influence of gravity as an initial step for obtaining information on the behavior of bubbles in 

 variable pressure fields. 



A body rising or falling under the influence of gravity reaches a constant velocity 

 (terminal velocity) when all forces acting on it are in equilibrium: 



Drag + Buoyant force + Weight = 



For rigid bodies, the drag will, in general, be a complicated function of the geometry of the 

 body, the velocity, and the physical properties of the medium, i.e., the density and viscosity. 

 For fluid bodies, such as drops and gas bubbles, the function is further complicated by the 

 fact that the body may be of changeable shape and that properties of the fluid inside the glob- 

 ule, such as density and viscosity, and interfacial effects may also be important factors. In 

 general, the shape that the fluid globule assumes is some complicated function of the hydro- 

 dynamic, viscous, and interfacial forces. 



The drag of fluid bodies may either be equal to (as is the case for small bubbles) or 

 less than that of the corresponding rigid body depending upon the conditions at the interface. 

 In the former case there exists, effectively, a rigid surface at the interface; in the latter case, 

 the fluid particles at the boundary have, in contrast to rigid bodies, nonvanishing tangential 

 velocities. The circulation inside the fluid body thus reduces the drag of the body. 



The experiments described in this report consisted of the determination of the terminal 

 velocity, shape, and path of single air bubbles rising freely in various liquids as a function 

 of bubble size. The possible effect of the walls of the container on the velocity of rise of 

 the bubble was also investigated. A summary of pertinent theoretical and experimental work 

 of other investigators is included. 



THEORETICAL SOLUTIONS 



Theoretical solutions for the drag of rigid and fluid spheres, moving slowly in an infi- 

 nite medium, have been obtained for the following boundary conditions at the surface of the 

 sphere: 



1. Rigid spheres 



a. Stokes' solution 2 

 (1) Velocity 



(a) The velocity vanishes. 



2. Fluid spheres 



a. Hadamard-Rybczynski's solution 2 * 3,4 

 (1) Velocity 



(a) The normal velocity component vanishes. 



(b) The tangential velocity components at both sides of the surface are equal. 



