THE DRAG AND SHAPE OF AIR BUBBLES MOVING IN LIQUIDS 



by 

 Benjamin Rosenberg 



ABSTRACT 



A survey is made of the available information on the motion of air bubbles in 

 liquids. These results show considerable scatter and uncertainty. Therefore, some 

 tests were repeated in order to determine the rate of rise of air bubbles in water. 



Dimensional analysis is used to obtain the parameters which can best be used 

 to describe the results. These are the drag coefficient, the Reynolds number, and a 

 third parameter which involves the properties of the liquid only. The dependence of 

 the drag, shape, and path of the bubble on the Reynolds number is determined. Since 

 the tests were confined to one liquid, the importance of the third parameter could not 

 be ascertained. Tire results indicate that this parameter may have considerable influ- 

 ence upon the motion and shape of a bubble for a large range of Reynolds numbers. 



INTRODUCTION 



The tests described in this report were initiated because of the 

 need for these data in conjunction with the work under project NS71 3-201 and 

 NE05-I-237. 



The behavior of bubbles in pressure gradients is of some interest in 

 hydrodynamic research, having been considered in connection with a variety of 

 problems. 1 ' 2 ' 3 Since a gravity field is the simplest pressure field in which 

 to study bubble shape and motion, the experiments consisted of the determina- 

 tion of the velocity of rise of air bubbles in water along with observations 

 of the shapes and paths of the rising bubbles as a function of their size. 

 In addition, some theoretical discussion is given concerning the parameters 

 which determine the bubble characteristics. Pertinent data from other ex- 

 periments are included and discussed. 



The results show that the velocity of rise, bubble shape, path, and 

 general kinematic behavior depend upon the bubble size, the pressure gradient, 

 the density and viscosity of the medium and, to a lesser extent not fully in- 

 dicated by available data, upon the surface tension. 



References are listed on page 22. 



