Evaluating Forces Acting on Pendant Drops Suspended from Small Pillars

This study shows drop retention on a pillar. We used centrifugal adhesion balance to generate a normal force and to pull a drop suspended from round and polygon pillars of 1.5-3.0 mm hydraulic diameter. The force applied on the drop, despite the confined contact area, cannot overcome the adhesion. Instead, it allows the accumulation of more liquid in the contact area, which destabilizes the drop and leads to a split, even when the contact with the edge is partial, like in polygon pillars. A liquid-liquid splitting phenomenon occurs without liquid-solid detachment, and the residual drop maintains the initial contact line. Our experiments revealed that the force required to split a pendant drop from aluminum pillars increases with the contact area, e.g., the force required to pull off a 15 μL drop is 2.5 times higher as the contact area of the pillar increases by 4 times. Additionally, an inverse relation was found between the required normal force to pull off the drop and its initial volume. This phenomenon can be attributed to the high surface energy, which facilitates the separation process. The examined pillar profiles─round, square, and triangular─demonstrate that the solid-liquid contact area is a critical parameter influencing pull-off force magnitude. This observation complements Tate's law, which describes the force required for the natural detachment of a pendant drop from a needle. This finding unifies the varied cases of pillar dimensions and shapes into a single curve that defines the required acceleration to detach a portion of each drop's initial volume.