304 



MOTION OF THE GAS SPHERE 



The observed size and displacement of the bubble are plotted in Fig. 

 8.11 for comparison with the predicted curves for Zo' = 2.0. Because 

 of the nonspherical shape of the contracted phase, one-half the hori- 

 zontal bubble diameter is plotted. It is seen that the first half cycle is 

 in good agreement with theory, but that the later migration is much 

 less than predicted. This difference is consistent with the greater 

 hydrodynamic resistance of the actual flattened bubble surface as com- 

 pared to the idealized sphere assumed in the calculations The ob- 



40 60 80 100 



TIME (msec) 



Fig. 8.11 Motion of spark generated bubbles for Zo' = 2.0. 



120 



served period of 45 msec, is appreciably less than the computed 54 

 msec, but the discrepancy is quantitatively explained by the effect of 

 the free surface. 



The model experiments under reduced pressure are seen to agree 

 rather satisfactorily, on the whole, with Taylor's theory, the discrep- 

 ancies being largest in the neighborhood of the unstable minima where 

 the velocities are large and the bubble surface far from spherical. The 

 differences observed are similar to those found for explosion bubbles, 

 and this similarity makes the spark technique a useful and significant 

 one in analyzing large scale explosions. It must be remembered that 

 the scaling does not and cannot readily be made to include exactly to 

 scale the viscosity and vapor pressure of the fluid and the way in which 

 energy is released. Fortunately, these sources of error, discussed by 

 Taylor and Davies, are not large enough to cause appreciable dif- 

 ferences in the results. Other experiments made by Taylor and Davies 

 include records corresponding to Zo' = 2.8, and a number of interesting 



