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Longitudinal instability of a liquid rim
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View: Figures


Image of FIG. 1.
FIG. 1.

Spatial configuration of the rim.

Image of FIG. 2.
FIG. 2.

Growth rate increment in function of the wavenumber in four different cases (a)–(d). The growth rate increases when the thickness of the sheet decreases and when the acceleration term is negative.

Image of FIG. 3.
FIG. 3.

Comparison between the “frozen” rim solution and Roisman linear theory (2006) for = 0.2 and . “frozen” rim (without r.r.e.): suppressing the “rim radius evolution (denoted by r.r.e.) in the “frozen” rim theory. The vertical line delimits the domain of validity of the linear theory (valid only for ).

Image of FIG. 4.
FIG. 4.

Time evolution of instability solving the full nonlinear system of Eq. (3) for which the rim radius is time dependent for different aspect ratio and initial acceleration . The linear-log scale shows that the exponential growth is valid only for few time units (a) and (b).

Image of FIG. 5.
FIG. 5.

Initial configuration of the rim and initial mesh. The mesh is refined around the neck wherever the curvature of the interface is large.

Image of FIG. 6.
FIG. 6.

Velocity profile in the median plane inside the liquid sheet when the steady state is reached. Here, the fit corresponds to: , where is the vertical coordinate of the neck, defined as the position of the minimum film thickness.

Image of FIG. 7.
FIG. 7.

Comparison of the time evolution of the amplitude of the perturbation and “frozen” rim theory for two different wavenumbers (a) and (b).

Image of FIG. 8.
FIG. 8.

Comparison between the present theory, the viscous theory, and the results of the full numerical simulation. The vertical line delimits the domain of validity of the linear theory (valid only for ).

Image of FIG. 9.
FIG. 9.

Liquid finger formation and rim breakup for / = 0.05, λ/ = 8.5, and (a)–(h).

Image of FIG. 10.
FIG. 10.

Relative growth of the symmetrical and antisymmetrical part of the rim instability for the case shown in Figure 9 , / = 0.05, λ/ = 8.5, and .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Longitudinal instability of a liquid rim