An empirical solution of Equation [5] can be obtained by determining the rate 

 of rise as a function of bubble size in different liquids. 



PREVIOUS EXPERIMENTAL WORK 



Much experimental work has been done on the rise of bubbles in liq- 

 uids. However, when an attempt was made to compile results from various 

 sources, it was found that the data were in poor agreement. The most success- 

 ful work appears to have been done by Allen 8 who determined the rate of rise 

 of very small bubbles in water and aniline. 



The scatter and unreliability of the previous results may be due to 

 several causes: 



1. Temperature Fluctuations. The parameter M contains the viscosity 

 of the medium as one of its factors. Since the viscosity varies considerably 

 with temperature and it is desirable to maintain M constant for any series of 

 tests, temperature control is Important. 



2. Inaccurate Methods of Measurement. The two important measurements 

 are the rate of rise and the size of the bubbles. Rate of rise was often de- 

 termined by timing the ascent of the bubble over a predetermined distance by 

 means of a stop watch. Most frequently the bubble size was measured by col- 

 lecting the bubble in an Inverted graduated cylinder and reading the volume 

 displaced, the usual uncertainty of measurement being about 0.1 cc. These 

 techniques were not considered very satisfactory for the accuracy desired, 

 particularly for non-spherical bubbles. Allen obtained results for spherical 

 bubbles only. He caught the individual bubble and then measured the radius 

 by means of a microscope equipped with a micrometer eyepiece. The rate of 

 rise was determined by use of a stop watch. For the small bubbles investi- 

 gated, the terminal velocity is so low and the tube used was sufficiently long 

 that a precise measurement of the rate of rise could be made. 



3. Wall Effect. The influence of the walls of the tube is such as to 

 reduce the terminal velocity of the bubbles. For bubbles in the viscous re- 

 gion of flow a correction to the terminal velocity often used was that devel- 

 oped by Ladenberg 9 



U. = (l + 2.4£r)u [6] 



where U is the terminal velocity of the bubble in the tube, 



U„ is the terminal velocity of the bubble in an infinite medium, 

 r is the radius of the bubble, and 

 R 1 is the radius of the tube. 



