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Theoretical analysis reveals that bubble velocity in vertical tubes is influenced by several factors, indicating new insights into bubble dynamics.
A theory of the steady motion of a long bubble rising through an infinite plane vertical tube of liquid is presented. It is shown that, contrary to current belief, the flow is not uniquely determined by the width h of the tube and the acceleration of gravity g alone, but that the speed U of the bubble can also be prescribed. However, a criterion of stability singles out the unique physically significant flow of this type as the one which maximizes the velocity of the bubble. With the aid of a difference-differential equation derived from the free-boundary condition, the Froude number U/(gh)1/2 for this latter case is estimated to exceed 0·2363, a value slightly higher than that indicated by earlier work on the problem.
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P. R. Garabedian (1957) studied this question.
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