ABSTRACT 



In connection with other investigations at the David Taylor Model Basin, 

 detailed information became necessary on the motion of air bubbles in variable 

 pressure fields. Since no information on the subject was available, a fundamen- 

 tal study of the motion of bubbles was undertaken. As an initial step, experi- 

 ments were conducted to determine the drag and shape of single air bubbles 

 rising freely in various liquids. 



The results of the experiments show that a complete description of the 

 motion of air bubbles is not possible by use of dimensionless parameters con- 

 taining the usual physical properties of the liquid (viscosity, surface tension, 

 density). Three types of bubble shapes were observed in each liquid, namely 

 spherical, ellipsoidal, and spherical cap. For a specific liquid, the shape of 

 the bubble was a function of its volume. 



For tiny spherical bubbles, the drag coefficients coincide with those of 

 corresponding rigid spheres. With increase in bubble size, a decrease in the 

 drag as compared to that of rigid spheres occurs in some liquids. Thus, the 

 drag curves of the spherical bubbles rising in various liquids fall between two 

 limiting curves, namely the drag curve of rigid and fluid spheres, respectively. 

 It was not possible to determine a criterion for the transition of the bubbles 

 from "rigid" to fluid spheres. The region of ellipsoidal bubbles extends over 

 different ranges of Reynolds numbers for the various liquids. The drag coef- 

 ficients of spherical cap bubbles are independent of bubble size and have a 

 constant value of 2.6. 



For bubbles (equivalent radius 0.03 to 0.30 cm) rising in tap water or 

 in water containing certain surface-active substances, experiments show an 

 increase in drag as compared to bubbles in pure water. 



Results of tests to determine the effect of the container walls on the 

 velocity of rise are presented. A description of the experimental apparatus 

 is given. A summary of the theoretical and experimental work of other in- 

 vestigators is also included. 



INTRODUCTION 



The tests described in this report are a continuation of experiments given in a previous 

 Taylor Model Basin report. 1 These experiments were initiated in conjunction with the work 

 under projects NS 713-201 and NE 051-237. The present tests, continued under NS 715-102, 

 were conducted for the purpose of investigating the motion of bubbles rising under the 



References are listed on page 43. 



