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Linear oscillations of weakly dissipative axisymmetric liquid bridges
Higuera, María and Nicolás, José A. and Vega de Prada, José Manuel
Linear oscillations of weakly dissipative axisymmetric liquid bridges.
"Physics of Fluids", v. 6
Linear oscillations of axisymmetric capillary bridges are analyzed for large values of the modified Reynolds number C−1. There are two kinds of oscillating modes. For nearly inviscid modes (the flow being potential, except in boundary layers), it is seen that the damping rate −ΩR and the frequency ΩI are of the form ΩR=ω1C1/2+ω2C+O(C3/2) and ΩI=ω0+ω1C1/2+O(C3/2), where the coefficients ω0≳0, ω1<0, and ω2<0 depend on the aspect ratio of the bridge and the mode being excited. This result compares well with numerical results if C≲0.01, while the leading term in the expansion of the damping rate (that was already known) gives a bad approximation, except for unrealistically large values of the modified Reynolds number (C≲10−6). Viscous modes (involving a nonvanishing vorticity distribution everywhere in the liquid bridge), providing damping rates of the order of C, are also considered.
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