Bubble rise through water in 2D using Basilisk

Predicting Bubble Rise Velocity in Liquids using ML and Basilisk

The rise of a gas bubble in a liquid is a classic multiphase flow problem, rich in fluid mechanics and practical relevance — from boiling and cavitation to bioreactors and nuclear cooling.

In this project, we simulate 2D bubbles rising in a quiescent liquid using the Volume of Fluid (VOF) method in Basilisk, and then train a machine learning model to predict the terminal rise velocity from physical parameters.

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⚙️ Governing Physics

The terminal rise velocity of a bubble in a liquid depends on several key parameters:

• Bubble diameter ($d_b$)
• Liquid density ($\rho_\ell$)
• Gas density ($\rho_g$)
• Liquid viscosity ($\mu$)
• Surface tension ($\sigma$)
• Gravity ($g$)

Dimensionless groups often used:

• Eötvös number:
  \(Eo = \frac{(\rho_\ell - \rho_g) g d_b^2}{\sigma}\)
• Morton number:
  \(Mo = \frac{g \mu^4 (\rho_\ell - \rho_g)}{\rho_\ell^2 \sigma^3}\)
• Reynolds number (based on terminal velocity):
  \(Re = \frac{\rho_\ell v_t d_b}{\mu}\)

The relationship between these numbers is nonlinear and often regime-dependent (spherical, ellipsoidal, skirted, etc.). Analytical formulas exist in limiting cases, but not in general.

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🎯 Goal

We will simulate multiple bubble rise scenarios by varying key parameters and extract the terminal velocity. These data points will be used to train an ML model to learn the mapping:

\[(d_b, \rho_\ell, \rho_g, \mu, \sigma) \longrightarrow v_t\]

Once trained, the model should be able to predict the rise velocity of a bubble given physical parameters — without needing to run new CFD simulations.