Ind. Eng. Chem. Fundam. 1980, 79, 133
LETTER TO THE EDITOR Comments on: “Prediction of Changes in Bubble Size Distribution Due to Interbubble Gas Diffusion in Foam” Sir: Recently, Lemlich (1978) and Ranadive and Lemlich (1979) presented theory and results for the effect of interbubble gas diffusion on the bubble size distribution of otherwise stable foam. The computation involved a multiple iterative technique that was rather comsumptive of computer time, requiring of the order of 2000 C.P.U. s with an Amdahl470 V6 computer. So, in accord with an idea of Ross (19791, we recalculated the results by means of a fourth-order Runge-Kutta approach. We employed a dimensionless radial interval of 0.001 and a dimensionless time interval of 0.01 to solve at each time step the several thousand simultaneous equations, along with deliberate conservation of gas volume. The results agree with what was obtained previously, yet required less than 10% of the original computer time. What is more, tripling the size of these intervals yields almost the same results and further reduces the computer time to about 1 % . As with the original, the new computational procedure can be applied to any initial bubble-size
distribution. Accordingly, for the forseeable future, we will send a printed copy of our computer program to any interested reader upon request to the second writer.
Literature Cited Lemlich, R., Ind. Eng. Chem. Fundam., 17, 89 (1978). Ranadlve, A. Y., Lemllch, R., J. COlloidInterface Sci., 70, 392 (1979). Ross, S., private communication, Feb 26, 1979.
Department of Chemical and Nuclear Engineering University of Cincinnati Cincinnati, Ohio 45221
Hsing Chung Cheng Robert Lemlich*
Received for review September 4 , 1979 Accepted September 13, 1979 This material is based upon work supported by the National Science Foundation under Grant No. ENG 77-09887.
