Post-pinch-off relaxation of two-dimensional droplets in a Hele-Shaw cell

We report on the shape relaxation of 2D droplets, formed right after the spontaneous pinch-off of a capillary bridge-droplet confined within a Hele-Shaw cell. An array of bridge-droplets confined within a microchip device first undergo neck thinning due to the evaporation driven volume change. Subsequently, an abrupt topological change transforms each bridge-droplet into a small central satellite droplet and the twin-droplets pinned at the edges of the cell. We monitor the shape relaxation with high temporal resolution optical microscopy. Capillary action drives the 2D shape relaxation, while the viscous dissipation in the film retards it. As a result, the tip of the twin-droplets exhibit a self-similar parabolic shape evolution. Based on these observations, the lubrication-approximation model accurately predicts the internal pressure evolution and the droplet tip displacement. The geometrical confinement substantially slows down the dynamics, facilitating visualization of the capillary-viscous regime, even for low viscosity liquids. The characteristic relaxation timescale shows an explicit dependence on the confinement ratio (width/gap) and the capillary-velocity of liquid. We verify the broad applicability of the model using different liquids.