The breakup dynamics of an asymmetric liquid bridge under quasi-static stretching

In this paper, we investigate the dynamics of an asymmetric liquid bridge under quasi-static stretching. By establishing a two-dimensional model to describe the liquid dynamics, we apply a constant-velocity stretching to a short liquid bridge and fully simulate the entire process from the onset of stretching to the local pinch-off. The process can be divided into three consecutive stages: quasi-static stage, instability stage, and local pinching stage. The asymmetry ratio of the liquid bridge and the fluid viscosity are the key parameters in this paper. We present the dynamics for a liquid bridge with different asymmetry ratios and viscosities and analyze the instability mechanism along with the relationship between the characteristic radii of the liquid bridge. For symmetric liquid bridges, only even-mode perturbation amplitudes play a role in capillary instability, ultimately leading to simultaneous pinch-off at both ends. As the asymmetry ratio increases, the odd-mode perturbation amplitudes become gradually dominant. At the onset of instability, the dominant perturbation modes are found to depend primarily on the asymmetry ratio rather than on viscosity. Furthermore, the study confirms that for low-viscosity liquid bridges, the post-flattening dynamics are governed by the characteristic radii at the moment of flattening. Our results could contribute to a deeper understanding of liquid bridge breakup behavior in both natural and industrial processes.