Frictional coalescence of droplets in a Hele-Shaw cell

Droplet coalescence driven by surface tension is ubiquitous in both nature and industrial applications. The description of coalescence typically requires analytical solutions of the Navier-Stokes equation. However, experiments have revealed discrepancies between Stokes-like behavior and complex systems where momentum is not conserved such as cell aggregates. Recent computational studies revealed new scaling laws in such "dry hydrodynamic," or "frictional" environments with a highly dissipative background via particle-based simulations and both continuum and boundary-integral solutions to hydrodynamic equations. Remarkably, such frictional coalescence can be described with Darcy flow in the context of a compact system governed by surface tension. We explore such frictional coalescence experimentally using a Hele-Shaw cell composed of two glass plates and viscous silicone oil. Our results revealed that the connecting neck growth is governed by two distinct regimes with respect to time, where the second regime of growth is slowed down significantly until it eventually arrests, likely due to sticking of the contact line. The initial regime of coalescence is determined by the ratio of numerous length scales including the gap between the plates, inverse neck curvature, neck size, and drop size. We show experimental results that are consistent with computational predictions of Darcy-driven coalescence and particle-based simulations of coalescing clusters, thus supporting a new link between porous media flow theory and continuum models of particle aggregates in dissipative liquids.