Spontaneous Formation of Micro-Well During Stretching of Liquid Bridge With Hole

Stretching of liquid bridges has a vast number of applications in engineering and biology. High-viscosity liquid bridges, stretched between two plates in the presence of a hole on the top plate, may be used to fabricate micro-well structures quickly and repetitively. To understand the flow dynamics in this system, we perform numerical simulations of the setup using diffuse-interface dual-grid level-set method. In the simulations, we introduce a hole in the bottom plate and then lift the top plate with constant velocity. We find that the air bubble originating from the hole shrinks in size at a low Capillary number (i.e., viscous to surface tension force). On the other hand, at a high Capillary number, the height of the air bubble increases during plate separation. The growth rate of the air bubble depends mainly on the size of the hole at the bottom plate. Once the hole diameter crosses a threshold, the air bubble grows faster than the separation rate of the plates, leading to spontaneous formation of a micro-well.