Producing Droplets on a Vibrating Liquid Bath Through Ligament Stretching and Breakup

The breakup of liquid threads into droplets is a well-studied phenomenon governed by surface tension and viscosity. Conventional methods for droplet generation often rely on specialized or costly equipment, limiting accessibility. Here, we introduce a simple, low-cost technique for generating single droplets from a vibrating liquid bath by using a standard click pen to draw and retract a liquid thread from a bath of silicone oil. We first demonstrate that this method reliably generates single droplets on a stationary bath and then establish its applicability to vibrating baths. By systematically varying the retraction speed, pen tip radius, and the retraction distance we control the dimensions of the liquid ligament and access a wide range of droplet sizes. We also quantify the pinch-off timescales and identify the regions of parameter space where single rather than multiple droplet formation is favored. This approach enables straightforward production of droplets with tunable sizes, providing a practical tool for experiments investigating bouncing droplets in pilot-wave hydrodynamics.