Liquid films in viscous flow

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Abstract
A trace of radioactive material dissolved in a liquid enables the thickness of a moving film to be determined by measurement of the radiation emitted. The method is rapid and accurate and an average thickness is obtained directly even though the surface of the film may be irregular. Six liquids, having viscosities ranging from 0.5 to 20 centipoises were observed in flow down the inner wall of a vertical tube. Liquids having viscosities of about 1 centipoise or less exhibit typical viscous behavior with respect to film thickness even when waves are present. Liquids having larger viscosities give values of the film thickness which are less than for true viscous flow. The departure from normal behavior increases with increasing viscosity and occurs only over the region where the liquid moves in wave flow. Surface tension is not a factor in either wave formation or wave flow.The wave motion appears at flow rates well within the viscous region and occurs when the Froude number exceeds unity. Equations derived for the viscous flow of liquid films on the inner wall of a vertical tube would be required where tube diameter is small or liquid viscosity large. Ordinarily the less complex equations for flow down a flat plate may be used. A theory of flow in the viscous region with waves present is suggested.

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