516 



Discussion 



G. L. CHAHINE 



I would like to congratulate the author on his 

 very fine work and to comment on his conclusion 

 that the Rayleigh-Plesset equation represents fairly 

 well the growth of bubbles attached to a wall. As 

 is well-known, the Rayleigh-Plesset equation relates 

 the growth and collapse of a spherical bubble, with- 

 out relative motion with respect to the unbounded 

 surrounding fluid, for a given variation of pressure 

 far from it. It then seems really surprising that 

 such an equation could describe so well the growth 

 of the bubble on a blunt nose as shown in Figure 31. 

 None of the requirements for the validity of the 

 Rayleigh-Plesset equation are fulfilled; 



a. the bubble is non-spherical, even if we 

 agree that the shape in the figure plan 

 is a portion of a circle, 



b. presence of a wall, 



c. shear flow around the bubble, 



d. relative motion between the bubble and the 

 fluid (as pointed out by the author) . 



Moreover, the presence of gas inside the 

 bubble is not taken into account, while the gas 

 behavior has been shown to be very important 

 [Chahine (1974, 1976)]. We believe that the good 

 agreement between experimental results and analyt- 

 ical computations shown in this paper is mainly 

 due to: 



a. the time of observation is too small com- 

 pared to the hypothetical lifetime of the 

 bubble. (For a bubble radius of 1.3 mm 

 and an external pressure of 5,000 N/m , 



R. differs only 4% from the experi- 



the Rayleigh time is about 0.7 ms and the 

 lifetime is greater than 1.5 ms ; say 10 

 times the observation time.) 

 b. in order to integrate numerically the 

 Rayleigh-Plesset equation one needs two 

 initial conditions: an initial radius 

 and an initial growth rate. If R. and R^ 

 replace these initial conditions it is 

 not surprising that the result deduced 

 for 



mental result. 

 Concerning Table 4, the calculated relatively 

 small effect of surface tension and viscosity is 

 in good agreement with previous asymptotic studies 

 [Chahine (1976) and Poritsky (1952)]. 



REFERENCES 



Chahine, G. L., (1974). Etude Asymptotique et 

 Experimentale des Oscillations et du Collapse 

 des Bulles de Cavitation. ENSTA Report 042, 

 CEDOCAR, MF 50831. 



Chahine, G. L., (1976). Etude Asymptotique du 

 Comportment d'une Bulle de Cavitation dans un 

 Champ de Pression Variable. Jl. de Meoanique, IS 

 (2), pp. 287-306. 



Poritsky, H. , (1952). The Collapse or Growth of 

 a Spherical Bubble or Cavity in a Viscous Fluid. 

 Proceeding of the First U.S. National Congress in 

 Applied Mechanias, ASME, pp. 813-821. 



