On the motion of bubbles in capillary tubes

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Abstract
The average thickness of the wetting film left behind during the slow passage of an air bubble in a water-filled capillary tube of circular cross-section has been determined experimentally as a function of bubble speed and bubble length. For bubbles of length many times the tube radius, the ratio of film thickness to tube radius is found to be a function of the capillary number only, in agreement with previous experimental studies. As has been found previously, the asymptotic result of Bretherton (1961) significantly underpredicts the film thickness, the discrepancy being greatest at the lowest speeds. For bubbles of length less than about 20 tube radii, on the other hand, good agreement with the Bretherton theory is obtained over two orders of magnitude in bubble speed. The theoretical profile of long bubbles is shown to be unstable; however the explanation of the observed behaviour is, as yet, incomplete.

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