# Direct numerical simulation of variable surface tension flows using a Volume-of-Fluid method

## TL;DR

This paper introduces a robust numerical method for simulating flows with variable surface tension using a Volume-of-Fluid approach, enabling accurate modeling of thermocapillary effects and fluid mixing.

## Contribution

A new numerical model that accurately computes surface gradients for variable surface tension in VOF-based Navier-Stokes simulations, applicable to temperature and concentration dependencies.

## Key findings

- Successfully modeled thermocapillary migration of bubbles.
- Simulated coalescence of drops with different surface tensions.
- Demonstrated robustness in handling large temperature jumps.

## Abstract

We develop a general methodology for the inclusion of variable surface tension into a Volume-of-Fluid based Navier-Stokes solver. This new numerical model provides a robust and accurate method for computing the surface gradients directly by finding the tangent directions on the interface using height functions. The implementation is applicable to both temperature and concentration dependent surface tension, along with the setups involving a large jump in the temperature between the fluid and its surrounding, as well as the situations where the concentration should be strictly confined to the fluid domain, such as the mixing of fluids with different surface tension coefficients. We demonstrate the applicability of our method to thermocapillary migration of bubbles and coalescence of drops characterized by different surface tension.