We can, of course, in principle extend this model without difficulty to include rate coefficients dependent on the polymer to any finite size, However, if this dependence had to be carried to any appreciable length of polymer, calculations in this sty1e circumstances it might be preferable to reformulate the whole problem in terms of a continuous dependence of the rate coefficients on size, and to seek approximate solutions to the resulting differential equations in terms of suitable distributional forms. The characteristics of upward gas-liquid flow in a vertical annular duct were investigated. The flow regime studied was the climbing film regime in which water flowed as a film up the inner core of the annulus while air flowed in the annular space, the outer wall of the annulus remaining dry. Friction losses, air velocity distributions, and film characteristics were studied, the latter by photographing the climbing film through the transparent outer tube. Friction loss and film thickness were correlated with Lockhart-Martinelli parameters, X, 0, and RL. The presence of the climbing film caused the point of maximum velocity of the air profile to move toward the outer tube, indicating that the film created a rough wall condition. The inner portion of the velocity profile was correlated by Nikuradse's rough tube equation, while the outer portion was correlated by a logarithmic equation which previous workers have reported for single-phase flow. Kapitza's theory of wave formation was applied to the climbing film and was found to predict reasonable values for the mean film thickness. However, it failed to predict reliable values for the wavelength of surface waves.

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