theless, it has been suggested that bubbles can still be 

 present. 41 A bubble of equilibrium size must satisfy the 

 following equation: 36 ' 43 



+ 21 



where 



p v - Pressure due to dissolved gas and water vapor 

 p - Hydrostatic pressure 



T - Surface tension 



r - Radius of bubble 



The last term caused by the surface tension can be 

 neglected when the radius of the bubble is large. The 

 partial pressure of the dissolved gases and the water vapor 

 must then balance the hydrostatic pressure. Equilibrium 

 bubbles are therefore only possible close to the surface. 

 However, these bubbles are unstable. A bubble slightly 

 larger than the equilibrium size will continue to grow since 

 the term due to the surface tensions gets smaller with 

 increasing diameter. These bubbles will soon rise to the 

 surface and disappear. A bubble smaller than equilibrium 

 size will be forced into solution due to the increasing pres- 

 sure from the surface tension. Bubbles have been utilized 

 in the past in the form of bubble screens, etc. , but the 

 bubbles must be produced continually for as long as the 

 effect is desired.^ It was observed on a few occasions that 

 small bubbles were stabilized in the water by adhering to 

 particulate matter. This partly increased the effective 

 surface of the bubble and thereby slowed its rate of rise to 

 the surface and partly added mass to the bubble counter- 

 acting the buoyant force. Samples in which this occurred 

 showed a large attenuation, and the results are not included 

 in the data presented. 



90 



