Effective Rheology of Bubbles Moving in a Capillary Tube
arXiv:1208.4538 · doi:10.1103/PhysRevE.87.025001
Abstract
We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.
4 pages, 1 figure
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