in lubricating oils. His results, however, show considerable scatter. Reports by Pickert, 26 

 Pekeris, 27 Worster, 28 and Datta et al 29 give summaries of the results of experiments of 

 other investigators. 



Gorodetskaya 30 investigated the effect of surface-active substances on the rate of 

 rise of air bubbles in water. Further tests on air bubbles are reported in References 31-36. 

 In addition, a limited number of tests using gas bubbles of oxygen, nitrogen, and a mixture 

 of carbon dioxide and oxygen have been carried out in artificial sea water. 37 ' 38 A number of 

 tests with oxygen bubbles were also conducted in water 37 and in aqueous solutions of sodium 

 hydroxide. 39 Recently, Stuke 40 investigated the rate of rise of oxygen bubbles in pure (pre- 

 sumably distilled) water and in water containing surface-active substances. The results of 

 the tests with gas bubbles (given in the Appendix) show no significant change in the rate 

 of rise of the bubbles with change in the gas inside the bubble. 



Because of the scatter of previous results of experiments on the rate of rise of air 

 bubbles in water, Rosenberg 1 repeated these tests for a large range of air bubble sizes. He 

 showed the geometric similarity between large bubbles of spherical cap shape and suggested 

 the use of three dimensionless parameters, the drag coefficient, the Reynolds number, and 

 the parameter M for describing bubble motion in liquids. 



WALL EFFECT 



Previous investigations on the motion of air bubbles in liquids were, with a few ex- 

 ceptions, conducted in containers of limited dimensions. Only for very large bubbles did 

 Exner 13 and Bryn 24 make their measurements in lakes. Inasmuch as the effect of the walls 

 of the container on the rate of rise of bubbles was unknown, it was generally neglected. 

 Miyagi 12 conducted a few tests in containers of different sizes and found that a reduction of 

 4: percent in the rate of rise occurred for the range of bubble sizes investigated. Dubs 41 de- 

 rived, from energy considerations, an analytical expression for the wall effect and concluded 

 that a bubble of the same radius as its cylindrical container has a velocity of rise of zero. 

 It is clear that this conclusion is in error, as experiments on cylindrical bubbles have shown. 



As indicated previously, no analytical solution has yet been obtained for flows beyond 

 the region of slow flow; consequently, the much more difficult problem of also including a 

 finite boundary in the equations of motion becomes less capable of solution. For very slow 

 flow about rigid spheres moving in an infinite cylindrical container, Ladenburg 42 obtained 

 an analytical solution for the effect of the boundary on the drag and, consequently, the veloc- 

 ity of the sphere. McNown et al 43 arrived experimentally at a wall correction coefficient for 

 rigid spheres descending in a cylindrical container. Since air bubbles of small volume rising 

 in water behave essentially like rigid spheres, this correction factor may be applied to such 

 bubbles as long as the flow is still in the Stokes region. 



With the exception of a number of tests 16,17 for large bubbles, no data concerning the 

 effect of the boundary on the rate of rise of gas bubbles beyond the region of slow flow are 



