Viscous to inertial coalescence of liquid lenses: a lattice Boltzmann investigation

TL;DR

This study uses advanced lattice Boltzmann simulations to analyze liquid lens coalescence, revealing distinct scaling laws in viscous and inertial regimes in both 2D and 3D cases.

Contribution

It introduces a massively parallel lattice Boltzmann approach to accurately simulate coalescence across a wide range of parameters, confirming theoretical scaling laws.

Findings

In 2D, viscous bridge growth is linear with time.

In 2D inertial regime, bridge growth follows t^{2/3}.

In 3D inertial regime, bridge height and width grow as t^{1/2}.

Abstract

Liquid lens coalescence is an important mechanism involved in many industrial and scientific applications. It has been investigated both theoretically and experimentally, yet it is numerically very challenging to obtain consistent results over the wide ranges of surface tension and viscosity values that are necessary to capture the asymptotic temporal behavior in the viscous and inertial limits. We report results of massively parallel simulations based on the color gradient lattice Boltzmann method, which overcome these limitations, and investigate the scaling laws of both regimes. For the two-dimensional case we find good agreement with the similarity solution of the thin-sheet equation, where in the viscous regime the connecting bridge grows linearly with time and in the inertial regime proportionally to $t^{2/3}$. In three dimensions, the viscous growth of the bridge also exhibits a linear time dependence, while in the inertial regime the growth of both the bridge height and the bridge width is proportional to $t^{1/2}$.