Definition of the Problem I - PRESENTATION

We can do several assumptions:

• the flow is stationnary and axisymmetric
• the bubble stays motionless and spheric We suppose mass transfert across bubble-air interface is null. Therefore, the corresponding boundary condition is :  Moreover, the viscosity of water is much more important than the viscosity of air, it involves : This means the shear stress vanishes on the air - water interface.

The definition of the two following numbers allows  to classify the different types of diphasic flows :  For a flow of liquid around a gas particle,  we have : (indeed, it is equal to 0.017)

II - THEORICAL RESULTS

In order to verify (or not) validity of FLUENT computation, we  use some theorical results.

We can define Reynold's number with  following characteristics : • Re <<1 : Stocke's solution:
The general expression of Drag coefficient for two phase flows is : Hence, we deduce : with the approximation : • Re = or < 1 : Weak inertial effects: • Re>1 : Major inertial effects - potential flow : Comment: Contrary to a flow around a  solid sphere, a flow around a spheric bubble don't remove for any Re. We hope this result will be verified.

III- PHYSICAL PARAMETERS    