Abstract
If a long air bubble is placed inside a vertical tube closed at the top it can rise by displacing the fluid above it. However, Bretherton found that if the tube radius, R, is smaller than a critical value (Formula presented.), where (Formula presented.) is the capillary length, there is no solution corresponding to steady rise. Experimentally, the bubble rise appears to have stopped altogether. Here we explain this observation by studying the unsteady bubble motion for (Formula presented.). We find that the minimum spacing between the bubble and the tube goes to zero in limit of large t like (Formula presented.), leading to a rapid slowdown of the bubble’s mean speed (Formula presented.). As a result, the total bubble rise in infinite time remains very small, giving the appearance of arrested motion.
Original language  English 

Pages (fromto)  656682 
Number of pages  27 
Journal  Journal of Statistical Physics 
Volume  167 
Issue number  3 
Early online date  13 Jun 2016 
DOIs  
Publication status  Published  May 2017 
Keywords
 Lubrication theory
 Singularities
 Surface tension
 Thin film flow
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Profiles

Professor Jens G Eggers
 Cabot Institute for the Environment
 School of Mathematics  Professor of Applied Mathematics
 Fluids and materials
 Applied Mathematics
Person: Academic , Member