Ephemeral Antibubbles: Spatiotemporal Evolution from Direct Numerical Simulations

TL;DR

This paper uses direct numerical simulations to study the evolution and breakup of antibubbles, demonstrating how their dynamics can be modeled by coupled Cahn-Hilliard-Navier-Stokes equations and validated against experimental data.

Contribution

It introduces a robust DNS approach combining CHNS and VoF methods to accurately simulate antibubble dynamics and breakup processes.

Findings

Antibubbles' lifetime depends on multiple parameters.

The retraction velocity of antibubble arms scales as the square root of surface tension.

Simulation results align with experimental observations.

Abstract

Antibubbles, which consist of a shell of a low-density fluid inside a high-density fluid, have several promising applications. We show, via extensive direct numerical simulations (DNSs), in both two and three dimensions (2D and 3D), that the spatiotemporal evolution of antibubbles can be described naturally by the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations for a binary fluid. Our DNSs capture elegantly the gravity-induced thinning and breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar order parameter field $\phi$, which varies continuously across interfaces, so we do not have to enforce complicated boundary conditions at the moving antibubble interfaces. To ensure that our results are robust, we supplement our CHNS simulations with sharp-interface Volume-of-Fluid (VoF) DNSs. We track the thickness of the antibubble and calculate the dependence of the lifetime of an antibubble on several parameters; we show that our DNS results agree with various experimental results; in particular, the velocity with which the arms of the antibubble retract after breakup scales as $\sigma^{1/2}$, where $\sigma$ is the surface tension.