17 



RESULTS 

 TERMINAL VELOCITY OF AIR BUBBLES 



The results of tests to determine the velocity of rise of air bubbles in various liquids 

 are most conveniently presented as a function of the equivalent radius of the bubble, defined 

 as the radius of a sphere having the same volume as the bubble. Figures 4-13 show the ter- 

 minal velocity of air bubbles rising freely in tap (unfiltered) and in filtered water (including 

 data from other investigators), in water containing Glim, in mineral oil, Varsol, turpentine, 

 methyl alcohol, and two corn syrup-water mixtures as a function of the equivalent radius. 

 Figure 14 presents Bryn's results in an ethyl alcohol-water mixture and two glycerine-water 

 mixtures. Figure 15 summarizes all velocity curves (except those for tap water). A compila- 

 tion of the properties of the liquids is given in Table 1 (see page 11). 



In general, the results as seen from Figure 15 indicate that for small (spherical) air 

 bubbles of given volume, the viscosity of the liquid is the most important property determining 

 the rate of rise. Very large bubbles (spherical caps) rise independently of the properties of 

 the liquid. 



WALL AND PROXIMITY EFFECTS 



As indicated previously, the effect of the container walls on the velocity of a bubble 

 had to be determined if the results of tests conducted in a tank of limited dimensions were 

 to b& applied to bubble motion in an infinite medium. Tests were, therefore, conducted in 

 tanks of different sizes in water, Varsol, and mineral oil. Figure 4 gives the results of tests 

 conducted with filtered water by several investigators including the Taylor Model Basin. 

 The cross sections of the containers used are also indicated in the figure. No wall effect 

 is noticeable from these results. For example, Gorodetskaya's results for bubbles ranging 

 from 0.01 to 0.07 cm rising in a tube of 5 cm diameter show no wall effect when compared 

 with results of tests conducted in larger containers. The results of the present experiments, 

 given in Figures 5, 6, 7, 9, and 10, show within experimental accuracy, the absence of any 

 wall effect for the range of bubble sizes tested. Subsequent tests in the other liquids were 

 made in the small tank only and the results may be applied to the case of an infinite medium. 



No systematic investigation was made of vertical proximity effect, i.e., the effect of 

 the wake created by the passage of a bubble on the motion of a bubble rising at a distance 



*The results of the 81 percent (by weight) glycerine-water mixture have been omitted. Bryn presented these 

 results in terms of drag coefficient and Reynolds number, from which the terminal velocity can be computed. 

 In the region of bubble size where the rate of rise is shown to be a function of size only (hence a common veloc- 

 ity curve for all liquids; see Figure 15), the velocity curve fbr the 81 percent mixture falls appreciably above 

 the common curve. The discrepancy is probably due to erroneous evaluation of the two dimensionless parameters 

 for the 81 percent glycerine-water mixture. 



