452 



FORMATION AND DISSOLUTION OF AIR BUBBLES 



bubble and to the difference between the pressure in 

 the bubble and the partial pressure of air dis- 

 solved in the water. The constant of proportionality 

 is again 4 X 10~' mole per sq cm per second per at- 

 mosphere. An alternative formulation, assuming a 

 spherical bubble, is in terms of the rate of decrease of 

 the bubble diameter per second. In water saturated 

 with air at the sm-face, this rate increases from 

 8 X 10~* cm per sec at a depth of 5 meters to 

 18 X 10~' cm per sec at a depth of 100 to 200 meters. 

 Beyond these depths there is no further significant 

 increase. 



0.005 0.01 0.02 0.06 0.1 0.2 0.5 1 2 



RADIUS OF BUBBLE IN CENTIMETERS 



FiGDRE 4. Rate of rise of air bubbles in still water. 

 A. Rectilinear motion, spherical shape. B. Helical 

 and twisting motion, flattened shape. C. Irregular. 

 D. Rectilinear motion, distorted mushroom shape. 



These theoretical ideas concerning the formation 

 and dissolution of bubbles have been tested in a 

 series of simple experiments; ^ their agreement with 

 the theory appears to be satisfactory. However, it 

 remains uncertain to what extent these conclusions 

 reached are applicable to the conditions prevailing 

 in wakes. According to the experiments, a bubble 

 0.1 cm in radius, which is the resonant size for 3 kc 

 sound, should dissolve completely in about 20 min- 

 utes. If the wake originally contains bubbles of all 

 sizes up to 10~^ cm radius, then as the smaller bubbles 

 contract, the larger bubbles also decrease in size; and 

 some bubbles of the smallest size should be found 20 

 minutes after the formation of the wake. In rough 

 agreement with theoretical expectations, acoustic 

 effects of wakes at supersonic frequencies are ob- 

 served to persist over periods from 15 to 45 min- 

 utes. In a wake, bubbles travel in a field of turbulent 

 motion, rising gradually to the ocean surface where 



they may disintegrate; this process constitutes an- 

 other important factor Umiting the lifetime of wakes. 

 The next point to be considered, therefore, is the 

 buoyancy and the rate of ascent of air bubbles in sea 

 water. 



27.2 BUOYANCY AND RATE OF ASCENT 



The unimpeded rise of bubbles through still water 

 has been analyzed in great detail.' From this analy- 

 sis of all available experimental data and from certain 

 theoretical considerations, a curve was constructed 

 which gives the rate of rise of air bubbles in water as 

 a function of the radius of the bubble and is repro- 

 duced in Figure 4. It will be noted that the velocity 

 reaches a maximum at a radius of about 0.1 cm and 

 varies only slightly with the radius thereafter. Sev- 

 eral distinct types of motion and shapes of bubbles 

 have been found to be characteristic in various 

 ranges of bubble radii and are shown in Figure 4. No 

 exact delineation of these radius intervals can, how- 

 ever, be made. All observers agree that tor very small 

 bubbles the motion is linear. For large bubbles the 

 motion is also approximately linear, although some 

 irregularities have been reported. A noteworthy 

 feature of the velocity curve for radii up to 0.04 cm 

 is that it coincides with the empirical curve for the 

 rate of fall through water of spheres of specific 

 gravity 2. In connection with the laboratory experi- 

 ments on bubble screens,^ which will be described in 

 the next chapter, this relation between bubble radius 

 and rate of rise has been tested empirically, and ex- 

 cellent agreement was found over a range of bubble 

 radii from 0.01 to 0.1 cm. These rates of rise of bub- 

 bles in still water, as predicted from purely gravita- 

 tional theory, would lead to the conclusion that all 

 bubbles of acoustically effective size would reach the 

 ocean surface in a time much shorter than the com- 

 monly observed lifetime of an acoustic wake. 



However, the motion of the ship's hull and the 

 action of its propellers continually set up throughout 

 the wake a strongly turbulent internal motion, which 

 interferes with the streaming of bubbles toward the 

 surface resulting from their buoyancy. This phe- 

 nomenon is analogous to the transportation of sus- 

 pended material in rivers. Most suspended material 

 is heavier than water and, therefore, would settle 

 out in nonturbulent flow. But through turbulence 

 this material is maintained in a state of suspension. 

 Similarly, in a wake the bubbles rise toward the sur- 

 face, .while turbulence counteracts this tendency. 



