24 



below. Such effects were avoided in the experiments by sufficient spacing between the bub- 

 bles. However, the results of a few special observations indicate that proximity effects may 

 be appreciable. For example, tests in mineral oil show an increase of 9 percent and 39 per- 

 cent for bubbles of equivalent radius of 0.17 cm, rising 7.7 cm and 3.2 cm apart, respectively. 

 Napier 20 observed an increase of 6 percent for bubbles of 0.14 cm radius in water, rising 

 6 cm apart. The presence of the wake in the liquid thus results in higher velocities of rise 

 of the bubble. 



NONDIMENSIONAL PRESENTATION OF BUBBLE DATA 



In a previous section it was pointed out that presentation of the experimental data on 

 air bubbles in terms of dimensionless products gives complete correlation provided the vari- 

 ables considered in the analysis are complete and pertinent. The results of the Taylor Model 

 Basin bubble tests and those of Arnold, 10 Bond and Newton, 11 and Bryn 24 are given in terms 

 of the drag coefficient, Reynolds number and the parameter M in Figure 16.* Figure 17 pre- 

 sents the bubble data in terms of the drag coefficient, Weber number, and the parameter M. 

 The curve for filtered or distilled water at a temperature of 19 deg C was drawn through points 

 obtained from the experiments of Bryn and the Taylor Model Basin tests. 



Examination of Figure 16 or 17 shows no systematic arrangement of the curves with 

 change in the parameter M, which is constant for a specific liquid. It can, therefore, be con- 

 cluded that neither of the nondimensional sets presented nor any other complete set using 

 the same six variables (namely, velocity, acceleration of gravity, density and viscosity of 

 the liquid, surface tension, and equivalent radius) is sufficient for a complete description of 

 bubble motion. 



The question now arises whether correlation of bubble data could be obtained by using 

 two additional dimensionless parameters, for example, the liquid to air viscosity and density 

 ratios or the Reynolds number inside the bubble and the density ratio, etc. The results of 

 the experiments conducted do not permit conclusions regarding the importance of these 

 parameters. A short discussion of the significance of the internal Reynolds number will be 

 given in subsequent sections. 



SPHERICAL BUBBLES 



It was observed in the experiments that, as the bubble size was increased, a change 

 in bubble shape from spherical to ellipsoidal to spherical cap shape occurred in all liquids. 

 Very small bubbles are spherical. Larger bubbles are flattened, i.e., ellipsoidal in shape, 

 whereas very large bubbles assume a spherical cap shape. Of course, the volumes at which 



*The results for tap water and for water containing Glim are not shown. They will be discussed in subsequent 

 sections. 



