Viscous to Inertial Crossover in Liquid Drop Coalescence (1012.1298v4)

Abstract: Using an electrical method and high-speed imaging we probe drop coalescence down to 10 ns after the drops touch. By varying the liquid viscosity over two decades, we conclude that at sufficiently low approach velocity where deformation is not present, the drops coalesce with an unexpectedly late crossover time between a regime dominated by viscous and one dominated by inertial effects. We argue that the late crossover, not accounted for in the theory, can be explained by an appropriate choice of length-scales present in the flow geometry.

Viscous to Inertial Crossover in Liquid Drop Coalescence

The paper "Viscous to Inertial Crossover in Liquid Drop Coalescence," authored by Joseph D. Paulsen, Justin C. Burton, and Sidney R. Nagel, offers a comprehensive analysis of the transition dynamics from viscous-dominated to inertially dominated regimes during the coalescence of liquid droplets. By employing both an electrical method and high-speed imaging, this paper observes the coalescence process at a remarkable temporal resolution of 10 nanoseconds. The research elucidates the factors influencing the crossover between these two fluid dynamic regimes, challenging the conventional understanding of this phenomenon.

Critical Observations

The paper's primary assertion is that, unlike the predictions from previous theoretical models, the crossover from viscous to inertial regimes occurs significantly later in the coalescence process than expected. The paper evidences this delay through meticulous experimentation varying the viscosity of the liquid over an extensive range. The primary numerical result demonstrates that the crossover takes place approximately 2 microseconds after contact initiation—three decades longer than the previously predicted 0.7 nanoseconds.

This discrepancy arises from a reevaluation of the length scale used in the Reynolds number computation for drop coalescence. The traditional models premised on the Reynolds number would predict an early transition due to an inaccurate choice of characteristic length and velocity scales. The researchers propose that the dominant flows, responsible for determining the crossover timing, are associated with the neck height rather than the neck radius as previously assumed.

Methodological Approach

The research utilizes glycerol-water-NaCl mixtures to vary viscosity while maintaining near-constant surface tension and density. The experiment measures the coalescence dynamics through a specially devised electrochemical setup, supplemented by high-frequency AC voltage application. This method enables the precise determination of the bridge resistance between the coalescing drops, which was then correlated with the evolving bridge radius.

The advanced temporal resolution achieved in these measurements bridges the gap present in earlier high-speed imaging approaches, which could not capture the initial viscous regime. The research findings were consistent across the dataset, with the bridge dynamics depicting the expected scaling relations both in the viscous and inertial regimes.

Theoretical Comparison and Implications

The surprising result of the delayed crossover prompted an alternative theoretical interpretation. The researchers propose that the Reynolds number for coalescence should incorporate the neck height as the primary characteristic length scale. This redefined Reynolds number leads to a quadratic dependence of crossover time on fluid viscosity, aligned with empirical results. Consequently, the findings motivate a reassessment of theoretical models concerning fluid transition dynamics in coalescence and similar contexts.

This paper holds significant implications for a deeper understanding of fluid mechanics, particularly in processes where rapid fluid integration or separation is present. The detection of a drastically smaller length control offers new insights into the intricate interplays of surface tension and fluid inertia.

Future Directions

The paper opens pathways for further research into the crossover dynamics in complex fluids, non-Newtonian fluids, and multiphase systems. Future work can explore the interaction with surrounding gases, which may also influence the coalescence at extremely small scales. Additionally, refined theoretical models considering these new insights could more accurately predict and control coalescence in industrial applications such as inkjet printing, emulsification, and spray drying technologies.

This research underscores the importance of revisiting and refining existing theoretical frameworks to accommodate new empirical observations, thus contributing to the advancement of fluid dynamics theory and application.