Abstract
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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