FIG. 6.
FIG. 6.

Comparison of the dispersion curves obtained from the stability analysis of the full Stokes flow model of Sec. IV (filled triangles) and the lubrication-type approach of Sec. III (solid line) for β = 1, δ = 0.5, = 10, and different values of ɛ: ɛ = 0.05 (top) and ɛ = 0.3 (bottom).

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/content/aip/journal/pof2/25/12/10.1063/1.4834376
2013-12-13
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Application of Floquet theory to the stability of liquid films on structured surfaces
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/12/10.1063/1.4834376
10.1063/1.4834376
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