Sequences of the contraction of a liquid filaments, taken from Ref. 15 with permission. The upper sequence shows from left to right the stable collapse of a low viscous ligament. We call the moment when the tail droplets are in contact, t M . The lower sequence shows the unstable collapse of a longer, more viscous ligament. At t 0 the filament breaks off from the big tail droplets. We call the moment when the filament breaks up everywhere t B . The initial properties are Γ = 9 and Oh R = 0.04 for filament the upper filament, and Γ = 29.2 and Oh R = 0.18 for the lower filament.
Parameter study of the stability of the contraction of a filament. The result of the linear theory, Γ c , is shown for ε = 0.01 in the dashed dotted line. The linear theory is confirmed by the results of the numerical model, 16 solid line. Stability of low viscous filaments has been studied numerically by Notz and Basaran, 13 dashed line. The experimental results by Ref. 15 are shown (circles for unstable, disks for stable regime). Linear theory correctly predicts the critical aspect ratio for filaments of Oh > 0.1.
Shape of the filament at t 0, just after the filament has pinched off from, e.g., a film or a large filament. The surface is perturbed, with an assumed sinusoidal perturbation superposed on R 0. The wavelength of the perturbation is λ. The amplitude of the perturbation at t 0 is δ. The filament considered is symmetric in the x = 0 plane.
Demonstration of the three different regimes, from top to bottom: Stable contraction, breakup due to the Rayleigh-Plateau instability, and breakup due to end pinching. For these numerical simulations, the Ohnesorge numbers are, respectively, 1, 0.1, and 0.01. The aspect ratio and the perturbation amplitude are kept constant at resp. Γ = 35 and ε = 0.01. The time between the consecutive contours is t cap .
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