One‐dimensional models for slender axisymmetric viscous liquid bridges

Abstract

A set of one‐dimensional models, previously derived for liquid jets, is generalized to viscous liquid bridges by applying suitably modified boundary conditions at the anchoring disks. A linear analysis for small‐amplitude perturbations around the cylindrical static solution is performed. The oscillation frequencies and growth factors so obtained are compared to the already known linear three‐dimensional results for a wide range in both the slenderness and viscosity. The relative error of each model is studied in terms of the typical axial length. Good agreement is found for slender enough bridges. The existence of boundary layers for weakly dissipative liquid bridges in the context of one‐dimensional models is also discussed.