Simulating the motion of gas bubbles in a liquid

Understanding the motion of gas bubbles in a liquid is a problem of both scientific and engineering importance. About 500 years ago, Leonardo da Vinci1 summarized his observations on the motion of air bubbles in a liquid: “The air that submerged itself with the water⃛ returns to the air, penetrating the water in sinuous movement, changing its substance into a great number of forms⃛ it never spreads itself out from its path except to the extent to which it avoids the water which covers it”. We have attempted to simulate the motion of single gas bubbles in a liquid using the volume-of-fluid (VOF) technique, which allows us to describe the complex bubble dynamics using only the fluid phase properties as inputs.