The Coalescence of Liquid Drops in a Viscous Fluid: Interface Formation Model

TL;DR

This paper applies the interface formation model to the initial stages of liquid drop coalescence in a viscous fluid, highlighting differences from conventional models and better agreement with experimental data.

Contribution

It introduces the interface formation model to describe coalescence, removing singularities and capturing the influence of ambient fluid and drop size effects.

Findings

The model predicts non-monotone bridge expansion speed for small drops.

It removes the initial singularity present in conventional models.

The model aligns better with experimental data on liquid bridge evolution.

Abstract

The interface formation model is applied to describe the initial stages of the coalescence of two liquid drops in the presence of a viscous ambient fluid whose dynamics is fully accounted for. Our focus is on understanding (a) how this model's predictions differ from those of the conventionally used one, (b) what influence the ambient fluid has on the evolution of the shape of the coalescing drops and (c) the coupling of the intrinsic dynamics of coalescence and that of the ambient fluid. The key feature of the interface formation model in its application to the coalescence phenomenon is that it removes the singularity inherent in the conventional model at the onset of coalescence and describes the part of the free surface `trapped' between the coalescing volumes as they are pressed against each other as a rapidly disappearing `internal interface'. Considering the simplest possible formulation of this model, we find experimentally-verifiable differences with the predictions of the conventional model showing, in particular, the effect of drop size on the coalescence process. According to the new model, for small drops a non-monotone time-dependence of the bridge expansion speed is a feature that could be looked for in further experimental studies. Finally, the results of both models are compared to recently available experimental data on the evolution of the liquid bridge connecting the coalescing drops, and the interface formation model is seen to give a better agreement with the data.