Motion of an air bubble under the action of thermocapillary and buoyancy forces

TL;DR

This paper introduces a robust volume-of-fluid method for simulating thermocapillary and buoyancy-driven bubble motion, accurately capturing interfacial forces without artificial smearing, validated against theoretical and experimental benchmarks.

Contribution

The authors develop a novel VoF-based solver that accurately models interfacial tension effects and thermocapillary migration without artificial surface tension smoothing.

Findings

The solver predicts terminal velocities consistent with theoretical values.

It accurately captures combined thermocapillary and buoyancy effects.

The method performs well for high viscosity and density ratios.

Abstract

A novel way to handle surface tension gradient driven flows is developed in the volume-of-fluid (VoF) framework. Using an open source Navier-Stokes solver, {\it Basilisk}, and the present formulation, we investigate thermocapillary migration of drops/bubbles in a surrounding medium. Several validation exercises have been performed, which demonstrate that the present solver is a robust one to investigate interfacial flows with variable surface tension. It is well known that it is a challenging task to numerically model the tangential and normal surface forces arising due to interfacial tension. We have shown that the present method does not require the artificial smearing of surface tension about the interface, and thus predicts the theoretical value of the terminal velocity of bubble/drop migrating due to an imposed temperature gradient very well. It is also demonstrated that the present solver provides accurate results for problems exhibiting the gravity and thermocapillary forces simultaneously, and useful for systems with high viscosity and density ratios.