Hello,

I am doing research about bubble flow in water. The bubble motion causes disturbance in water. What is the governing equation of this case ? How do I apply the shear stress term ? Thank you for your answer

The governing equations are NS. Apply them separately to water and air bubbles and match the boundary conditons to converge

Your explanation too general for me because, I'm sorry, I'am a beginner in this case. Could you explain in detail, please ? Thanks again for your answer.

(1). You have governing equations for the bubble, and governing equations for the water. (2). So, you have conservation laws for the water, the bubble, and the combined system. Conservation laws are mass, momentum and energy conservations.(3). Relatively speaking, you will have flow over the bubble, and it will create flow motions in water. (you will also get flow motion in the bubble.)

Navier-Stokes' equation is the governing equations. When in the water phase, use the fluid properties of water (density, viscosity), while in the air phase, use the properties of air. The conditions on the water/air interface should match. So, one of the issues is to track the locations of the interfaces. Several methods have been developed for this: Level Set, VOF (volume-of-fluid), Front tracking...etc. Each has its weakness and strength. So, which one to use depends on the problem you are solving.

If the medium of the bubble is not air and the density ratio between the bubble and water (or surrounding fluid) is less than 200, you might want to consider Lattice Boltzmann method. There is no need to track the interface explicitly.

There is a book by cliff, grace and weber

Bubbles drops and particles

Commonly refered to as the "Bubble Bible". I would suggest you start here. It covers everything and more.

A very interesting subject

Hey Bronze

Please give us the full reference for the Bubble bible, We are very interested! i.e. authors publishers etc etc

Thanx Barry

R. Clift, J. R. Grace, and M.E. Weber, 1978, Bubbles, Drops, and Particles, Academic Press, NY, ISBN 0-12-176950-X

Thanx a million Bronze