Dynamics of a deformable droplet inside a microfluidic chamber under gravity

Biomicrofluidics research like cell-perfusion, cell-sorting, and droplet-based microchemical reactors often involves isolating a single cell or drop in a bioreactor chamber and exposing it to controlled flow of nutrient-rich solution. This chamber enables hydrodynamic trapping of the small cell or drop in microwell. We use a moving-frame boundary-integral simulation to study the motion of a three-dimensional deformable droplet under gravity in a chamber with nearly sharp corners in the Stokes flow regime. The dynamics of the droplet is influenced by the drop-to-bulk fluid viscosity ratio, capillary number, Bond number, chamber size, and the smoothing radii of the arced corner. Increasing the Bond number causes the drop to settle towards the bottom of the chamber, while a smaller Bond number allows the drop to escape without any hook or tail. A moderate Bond number may result in droplet breakup with thin neck formation near the corner. Under the same flow conditions, a smaller chamber size results in droplet trapping, while a larger chamber size facilitates droplet escape. Higher capillary numbers lead to large drop deformation, with the tail becoming trapped and the head elongating out of the channel.