39 



of these particles would be found at the surface of the bubble. The particles at the surface 

 would travel with the bubble, hence imparting, in effect, a rigid surface to the bubble. With 

 increasing bubble velocities, the shear forces become large in comparison to the forces hold- 

 ing the particles to the surface and hence at a certain critical velocity no high concentration 

 of particles on the surface can exist. 



Figure 28 compares the drag curve of bubbles in tap water obtained in the Model Basin 

 study and the experimental data of air bubbles rising in water at room temperature as obtained 

 by various other investigators. Reports of these other studies give no information regarding 

 the type (tap, filtered, or distilled) of water used, but presumably these experiments were 

 also conducted in tap water. 



EFFECT OF SURFACE-ACTIVE SUBSTANCES 



The effect of surface-active substances on the rate of rise of air bubbles has previous- 

 ly been investigated by Gorodetskaya, 30 who added small concentrations of various alcohols 

 to water and concluded that, beyond a certain critical concentration of the surface-active sub- 

 stance, the rate of rise of the air bubbles is not affected. Stuke 40 ran experiments with oxy- 

 gen bubbles rising in water containing small concentrations of caproic acid. The concentra- 

 tions of the alcohols and the caproic acid were relatively small, hence the decrease in the 

 surface tension was only about 1 dyne/cm. In the present study, the authors conducted tests 

 in water containing Glim, a liquid detergent. The concentration of Glim (0.42 percent by vol- 

 ume) was high enough to decrease the surface tension by 40 dynes/cm. No measurable change 

 in the viscosity and density of the test liquid due to the presence of Glim was noted (see 

 Table 1). This was also true for the alcohol and caproic acid solutions. Results from these 

 experiments are presented in terms of the drag coefficient and Reynolds number in Figure 29. 



The drag curve for bubbles in the Glim solution, as well as the experimental data from 

 the other investigators in water containing at least the critical concentration of the surface- 

 active substance, follows the drag curve of rigid spheres to a Reynolds number of about 200. 

 In the region of Reynolds numbers of 10 to 200, the drag curve for bubbles rising in a pure 

 liquid having an "M" number very close to that of the Glim solution follows the drag 

 curve of fluid spheres. Thus, the motion of bubbles in water containing surface-active ma- 

 terials cannot be compared with that of bubbles in pure liquids on the basis of drag coefficient, 

 Reynolds number, and "M" number, even in the region of ellipsoidal bubbles. Although the 



*As shown in the Appendix, no significant difference in the terminal velocity of oxygen and air bubbles rising 

 in distilled water is obtained. Hence, inclusion of the results of the tests with oxygen bubbles in water contain- 

 ing surface-active substances is justified. 

 **For concentrations below the critical, the drag curve lies between that of pure water and the curve shown in 



Figure 29. 



40 



10 



***The "M" number of Glim was 2.78 X 10 , that of Varsol, for example, was 4.3 X 10 



