The Dynamics of Liquid Drops Coalescing in the Inertial Regime

TL;DR

This paper investigates the inertial regime of liquid drop coalescence, extending existing scaling laws to include azimuthal curvature, resulting in a more accurate predictive formula validated against computational and experimental data.

Contribution

The authors extend the classical scaling law for drop coalescence to incorporate azimuthal curvature, improving accuracy across a broader range of the inertial regime.

Findings

The extended scaling law accurately predicts the coalescence speed in the inertial regime.

The classical law's limited applicability is due to neglecting azimuthal curvature.

The new formula matches well with computational and experimental results.

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.