Stability analysis of liquid bridges Author:

Drop formation is a very interesting and common phenomenon that can be seen in a wide range of occurrences, both natural and man-made, from rain drops to ink-jet printers and spray atomizers. It is also a topic that fascinated scientists for centuries and the mathematical description pioneered by Young and Laplace opened the door to their systematic study. Drop formation starts with an elon-gated filament, or liquid bridge, which connects the drop to the body of liquid that subsequently necks by capillary action and breaks into droplets. The main goal of this thesis is to develop a tool for investigating the stability of the equilibrium state of liquid bridges, which is the last connection between the drop and the body of liquid. For this aim, bifurcation theory and linear stability analysis have been used by developing a MATLAB code, and adopting numerical tool, like pseudo-arclength continuation and the Newton-Raphson method. After some historical considerations, the one-dimensional model by Eggers and Dupont is presented. A brief description of bifurcation and linear stability analysis is provided with some examples linked to our topic. On this basis