Physics
Scientific paper
Jan 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990aipc..197..518t&link_type=abstract
Drops and bubbles: third international colloquium. AIP Conference Proceedings, Volume 197, pp. 518-532 (1990).
Physics
Particle-Laden Flows
Scientific paper
The effect of surface tension on the determinatin of shape and velocity of a steadily translating bubble in a Hele-Shaw cell as well as its linear stability are presented in this paper. For zero surface tension, there is a continuum of steady bubble solutions for which the bubble velocity and the distance of the bubble centroid from the channel centerline are arbitrary. However, for arbitrarily small surface tension, only a discrete set of bubble solutions are possible with the bubble being symmetric about the channel centerline. Of this discrete set, only branch of the solution for which the bubble velocity is the largest is linearly stable in accordance with similar results for the finger. Transcendentally small terms in surface tension play a crucial role in the determination of bubble velocity, symmetry as well as linear stability. The discrepancy of experimental observations with these theoretical results based on a simplified set of boundary conditions are pointed out. Recent theoretical development that may account for a part of the discrepancy is discussed and open problems pointed out.
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