Local scale

This study place in the scale of a bubble. The shearing takes also place in the boundary layer. With the software Matlab, I've developed a small program to estimate the upstroke velocity, the Reynolds number and the shearing in the boundary layer with a simple approach. This approach is aimed to find magnitude orders in order to better model the system. The model mustn't become simplistic, notably about the estimation of the drag coefficient.

The different steps are described below :

• Calculation of the upstroke velocity thanks to a forces assessment. The final equation to solve is :
  
  
• Calculation of the Reynolds number with the following relation (r is the bubble radius) :
  
  
• Comparison of the drag coefficient from la relation
  
  (valable pour de grand Reynolds)
  
  with this overaller relation
  
  
  This comparison allow us to approve the preceding and next calculations. In fact, it shows if the drag coefficient is well estimated.
• Estimation of the boundary layer :
  
  
• Estimation of the shearing
  
  

The program finds the following results (click on to enlarge):