The Dynamics of Liquid Drops Coalescing in the Inertial Regime

Abstract

We examine the dynamics of two coalescing liquid drops in the `inertial regime', where the effects of viscosity are negligible and the propagation of the bridge front connecting the drops can be considered as `local'. The solution fully computed in the framework of classical fluid-mechanics allows this regime to be identified and the accuracy of the approximating scaling laws proposed to describe the propagation of the bridge to be established. It is shown that the scaling law known for this regime has a very limited region of accuracy and, as a result, in describing experimental data it has frequently been applied outside its limits of applicability. The origin of the scaling law's shortcoming appears to be the fact that it accounts for the capillary pressure due only to the longitudinal curvature of the free surface as the driving force for the process. To address this deficiency, the scaling law is extended to account for both the longitudinal and azimuthal curvatures at the bridge front which, fortuitously, still results in an explicit analytic expression for the front's propagation speed. This new expression is then shown to offer an excellent approximation for both the fully-computed solution and for experimental data from a range of flow configurations for a remarkably large proportion of the coalescence process. The derived formula allows one to predict the speed at which drops coalesce for the duration of the inertial regime which should be useful for the analysis of experimental data.

arXiv commentAccepted for publication in Physical Review E

References in corpus (7)

• Coalescence of Liquid Drops
• Inviscid coalescence of drops
• Viscous to Inertial Crossover in Liquid Drop Coalescence
• The inexorable resistance of inertia determines the initial regime of drop coalescence
• Coalescence of Liquid Drops: Different Models Versus Experiment
• The Dynamics of Liquid Drops and their Interaction with Solids of Varying Wettabilites
• Finite Element Simulation of Dynamic Wetting Flows as an Interface Formation Process

Cited by in corpus (5)

• Capillary Breakup of a Liquid Bridge: Identifying Regimes and Transitions
• A Parametric Study of the Coalescence of Liquid Drops in a Viscous Gas
• Air Entrainment in Dynamic Wetting: Knudsen Effects and the Influence of Ambient Air Pressure
• Bridge evolution during the coalescence of immiscible droplets
• Coalescence of immiscible sessile droplets on a partial wetting surface