The inexorable resistance of inertia determines the initial regime of drop coalescence (1204.4174v1)

Abstract: Drop coalescence is central to diverse processes involving dispersions of drops in industrial, engineering and scientific realms. During coalescence, two drops first touch and then merge as the liquid neck connecting them grows from initially microscopic scales to a size comparable to the drop diameters. The curvature of the interface is infinite at the point where the drops first make contact, and the flows that ensue as the two drops coalesce are intimately coupled to this singularity in the dynamics. Conventionally, this process has been thought to have just two dynamical regimes: a viscous and an inertial regime with a crossover region between them. We use experiments and simulations to reveal that a third regime, one that describes the initial dynamics of coalescence for all drop viscosities, has been missed. An argument based on force balance allows the construction of a new coalescence phase diagram.

The Inexorable Resistance of Inertia and Its Role in Drop Coalescence

The phenomenon of drop coalescence, a prevalent process in atmospheric, industrial, and scientific domains, requires a reevaluation in the context of its initial dynamic stages. The paper by Paulsen et al. brings forth an innovative perspective, identifying a previously overlooked third regime in the coalescence dynamics of liquid drops. This paper challenges the long-standing binary understanding that drop coalescence comprises solely of a viscous regime and an inertial regime.

Key Findings and Methodology

The authors present a comprehensive analysis through both experimental and computational approaches to unveil a new dynamical regime that they refer to as the "inertially-limited-viscous" regime. The recognition of this regime stems from a thorough examination of the initial dynamics of drop coalescence, where it becomes apparent that inertia plays a non-negligible role in this early stage for droplets characterized by various viscosities.

The investigation employs two primary methodologies: high-speed visual imaging and electrical measurement techniques to capture the dynamics of drop coalescence in real time. Computational simulations further bolster these experimental results, using Navier-Stokes equations resolved through a finite-element algorithm to depict the fluid dynamics at play as the liquid neck between merging droplets grows.

A significant insight from this work is the transition and interaction between regimes, characterized by force-balance arguments, which elucidate why pure Stokes flow models prove inadequate in explaining the dynamics as two droplets begin to merge. The research effectively delineates a new phase diagram for coalescence that maps out the inertial, Stokes, and inertially-limited-viscous regimes, alongside their respective transitional boundaries.

Implications and Future Directions

The identification of the inertially-limited-viscous regime has profound implications in both theoretical modeling and practical applications. The results suggest revisions to the understanding of phenomena where drop coalescence is a critical factor, such as in the manipulation of emulsions in chemical engineering or atmospheric modeling of raindrop formation processes.

From a theoretical vantage, the delineation of a new regime prompts a reconsideration of the scaling laws traditionally applied to such fluid dynamic systems. The discovery of this regime underscores the complexity involved in fluid dynamics, particularly under the influence of significant inertial forces at microscopic scales.

Future research might further investigate the implications of inertia in multi-phase fluid systems under varying boundary conditions, or explore the effects of external fields on coalescence dynamics. Additionally, extending the analysis to drops immersed in different liquid environments could yield insights applicable to a broader range of practical scenarios.

In conclusion, this paper offers a pivotal contribution to the fluid dynamics field, emphasizing the intricate nature of drop coalescence. By unveiling a third distinct regime, Paulsen et al. beckon the scientific community to reevaluate previous models and consider new frameworks that incorporate the influence of inertia during the initial stages of drop merging. This work stands as a testament to the evolving understanding of liquid systems and the need for continuous inquiry in elucidating complex natural processes.