Confined Coalescence Unveils New Regimes of Frictional Fluid Mechanics

Droplet coalescence is essential in a host of biological and industrial processes involving complex systems as diverse as cellular aggregates, colloidal suspensions, and polymeric liquids. Classical solutions for the time evolution of coalescing clusters are typically based on tractable limiting physics, such as analytical solutions to the Stokes equation, and discrepancies between experiments and these classical solutions can indicate relevant physical effects governing the behavior of different systems. By combining computational and theoretical analyses, we show that there is an unexplored family of ``dry hydrodynamic'' or ``frictional'' coalescence processes: those governed by highly dissipative coupling to the environment. This leads to new scaling laws characterizing droplet coalescence, as well as new time-invariant parameterizations of the shape evolution of the coalescing system. We demonstrate these effects via particle-based simulations and with both continuum and boundary-integral solutions to hydrodynamic equations, which we then understand in the context of a generalized Navier-Stokes-like equation. Our theoretical description of highly frictional coalescence mathematically maps onto Darcy flow in the presence of surface tension effects, and preliminary experiments show excellent agreement with particle-based simulations, opening up exciting avenues of research in applying well-studied fluid dynamical techniques to a broad range of novel systems.