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Surface tension effects on the motion of a free-falling liquid sheet
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10.1063/1.4810751
/content/aip/journal/pof2/25/6/10.1063/1.4810751
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4810751
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the geometrical configuration of the sheet.

Image of FIG. 2.
FIG. 2.

Values of (0) as a function of the guess value () for various We numbers. ɛ = 1, = 20.

Image of FIG. 3.
FIG. 3.

Convergence history for ɛ = 0.25, We = 0.5. Continuous lines (red) refer to boundary conditions of Eq. (48) , dashed lines refer to ′() = ″() = 0.

Image of FIG. 4.
FIG. 4.

Normalized derivative of thickness (a), and normalized pressure (b), at = 0 for different locations at which the free-fall boundary condition is applied for ɛ = 0.25. We = 0.1 (solid line), We = 0.5 (dashed-dotted line), We = 1 (dashed line).

Image of FIG. 5.
FIG. 5.

Sheet profile (a) and axis pressure distribution (b) for ɛ = 0.25 and We = 0.1, 0.5, 1, 1.5, 2. Dashed line (red) is the free-fall solution.

Image of FIG. 6.
FIG. 6.

Sheet profile (a) and axis pressure distribution (b) for We = 1 and ɛ = 0.05, 0.1, 0.2, 0.3, 0.4. Dashed line (red) is the free-fall solution. In the inset, the sheet shape is reported as a function of the scaled streamwise distance /ɛ.

Image of FIG. 7.
FIG. 7.

Variation with We of pressure (a) and d /d (b) at inlet location = 0 for ɛ = 0.05, 0.1, 0.2, 0.3, 0.4. Dashed line (red) is the free-fall solution.

Image of FIG. 8.
FIG. 8.

Variation with ɛ of pressure (a) and d /d (b) at = 0 for We = 0.05, 0.2, 0.4, 0.6, 0.8, 1. Dashed line (red) is the free-fall solution.

Image of FIG. 9.
FIG. 9.

Variation with We of inlet liquid pressure for ɛ = 0.0625 (a) and ɛ = 0.25 (b). Continuous thick line is the numerical solution, continuous thin line (red) corresponds to the zeroth order asymptotic solution for , dashed-dotted line corresponds to the first order asymptotic solution for .

Image of FIG. 10.
FIG. 10.

Variation with ɛ of inlet liquid pressure for We = 0.1 (a) and We = 0.5 (b). Continuous thick line is the numerical solution, continuous thin line (red) corresponds to the zeroth order asymptotic solution for , dashed-dotted line corresponds to the first order asymptotic solution for . The dashed line (barely distinguishable from the thin continuous line) is the pressure calculated with the formula (43) of Sec. III A .

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/content/aip/journal/pof2/25/6/10.1063/1.4810751
2013-06-21
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Surface tension effects on the motion of a free-falling liquid sheet
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4810751
10.1063/1.4810751
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