Coalescing clusters unveil regimes of frictional fluid mechanics

Abstract

The coalescence of droplets is essential in a host of biological and industrial processes, where it can be a crucial limiting factor and a convenient tool to probe material properties. Controlling and understanding this phenomenon relies on theoretical models of droplet coalescence, and classical solutions for the time evolution of contacting drops (such as analytical solutions to the Stokes equation) have proven invaluable for understanding the behavior of many simple liquids. In many systems, especially biological systems on substrates, there are an increasing number of examples of discrepancies between known solutions to continuum models and experimental results. By combining computational and theoretical analyses, we show that there is an unexplored family of dry hydrodynamic or frictional coalescence processes: those governed by a highly dissipative coupling to the environment. This leads to a universality class of coalescing behavior, with unique scaling laws and time-invariant parametrizations for the time evolution of coalescing drops. To demonstrate this, we combine particle-based simulations and both continuum and boundary-integral solutions to hydrodynamic equations, which we then understand in the context of a generalized Navier-Stokes-like equation. Our work suggests a theoretical basis for further studies of coalescence, as well as other fluidlike phenomena in these friction-dominated systems, and significantly alters the interpretation of related experimental measurements. Published by the American Physical Society 2024