19 



velocity of rise of bubbles in liquids other than water. 8 ' 15 Data from these 

 experiments are combined and presented in Figure 14. Because these are incom- 

 plete and show apparent inconsistencies, the conclusions which can be drawn 

 are rather meager and tentative. A few generalizations appear justified both 

 on the basis of the data and from the expected influence of the variables in- 

 corporated in the parameter M. 



100 





















































80 





















































60 























































\ 



















































20 



N 



V 

















































.M 10 





\ 

















































^ b 







^ 















































o|ro 6 



M-ZxIO'- 2 /^ 

 M ■ 1 x lO"-*/ 



>v- 















































\ 



^ 















M-lxlO~-^ 



a° 



-o-o 









M«2.6xlO""(TMB) 



2 ■ 







& 











o 



o 













s 



^ 



J\ 









y 



f 







r 



» Woter + 13% Ethyl Alcohol (Bryn) 

 □ Water + 42% Glycerins (Bryn) 



















s 









i 









T 



• Aniline (Allen) 



o Water + 56% Glycerine (Bryn) 



a Water + 81 % Glycerine (Bryn) 



























I 







/ 





0.4 















U'9.3x\0'^ 



s 





j 





i 



























V 



X 





/ 

























1 





















































40 60 100 200 400 1000 2000 4000 

 Reynolds Number 2,or e U 

 M 



40,000 100,000 



Figure 14 - Drag Coefficient as a Function of Reynolds Number for 



Different Values of the Parameter M as Obtained from Data on the 



Terminal Velocity of Bubbles in Various Liquids 



For very low Reynolds numbers, the bubble behavior is almost inde- 

 pendent of the value of the parameter M, the bubbles acting as rigid spheres. 

 A puzzling aspect of the problem is provided by the fact that there is a crit- 

 ical value of the Reynolds number beyond which the drag coefficient of the bub- 

 ble departs from that of rigid spheres, yet the bubbles are still spherical. 

 The available data are not sufficient to indicate definitely whether the Reyn- 

 olds number at which this break takes place is a function only of M or whether 

 the phenomenon depends upon some property of the fluids not considered in the 

 foregoing analysis. A tentative observation is that the greater the value of 

 M, the lower is the critical Reynolds number. 



