A Parametric Study of the Coalescence of Liquid Drops in a Viscous Gas

TL;DR

This study numerically investigates the initial stages of liquid drop coalescence in a viscous gas, revealing the influence of gas viscosity, limitations of existing scaling laws, and providing a new phase diagram of parameter space.

Contribution

It offers a detailed numerical analysis of early coalescence, highlighting the role of gas viscosity and critiquing existing scaling laws with a new phase diagram.

Findings

Gas viscosity suppresses toroidal bubble formation.

Conventional model qualitatively matches experimental features.

Quantitatively overpredicts coalescence speed.

Abstract

The coalescence of two liquid drops surrounded by a viscous gas is considered in the framework of the conventional model. The problem is solved numerically with particular attention to resolving the very initial stage of the process which only recently has become accessible both experimentally and computationally. A systematic study of the parameter space of practical interest allows the influence of the governing parameters in the system to be identified and the role of viscous gas to be determined. In particular, it is shown that the viscosity of the gas suppresses the formation of toroidal bubble predicted in some cases by early computations where the gas' dynamics was neglected. Focussing computations on the very initial stages of coalescence and considering the large parameter space allows us to examine the accuracy and limits of applicability of various `scaling laws' proposed for different `regimes' and, in doing so, reveal certain inconsistencies in recent works. A comparison to experimental data shows that the conventional model is able to reproduce many qualitative features of the initial stages of coalescence, such as a collapse of calculations onto a `master curve' but, quantitatively, overpredicts the observed speed of coalescence and there are no free parameters to improve the fit. Finally, a phase diagram of parameter space, differing from previously published ones, is used to illustrate the key findings.