37 



rocking is obtained. For the bubbles rising in mineral oil and the corn syrup mixtures, only 

 rectilinear motion without rocking was observed. The maximum Reynolds number reached 

 during those tests was 150. 



The helical path of the bubbles assumes either a clockwise or counterclockwise direc- 

 tion, depending upon conditions at generation. The velocity of rise of these bubbles is not 

 affected by the sense in which the bubble revolves. The major axis of ellipsoidal bubbles 

 is always perpendicular to the direction of motion. 



The oscillatory motion of bubbles is probably caused by the periodic shedding of vor- 

 tices behind the bubble. Such vortex shedding has been observed experimentally for rigid 

 spheres at the same magnitudes of Reynolds numbers as for bubbles. 50 



BUBBLES IN FILTERED AND TAP WATER 



The results of the experiments in filtered water at room temperature and in cold filtered 

 water are presented in terms of drag coefficient and Reynolds number in Figure 26. The re- 

 sults of Bryn, 24 Allen, 9 and Gorodetskaya 30 are also included. It is seen that the drag curves 

 at the two different temperatures coincide in the spherical and spherical cap region. In the 

 region of ellipsoidal bubbles, the drag coefficient at a given Reynolds number increases with 

 increase in "A/" number. Gorodetskaya and Allen conducted their experiments in distilled 

 water. A comparison of their experimental data with those obtained in filtered water shows, 

 within experimental accuracy, no difference in the drag of air bubbles rising in filtered and 

 distilled water. 



The drag coefficients for air bubbles rising in tap water at two different temperatures 

 are given in Figure 27. Gorodetskaya's results in tap water at room temperature are included 

 in the figure. For comparison, the drag curves for bubbles in filtered water at room tempera- 

 ture and for rigid spheres are also shown. Again, in the region of spherical and spherical cap 

 bubbles, the drag curves at the two temperatures coincide. The value of the minimum drag 

 coefficient is, however, greater than that of the corresponding filtered water. In general, for 



Reynolds numbers up to about 300, the drag curves of bubbles in tap water follow closely the 



* 

 curve of rigid spheres. 



Thus, the results of the experiments (given in Figures 5, 26, and 27) show that for bub- 

 bles (ranging in equivalent radius from 0.035 to 0.25 cm) it is important whether the motion 

 occurs in filtered (distilled) or tap water. 



In view of the fact that merely filtering the water was sufficient to produce a change in 

 the drag of the bubbles, it is indicated that the presence of minute particles causes this 

 change. Minute particles, most of which can be removed by filtering, are known to exist in 

 ordinary tap water. Specifically, if such particles are present in the water a high concentration 



♦It should be noted here that the physical properties of tap water did not differ from those of filtered water. 



