José A. Nicolás

Linear oscillations of weakly dissipative axisymmetric liquid bridges

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.

Linear oscillations of axisymmetric viscous liquid bridges

Abstract. Small amplitude free oscillations of axisymmetric capillary bridges are considered for varying values of the capillary Reynolds number C-1 and the slenderness of the bridge

On the steady streaming flow due to high-frequency vibration in nearly inviscid liquid bridges

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Weakly nonlinear oscillations of nearly inviscid axisymmetric liquid bridges

. A semi-analytical method is presented that provides cheap and accurate results for arbitrary values of C-1 and

A note on the effect of surface contamination in water wave damping

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The viscous damping of capillary-gravity waves in a brimful circular cylinder

; several asymptotic limits (namely,

Linear nonaxisymmetric oscillations of nearly inviscid liquid bridges

C\ll 1, C\gg1, \Lambda\ll 1 \ \rm{and} \ |\pi-\Lambda|\ll 1

Effects of static contact angles on inviscid gravity-capillary waves

) are considered in some detail, and the associated approximate results are checked. A fairly complete picture of the (fairly complex) spectrum of the linear problem is obtained for varying values of C and

Three-dimensional streaming flows driven by oscillatory boundary layers

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Weakly nonlinear nonaxisymmetric oscillations of capillary bridges at small viscosity

. Two kinds of normal modes, called capillary and hydrodynamic respectively, are almost always clearly identified, the former being associated with free surface deformation and the latter, only with the internal flow field; when C is small the damping rate associated with both kind of modes is comparable, and the hydrodynamic ones explain the appearance of secondary (steady or slowly-varying) streaming flows.