Theoretical and experimental study of the vibration of axisymmetric viscous liquid bridges

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Abstract
N this paper the dynamics of axisymmetric liquid columns held by capillary forces between two circular, concentric, solid disks is considered. The problem has been solved by using a one‐dimensional model known in the literature as the Cosserat model, which includes viscosity effects, where the axial velocity is considered constant in each section of the liquid bridge. The dynamic response of the bridge to an excitation consisting of a small‐amplitude vibration of the supporting disks has been solved by linearizing the Cosserat model. It has been assumed that such excitation is harmonic so that the analysis has been performed in the frequency domain. The particular case of a cylindrical liquid bridge has been analytically studied and the transfer function has been calculated in the cases of oscillation of both disks (either in phase or in counterphase) or only of one of them. The resolution of the general formulation for a noncylindrical liquid bridge has been numerically made by using an implicit finite difference method. In this case, the influence of the volume of the liquid column and of the residual gravity level on the first resonance has been studied, and the results compared, for the inviscid case, with other potential models, both one and three dimensional. To demonstrate the usefulness of this theoretical model in predicting the vibrational behavior of axisymmetric viscous liquid bridges, some experiments have been performed by using the neutral buoyancy technique (also known as the Plateau technique) to simulate reduced gravity conditions, with good agreement between the results of the model and experiments