Dynamic stretching of a planar liquid bridge

Abstract

A thin incompressible viscous planar free liquid film in a void and under zero gravity is analyzed by means of a reduced-dimension (lubrication) approach. Linear analysis focuses on films with harmonic modulations in the axial film velocity enforced at the ends of the planar bridge. Effects of changes in the problem parameters on the overall distortion characteristics of the film are discussed. Nonlinear film distortion and break-up are investigated for the case of temporally increasing velocity at the end of the film resulting in continuous film stretching eventually leading to film rupture. Implementation of the employed numerical model is validated for the linear limit by comparison with the analytical linear solutions and for harmonically modulated film-end velocities. Within the nonlinear analysis of the continuously stretched film bridge, several distinct film topologies are identified depending on liquid Weber number and Reynolds number, i.e., the magnitude of the stretching rate (end velocity) compared to signal propagation rates through the liquid via capillary waves and viscous action. That is, the Weber number is the square of the ratio of stretching rate to capillary wave velocity while the Reynolds number is the ratio of stretching rate to the characteristic viscous velocity. Here, film topology is typically characterized by three distinct regions, i.e., a film wedge forming at the pulling end(s), the film center region and a transition region. The size and shape of these regions greatly depend on the particular case under investigation. Film distortion characteristics observed for continuously compressed planar films conform with observations made by other authors for the similar case of contracting free liquid films.