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

Abstract

We report on the shape relaxation of two-dimensional (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 undergoes 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 exhibits 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.

Dynamics of microflow at the plasma–liquid interface

“…The quantification of dissipated plasma-power directly at the liquid interface and the subsequent liquid mass displacement are of crucial importance in emerging applications of plasmas in microfluidics and medicine 12 , 14 , 15 . The presented system and the developed methodology also offer a new opportunity for systematic study of the liquid channel breakup and droplet pinch-off due to a complex external force in 2D geometry of Hele-Shaw cell at low Reynolds numbers and high viscosity contrast, an issue of general importance 33 – 35 .…”

Dynamics of capillary coalescence and breakup: Quasi-two-dimensional nematic and isotropic droplets

“…So, fluctuations and distortions of the bridge forming thinner regions can be much larger and become important. Sinusoidal modulation, formation of the elongated domain, central and satellite domains are remarkably similar to the cascade of pinch-offs during 3D filament or stretched droplet breakup [16][17][18][19] which are connected with Rayleigh-Plateau instability [13,14].…”

“…The study of droplet transformation driven by surface tension is a classical direction in fluid physics. Cardinal transformations occur at coalescence of three-dimensional (3D) [1][2][3][4][5] or 2D [6][7][8][9][10][11][12] droplets or inversely when satellite droplets are formed from a jet or a bigger stretched droplet [13][14][15][16][17][18][19]. Coalescence and breakup belong to the class of free surface problems.…”