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Consider a gas bubble rising in a liquid - filled tube. If the bubble volume ( V B ) and tube radius ( R T
Consider a gas bubble rising in a liquidfilled tube. If the bubble volume and tube radius are such that
then the bubble will be highly elongated. Assume that the bulk of the bubble forms a cylinder of radius and length as shown inthe figure The liquid film between the bubble and tube wall is expected to be very thin Consequently, local rectangular coordinates can be used in the film, as shown in the figure It is convenient to fix the coordinate origin on the wall.
Assuming that the flow in the liquid film is fully developed and that the bubble dimensions are known, derive an expression for the steady rise velocity of the bubble, State any additional assumptions that are needed. Hint: The bubble velocity is not uniform, so that the velocity at the gasliquid interface differs from the mean value for the bubble.
The Xmomentum P
The momentum and
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