The Motion of Long Bubbles in Conical Tubes
Date Issued
2011
Date
2011
Author(s)
Liu, Shih-Wei
Abstract
Abstract
The present study is aimed at investigating theoretically the migration and deformation of a long bubble moving through a liquid-filled conical tube.
A tapered cylindrical body bounded by two spherical caps with different radii is proposed as a simplified physical model for the long bubble in a conical tube. As the long bubble migrates through the conical tube, three flow regimes were defined for the surrounding liquid flow according to their flow characteristics: the nearly stagnant region near the two spherical caps, the thin film region with creeping flow between the tube wall and side surface of the bubble, and the transition region in between.
The lubrication approximation is then applied to simulate the creeping flow in the thin film region. The velocity distribution and volume flow rate therein are thus derived. With the constant-volume constraint and the conservation of the bubble, the migration speed, the length change of the bubble, and the variation of the thin film thickness are computed finally. The results indicate that the thin film thickness always grows with the radial coordinate, r, to the 1⁄3 power. It is also found that as the bubble migrates, both the migration speed and length of the bubble decrease, approaching a sphere eventually as required by the second law of thermodynamics. The most important and interesting conclusion of this study is that even with a decelerating motion, the resultant force acting on the bubble always vanishes, indicating that such a migration is not the same as a rigid body motion according to the Newton’s second law. Its global migration is due to the unequal deformation of the two ends of the long bubble. Such a migration due to unequal deformation is thus named “deformotion” by the present study!
Subjects
bubble
conical tube
capillary pressure
thin-film flow
migration
deformotion
Type
thesis
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