12 



TABLE 1 



Description of the Motion and Shape of Air Bubbles 

 in Water as a Function of the Bubble Size 



centimeters 



Re 



Description 



< 0.04 



0.04 - 0.062 



0.062 - 0.077 



0.077 - 0.24 



0.24 - 0.35 



0.35 - 0.88 



>0.88 



<70 



70 - 400 



400 - 500 



500 - 1100 



1100 - 1600 



1600 - 5000 



>5000 



Spherical bubbles traveling 

 in rectilinear paths; same 

 C D as for rigid spheres . 



Spherical bubbles traveling 

 in rectilinear paths; C D 

 less than for solid spheres. 



Oblate spheroid, rectilinear 

 motion. 



Oblate spheroid, helical 

 motion. 



Oblate spheroid, essentially, 

 but shape becomes increasing- 

 ly irregular with increasing 

 Re; motion is almost recti- 

 linear . 



Transition - oblate spheroid 

 to spherical caps, shape is 

 very irregular and fluctu- 

 ates continuously, motion is 

 almost rectilinear. 



Spherical caps, rectilinear 

 motion; C n almost constant 

 at about u 2.6. 



Figures 7 and 8 show the shapes and paths of representative bubbles. 

 Except for the spherical bubbles, the shape fluctuates as the bubble rises. 

 A bubble moving in a helical path always maintains its axis of symmetry par- 

 allel to the direction of motion. The paths for bubbles of the same size may 

 vary considerably due to differences in conditions at generation and to dis- 

 turbances such as turbulence and thermal currents. It was found that the heli- 

 cal paths generally decreased in pitch and diameter as the bubble size in- 

 creased. As the bubble radius Increased from 0.075 to 0.22 cm the pitch de- 

 creased from 7 cm to 4 cm while the diameter of the helix decreased from 1 cm 

 to 0.4 cm. 



