A note on the use of one-dimensional models to describe the linear dynamics of liquid bridges

In this work, the capacity of the one-dimensional approximation to describe the linear dynamics of liquid bridges is studied in detail. The frequency and damping rate that characterize the first oscillation mode of a cylindrical liquid bridge are calculated from the one-dimensional models and the Navier-Stokes equations. The results are systematically compared varying Λ and C. This comparison allows one to observe the accuracy of the 1-D models and to select the most suitable one for any given values of Λ and C. This selection is expected to be correct for non-cylindrical equilibrium shapes as well. For the sake of illustration, the 1-D models are also solved numerically for non-cylindrical axisymmetric equilibrium shapes.