THE UNIVERSITY OF MICHIGAN College of Engineering Department of Mechanical Engineering Cavitation and Multiphase Flow Laboratory Report No. UMICH 033710-14-I DISCUSSION BY F. G. HAMMITT OF "A Photographic Study of the Effect of an Air Bubble on the Growth and Collapse of a Vapor Bubble Near a Surface," byR.H. Smith and R.B. Mesler by Frederick G. Hammitt Profes sor-in-Charge Financial Support Provided by: National Science Foundation Grant No. GK-730 April 1972

I believe this is a very interesting paper in an area where relatively little has been done, i.e., the study of the detailed effects and mechanisms involved in the interactions between bubbles in a liquid. I would like to include in the record at this point somewhat related experiments which we have done with spark generated bubbles in a small, transparent tank in water. High-speed motion pictures (Fig. l-a,b, c of discussion; reproduced from ref. 1 of discussion for convenience) show collapse sequences al close to a solid plate, b) two bubbles of similar size collapsing in proximity to one another, ca a bubble collapsing close to a rubber diaphragm (backed by an air cushion). As expected from numerous theoretical analyses (ref. 2 of discussion, e.g. the bubble collapsing close to a solid surface is attracted toward the surface during the collapse. The "double-bubble" case (Fig. 1-b of discussion) is similar in that it is almost equivalent to a single bubble near a solid wall. A hypothetical solid wall would thus form a plane of symmetry for the double-bubble case. The bubble collapsing close to a flexible membrane has been investigated recently by Gibson (ref. 3 of discussionS. The case is some*what similar to a bubble near a free surface, where it is known that the bubble will be repelled from the surface during its collapse (ref. 4 of discussion, e.g.. The same is true of a sufficiently flexible membrane as is shown by Fig. 1-c of this discussion. In addition the jet formed during collapse is oriented away from the surface. Fig. 2 (from ref. 1 also) shows the velocity of upper and lower bubble walls during each of these collapse sequences. These latter facts may be of considerable importance in explaining the surprising cavitation damage resistance capability of some rubber and elastomeric coatings. Experiments of this type also appear to offer hope for a rational design of a cavitation-resistent soft material.

2 References 1) Timm, E. E. and Hammitt, F. G., "Bubble Collapse Adjacent to to a Rigid Wall, a Flexible Wall, and a Second Bubble, " 1971 ASME Cavitation Forum, 18-20. 2) Kling, C. L. and Hammitt, F. G., "A Photographic Study of SparkInduced Cavitation Bubble Collapse, " ASME Paper No. 72-FE-20 (to be published, Trans ASME, J. Basic Engr. ). 3) Gibson, D. C., "The Kinetic and Thermal Expansion of Vapour Bubbles," CSIRO, Division of Mechanical Engineering, Melbourne Australia, 1970. 4) Cole, R.H., Underwater Explosions, Princeton University Press, 1948. List of Figures i a-c. Spark bubble collapse as function of adjacent objects. 2 a-c. Wall motion of collapsing bubble near adjacent objects.

3 t = 2cC 2s t - 200 t 200 As lfc==^ >.c< S. ~ 6 r.. 4" 4 _ A 4 t^^ y ~ o ^ _t_-s - t 6670 t5_0__.L -0. 4.4 -0 Scale t i 800 s t 1040 Q Fig. 1 a. Fig. 1 b Fig. 1 c Fig 1 a-c. Spark bubble collapse as function of adjacent objects. 3264

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